@article{ZhangWangLahmeretal., author = {Zhang, Chao and Wang, Cuixia and Lahmer, Tom and He, Pengfei and Rabczuk, Timon}, title = {A dynamic XFEM formulation for crack identification}, series = {International Journal of Mechanics and Materials in Design}, journal = {International Journal of Mechanics and Materials in Design}, pages = {427 -- 448}, abstract = {A dynamic XFEM formulation for crack identification}, subject = {Angewandte Mathematik}, language = {en} } @article{ZhangNanthakumarLahmeretal., author = {Zhang, Chao and Nanthakumar, S.S. and Lahmer, Tom and Rabczuk, Timon}, title = {Multiple cracks identification for piezoelectric structures}, series = {International Journal of Fracture}, journal = {International Journal of Fracture}, pages = {1 -- 19}, abstract = {Multiple cracks identification for piezoelectric structures}, subject = {Angewandte Mathematik}, language = {en} } @article{NguyenTuanLahmerDatchevaetal., author = {Nguyen-Tuan, Long and Lahmer, Tom and Datcheva, Maria and Stoimenova, Eugenia and Schanz, Tom}, title = {A novel parameter identification approach for buffer elements involving complex coupled thermo-hydro-mechanical analyses}, series = {Computers and Geotechnics}, journal = {Computers and Geotechnics}, pages = {23 -- 32}, abstract = {A novel parameter identification approach for buffer elements involving complex coupled thermo-hydro-mechanical analyses}, subject = {Angewandte Mathematik}, language = {en} } @article{VuBacLahmerZhuangetal., author = {Vu-Bac, N. and Lahmer, Tom and Zhuang, Xiaoying and Nguyen-Thoi, T. and Rabczuk, Timon}, title = {A software framework for probabilistic sensitivity analysis for computationally expensive models}, series = {Advances in Engineering Software}, journal = {Advances in Engineering Software}, pages = {19 -- 31}, abstract = {A software framework for probabilistic sensitivity analysis for computationally expensive models}, subject = {Angewandte Mathematik}, language = {en} } @article{KnabeDatchevaLahmeretal., author = {Knabe, Tina and Datcheva, Maria and Lahmer, Tom and Cotecchia, F. and Schanz, Tom}, title = {Identification of constitutive parameters of soil using an optimization strategy and statistical analysis}, series = {Computers and Geotechnics}, journal = {Computers and Geotechnics}, pages = {143 -- 157}, abstract = {Identification of constitutive parameters of soil using an optimization strategy and statistical analysis}, subject = {Angewandte Mathematik}, language = {en} } @article{NanthakumarLahmerZhuangetal., author = {Nanthakumar, S.S. and Lahmer, Tom and Zhuang, Xiaoying and Park, Harold S. and Rabczuk, Timon}, title = {Topology optimization of piezoelectric nanostructures}, series = {Journal of the Mechanics and Physics of Solids}, journal = {Journal of the Mechanics and Physics of Solids}, pages = {316 -- 335}, abstract = {Topology optimization of piezoelectric nanostructures}, subject = {Angewandte Mathematik}, language = {en} } @article{SteinLahmerBock, author = {Stein, Peter and Lahmer, Tom and Bock, Sebastian}, title = {Synthese und Analyse von gekoppelten Modellen im konstruktiven Ingenieurbau}, series = {Bautechnik}, journal = {Bautechnik}, pages = {8 -- 11}, abstract = {Synthese und Analyse von gekoppelten Modellen im konstruktiven Ingenieurbau}, subject = {Angewandte Mathematik}, language = {de} } @article{LahmerKnabeNikullaetal., author = {Lahmer, Tom and Knabe, Tina and Nikulla, Susanne and Reuter, Markus}, title = {Bewertungsmethoden f{\"u}r Modelle des konstruktiven Ingenieurbaus}, series = {Bautechnik}, journal = {Bautechnik}, pages = {60 -- 64}, abstract = {Bewertungsmethoden f{\"u}r Modelle des konstruktiven Ingenieurbaus}, subject = {Angewandte Mathematik}, language = {de} } @article{LahmerIlgLerch, author = {Lahmer, Tom and Ilg, J. and Lerch, Reinhard}, title = {Variance-based sensitivity analyses of piezoelectric models}, series = {Computer Modeling in Engineering \& Sciences}, journal = {Computer Modeling in Engineering \& Sciences}, pages = {105 -- 126}, abstract = {Variance-based sensitivity analyses of piezoelectric models}, subject = {Angewandte Mathematik}, language = {en} } @article{Lahmer, author = {Lahmer, Tom}, title = {Optimal experimental design for nonlinear ill-posed problems applied to gravity dams}, series = {Inverse Problems}, journal = {Inverse Problems}, abstract = {Optimal experimental design for nonlinear ill-posed problems applied to gravity dams}, subject = {Angewandte Mathematik}, language = {en} } @article{NguyenVinhBakarMsekhetal., author = {Nguyen-Vinh, H. and Bakar, I. and Msekh, Mohammed Abdulrazzak and Song, Jeong-Hoon and Muthu, Jacob and Zi, Goangseup and Le, P. and Bordas, St{\´e}phane Pierre Alain and Simpson, R. and Natarajan, S. and Lahmer, Tom and Rabczuk, Timon}, title = {Extended Finite Element Method for Dynamic Fracture of Piezo-Electric Materials}, series = {Engineering Fracture Mechanics}, journal = {Engineering Fracture Mechanics}, doi = {10.1016/j.engfracmech.2012.04.025}, pages = {19 -- 31}, abstract = {We present an extended finite element formulation for dynamic fracture of piezo-electric materials. The method is developed in the context of linear elastic fracture mechanics. It is applied to mode I and mixed mode-fracture for quasi-steady cracks. An implicit time integration scheme is exploited. The results are compared to results obtained with the boundary element method and show excellent agreement.}, subject = {Angewandte Mathematik}, language = {en} } @article{NguyenTuanKoenkeBettziecheetal., author = {Nguyen-Tuan, Long and K{\"o}nke, Carsten and Bettzieche, Volker and Lahmer, Tom}, title = {Numerical modeling and validation for 3D coupled-nonlinear thermo-hydro-mechanical problems in masonry dams}, series = {Computers \& Structures}, journal = {Computers \& Structures}, pages = {143 -- 154}, abstract = {Numerical modeling and validation for 3D coupled-nonlinear thermo-hydro-mechanical problems in masonry dams}, subject = {Angewandte Mathematik}, language = {en} } @article{GhorashiLahmerBagherzadehetal., author = {Ghorashi, Seyed Shahram and Lahmer, Tom and Bagherzadeh, Amir Saboor and Zi, Goangseup and Rabczuk, Timon}, title = {A stochastic computational method based on goal-oriented error estimation for heterogeneous geological materials}, series = {Engineering Geology}, journal = {Engineering Geology}, abstract = {A stochastic computational method based on goal-oriented error estimation for heterogeneous geological materials}, subject = {Angewandte Mathematik}, language = {en} } @article{NanthakumarLahmerZhuangetal., author = {Nanthakumar, S.S. and Lahmer, Tom and Zhuang, Xiaoying and Zi, Goangseup and Rabczuk, Timon}, title = {Detection of material interfaces using a regularized level set method in piezoelectric structures}, series = {Inverse Problems in Science and Engineering}, journal = {Inverse Problems in Science and Engineering}, pages = {153 -- 176}, abstract = {Detection of material interfaces using a regularized level set method in piezoelectric structures}, subject = {Angewandte Mathematik}, language = {en} } @article{AchenbachLahmerMorgenthal, author = {Achenbach, Marcus and Lahmer, Tom and Morgenthal, Guido}, title = {Global Sensitivity Analysis of Reinforced Concrete Walls Subjected to Standard Fire - A Comparison of Methods}, series = {14th International Probabilistic Workshop}, journal = {14th International Probabilistic Workshop}, pages = {97 -- 106}, abstract = {Global Sensitivity Analysis of Reinforced Concrete Walls Subjected to Standard Fire—A Comparison of Methods}, subject = {Angewandte Mathematik}, language = {en} } @article{LahmerBockHildebrandetal., author = {Lahmer, Tom and Bock, Sebastian and Hildebrand, J{\"o}rg and G{\"u}rlebeck, Klaus}, title = {Non-destructive identification of residual stresses in steel under thermal loadings}, series = {Inverse Problems in Science and Engineering}, journal = {Inverse Problems in Science and Engineering}, pages = {1 -- 17}, abstract = {Non-destructive identification of residual stresses in steel under thermal loadings}, subject = {Angewandte Mathematik}, language = {en} } @article{GoebelLahmerOsburg, author = {G{\"o}bel, Luise and Lahmer, Tom and Osburg, Andrea}, title = {Uncertainty analysis in multiscale modeling of concrete based on continuum micromechanics}, series = {European Journal of Mechanics-A/Solids}, journal = {European Journal of Mechanics-A/Solids}, abstract = {Uncertainty analysis in multiscale modeling of concrete based on continuum micromechanics}, subject = {Angewandte Mathematik}, language = {en} } @article{AreiasRabczuk, author = {Areias, Pedro and Rabczuk, Timon}, title = {Finite strain fracture of plates and shells with configurational forces and edge rotation}, series = {International Journal for Numerical Methods in Engineering}, journal = {International Journal for Numerical Methods in Engineering}, abstract = {Finite strain fracture of plates and shells with configurational forces and edge rotation}, subject = {Angewandte Mathematik}, language = {en} } @article{MackeHiguchi, author = {Macke, M. and Higuchi, Shoko}, title = {Optimizing maintenance interventions for deteriorating structures using cost-benefit criteria}, series = {Journal of Structural Engineering}, journal = {Journal of Structural Engineering}, pages = {925 -- 934}, abstract = {Optimizing maintenance interventions for deteriorating structures using cost-benefit criteria}, subject = {Angewandte Mathematik}, language = {en} } @article{FaridmehrTahirLahmer, author = {Faridmehr, Iman and Tahir, Mamood Md. and Lahmer, Tom}, title = {Classification System for Semi-Rigid Beam-to-Column Connections}, series = {LATIN AMERICAN JOURNAL OF SOLIDS AND STRUCTURES 11}, journal = {LATIN AMERICAN JOURNAL OF SOLIDS AND STRUCTURES 11}, doi = {10.1590/1679-78252595}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170401-30988}, pages = {2152 -- 2175}, abstract = {The current study attempts to recognise an adequate classification for a semi-rigid beam-to-column connection by investigating strength, stiffness and ductility. For this purpose, an experimental test was carried out to investigate the moment-rotation (M-theta) features of flush end-plate (FEP) connections including variable parameters like size and number of bolts, thickness of end-plate, and finally, size of beams and columns. The initial elastic stiffness and ultimate moment capacity of connections were determined by an extensive analytical procedure from the proposed method prescribed by ANSI/AISC 360-10, and Eurocode 3 Part 1-8 specifications. The behaviour of beams with partially restrained or semi-rigid connections were also studied by incorporating classical analysis methods. The results confirmed that thickness of the column flange and end-plate substantially govern over the initial rotational stiffness of of flush end-plate connections. The results also clearly showed that EC3 provided a more reliable classification index for flush end-plate (FEP) connections. The findings from this study make significant contributions to the current literature as the actual response characteristics of such connections are non-linear. Therefore, such semirigid behaviour should be used to for an analysis and design method.}, subject = {Tragf{\"a}higkeit}, language = {en} } @inproceedings{NguyenTuanLahmerDatchevaetal., author = {Nguyen-Tuan, Long and Lahmer, Tom and Datcheva, Maria and Stoimenova, Eugenia and Schanz, Tom}, title = {PARAMETER IDENTIFICATION APPLYING IN COMPLEX THERMO-HYDRO-MECHANICAL PROBLEMS LIKE THE DESIGN OF BUFFER ELEMENTS}, series = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar}, booktitle = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar}, editor = {G{\"u}rlebeck, Klaus and Lahmer, Tom}, organization = {Bauhaus-Universit{\"a}t Weimar}, issn = {1611-4086}, doi = {10.25643/bauhaus-universitaet.2816}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28162}, pages = {6}, abstract = {This study contributes to the identification of coupled THM constitutive model parameters via back analysis against information-rich experiments. A sampling based back analysis approach is proposed comprising both the model parameter identification and the assessment of the reliability of identified model parameters. The results obtained in the context of buffer elements indicate that sensitive parameter estimates generally obey the normal distribution. According to the sensitivity of the parameters and the probability distribution of the samples we can provide confidence intervals for the estimated parameters and thus allow a qualitative estimation on the identified parameters which are in future work used as inputs for prognosis computations of buffer elements. These elements play e.g. an important role in the design of nuclear waste repositories.}, subject = {Angewandte Informatik}, language = {en} } @article{BanihaniRabczukAlmomani, author = {Banihani, Suleiman and Rabczuk, Timon and Almomani, Thakir}, title = {POD for real-time simulation of hyperelastic soft biological tissue using the point collocation method of finite spheres}, series = {Mathematical Problems in Engineering}, journal = {Mathematical Problems in Engineering}, doi = {10.1155/2013/386501}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170413-31203}, abstract = {The point collocation method of finite spheres (PCMFS) is used to model the hyperelastic response of soft biological tissue in real time within the framework of virtual surgery simulation. The proper orthogonal decomposition (POD) model order reduction (MOR) technique was used to achieve reduced-order model of the problem, minimizing computational cost. The PCMFS is a physics-based meshfree numerical technique for real-time simulation of surgical procedures where the approximation functions are applied directly on the strong form of the boundary value problem without the need for integration, increasing computational efficiency. Since computational speed has a significant role in simulation of surgical procedures, the proposed technique was able to model realistic nonlinear behavior of organs in real time. Numerical results are shown to demonstrate the effectiveness of the new methodology through a comparison between full and reduced analyses for several nonlinear problems. It is shown that the proposed technique was able to achieve good agreement with the full model; moreover, the computational and data storage costs were significantly reduced.}, subject = {Chirurgie}, language = {en} } @article{ZhaoLuZhangetal., author = {Zhao, Jun-Hua and Lu, Lixin and Zhang, Zhiliang and Guo, Wanlin and Rabczuk, Timon}, title = {Continuum modeling of the cohesive energy for the interfaces between _lms, spheres, coats and substrates}, series = {Computational Materials Science}, journal = {Computational Materials Science}, pages = {432 -- 438}, abstract = {Continuum modeling of the cohesive energy for the interfaces between _lms, spheres, coats and substrates}, subject = {Angewandte Mathematik}, language = {en} } @article{BenZhaoZhangetal., author = {Ben, S. and Zhao, Jun-Hua and Zhang, Yancheng and Rabczuk, Timon}, title = {The interface strength and debonding for composite structures: review and recent developments}, series = {Composite Structures}, journal = {Composite Structures}, abstract = {The interface strength and debonding for composite structures: review and recent developments}, subject = {Angewandte Mathematik}, language = {en} } @article{ZhaoJiaWeietal., author = {Zhao, Jun-Hua and Jia, Yue and Wei, Ning and Rabczuk, Timon}, title = {Binding energy and mechanical stability of two parallel and crossing carbon nanotubes}, series = {Journal of Applied Mechanics}, journal = {Journal of Applied Mechanics}, abstract = {Binding energy and mechanical stability of two parallel and crossing carbon nanotubes}, subject = {Angewandte Mathematik}, language = {en} } @article{KumarSinghMishraetal., author = {Kumar, S. and Singh, I. and Mishra, B.K. and Rabczuk, Timon}, title = {Modeling and Simulation of Kinked Cracks by Virtual Node XFEM}, series = {Computer Methods in Applied Mechanics and Engineering}, journal = {Computer Methods in Applied Mechanics and Engineering}, pages = {1425 -- 1466}, abstract = {Modeling and Simulation of Kinked Cracks by Virtual Node XFEM}, subject = {Angewandte Mathematik}, language = {en} } @article{NanthakumarLahmerRabczuk, author = {Nanthakumar, S.S. and Lahmer, Tom and Rabczuk, Timon}, title = {Detection of flaws in piezoelectric structures using extended FEM}, series = {International Journal for Numerical Methods in Engineering}, journal = {International Journal for Numerical Methods in Engineering}, pages = {373 -- 389}, abstract = {Detection of flaws in piezoelectric structures using extended FEM}, subject = {Angewandte Mathematik}, language = {en} } @article{ZhaoWeiFanetal., author = {Zhao, Jun-Hua and Wei, Ning and Fan, Z. and Jiang, Jin-Wu and Rabczuk, Timon}, title = {Mechanical properties of three types of carbon allotropes}, series = {Nanotechnology}, journal = {Nanotechnology}, abstract = {Mechanical properties of three types of carbon allotropes}, subject = {Angewandte Mathematik}, language = {en} } @article{AreiasRabczukDiasdaCostaetal., author = {Areias, Pedro and Rabczuk, Timon and Dias-da-Costa, D. and Piresh, E.B.}, title = {Implicit solutions with consistent additive and multiplicative components}, series = {Finite Elements in Analysis and Design}, journal = {Finite Elements in Analysis and Design}, doi = {10.1016/j.finel.2012.03.007}, pages = {15 -- 31}, abstract = {This work describes an algorithm and corresponding software for incorporating general nonlinear multiple-point equality constraints in a implicit sparse direct solver. It is shown that direct addressing of sparse matrices is possible in general circumstances, circumventing the traditional linear or binary search for introducing (generalized) constituents to a sparse matrix. Nested and arbitrarily interconnected multiple-point constraints are introduced by processing of multiplicative constituents with a built-in topological ordering of the resulting directed graph. A classification of discretization methods is performed and some re-classified problems are described and solved under this proposed perspective. The dependence relations between solution methods, algorithms and constituents becomes apparent. Fracture algorithms can be naturally casted in this framework. Solutions based on control equations are also directly incorporated as equality constraints. We show that arbitrary constituents can be used as long as the resulting directed graph is acyclic. It is also shown that graph partitions and orderings should be performed in the innermost part of the algorithm, a fact with some peculiar consequences. The core of our implicit code is described, specifically new algorithms for direct access of sparse matrices (by means of the clique structure) and general constituent processing. It is demonstrated that the graph structure of the second derivatives of the equality constraints are cliques (or pseudo-elements) and are naturally included as such. A complete algorithm is presented which allows a complete automation of equality constraints, avoiding the need of pre-sorting. Verification applications in four distinct areas are shown: single and multiple rigid body dynamics, solution control and computational fracture.}, subject = {Angewandte Mathematik}, language = {en} } @article{JiangRabczukPark, author = {Jiang, Jin-Wu and Rabczuk, Timon and Park, Harold S.}, title = {A Stillinger-Weber Potential for Single-Layer Black Phosphorus, and the Importance of Cross-Pucker Interactions for Negative Poisson's Ratio and Edge Stress-Induced Bending}, series = {Nanoscale}, journal = {Nanoscale}, doi = {10.1039/C4NR07341J}, abstract = {The distinguishing structural feature of single-layered black phosphorus is its puckered structure, which leads to many novel physical properties. In this work, we first present a new parameterization of the Stillinger-Weber potential for single-layered black phosphorus. In doing so, we reveal the importance of a cross-pucker interaction term in capturing its unique mechanical properties, such as a negative Poisson's ratio. In particular, we show that the cross-pucker interaction enables the pucker to act as a re-entrant hinge, which expands in the lateral direction when it is stretched in the longitudinal direction. As a consequence, single-layered black phosphorus has a negative Poisson's ratio in the direction perpendicular to the atomic plane. As an additional demonstration of the impact of the cross-pucker interaction, we show that it is also the key factor that enables capturing the edge stress-induced bending of single-layered black phosphorus that has been reported in ab initio calculations.}, subject = {Angewandte Mathematik}, language = {en} } @article{HiguchiMacke, author = {Higuchi, Shoko and Macke, M.}, title = {Cost-benefit based optimization of maintenance interventions for deteriorating structures}, series = {Structural Engineering/Earthquake Engineering}, journal = {Structural Engineering/Earthquake Engineering}, pages = {131 -- 147}, abstract = {Cost-benefit based optimization of maintenance interventions for deteriorating structures}, subject = {Angewandte Mathematik}, language = {en} } @article{TalebiSilaniRabczuk, author = {Talebi, Hossein and Silani, Mohammad and Rabczuk, Timon}, title = {Concurrent Multiscale Modelling of Three Dimensional Crack and Dislocation Propagation}, series = {Advances in Engineering Software}, journal = {Advances in Engineering Software}, pages = {82 -- 92}, abstract = {Concurrent Multiscale Modelling of Three Dimensional Crack and Dislocation Propagation}, subject = {Angewandte Mathematik}, language = {en} } @article{XuMourrainGalligoetal., author = {Xu, G. and Mourrain, B. and Galligo, A. and Rabczuk, Timon}, title = {High-quality construction of analysis-suitable trivariate NURBS solids by reparameterization methods}, series = {Computational Mechanics}, journal = {Computational Mechanics}, abstract = {High-quality construction of analysis-suitable trivariate NURBS solids by reparameterization methods}, subject = {Angewandte Mathematik}, language = {en} } @article{PhanDaoNguyenXuanThaiHoangetal., author = {Phan-Dao, H. and Nguyen-Xuan, Hung and Thai-Hoang, C. and Nguyen-Thoi, T. and Rabczuk, Timon}, title = {An edge-based smoothed finite element method for analysis of laminated composite plates}, series = {International Journal of Computational Methods}, journal = {International Journal of Computational Methods}, abstract = {An edge-based smoothed finite element method for analysis of laminated composite plates}, subject = {Angewandte Mathematik}, language = {en} } @article{SilaniZiaeiRadTalebietal., author = {Silani, Mohammad and Ziaei-Rad, S. and Talebi, Hossein and Rabczuk, Timon}, title = {A Semi-Concurrent Multiscale Approach for Modeling Damage in Nanocomposites}, series = {Theoretical and Applied Fracture Mechanics}, journal = {Theoretical and Applied Fracture Mechanics}, abstract = {A Semi-Concurrent Multiscale Approach for Modeling Damage in Nanocomposites}, subject = {Angewandte Mathematik}, language = {en} } @article{AmaniBagherzadehRabczuk, author = {Amani, Jafar and Bagherzadeh, Amir Saboor and Rabczuk, Timon}, title = {Error estimate and adaptive refinement in Mixed Discrete Least Squares Meshless method}, series = {Mathematical Problems in Engineering}, journal = {Mathematical Problems in Engineering}, abstract = {Error estimate and adaptive refinement in Mixed Discrete Least Squares Meshless method}, subject = {Angewandte Mathematik}, language = {en} } @article{JiangWangRabczuk, author = {Jiang, Jin-Wu and Wang, Bing-Shen and Rabczuk, Timon}, title = {Acoustic and breathing phonon modes in bilayer graphene with Moire-acute patterns}, series = {Applied Physics Letters}, journal = {Applied Physics Letters}, doi = {10.1063/1.4735246}, abstract = {The lattice dynamics properties are investigated for twisting bilayer graphene. There are big jumps for the inter-layer potential at twisting angle θ=0° and 60°, implying the stability of Bernal-stacking and the instability of AA-stacking structures, while a long platform in [8,55]° indicates the ease of twisting bilayer graphene in this wide angle range. Significant frequency shifts are observed for the z breathing mode around θ=0° and 60°, while the frequency is a constant in a wide range [8,55]°. Using the z breathing mode, a mechanical nanoresonator is proposed to operate on a robust resonant frequency in terahertz range.}, subject = {Angewandte Mathematik}, language = {en} } @article{GhasemiBrighentiZhuangetal., author = {Ghasemi, Hamid and Brighenti, Roberto and Zhuang, Xiaoying and Muthu, Jacob and Rabczuk, Timon}, title = {Optimum fiber content and distribution in fiber-reinforced solids using a reliability and NURBS based sequential optimization approach}, series = {Structural and Multidisciplinary Optimization}, journal = {Structural and Multidisciplinary Optimization}, pages = {99 -- 112}, abstract = {Optimum _ber content and distribution in _ber-reinforced solids using a reliability and NURBS based sequential optimization approach}, subject = {Angewandte Mathematik}, language = {en} } @article{AreiasRabczukCesardeSaetal., author = {Areias, Pedro and Rabczuk, Timon and Cesar de Sa, J.M. and Jorge, R.N.}, title = {A semi-implicit _nite strain shell algorithm using in-plane strains based on least-squares}, series = {Computational Mechanics}, journal = {Computational Mechanics}, abstract = {A semi-implicit _nite strain shell algorithm using in-plane strains based on least-squares}, subject = {Angewandte Mathematik}, language = {en} } @article{ZhaoJiangWangetal., author = {Zhao, Jiyun and Jiang, Jin-Wu and Wang, L. and Guo, Wanlin and Rabczuk, Timon}, title = {Coarse-grained potentials of single-walled carbon nanotubes}, series = {Journal of the Mechanics and Physics of Solids}, journal = {Journal of the Mechanics and Physics of Solids}, abstract = {Coarse-grained potentials of single-walled carbon nanotubes}, subject = {Angewandte Mathematik}, language = {en} } @article{JiangWangRabczuk, author = {Jiang, Jin-Wu and Wang, Bing-Shen and Rabczuk, Timon}, title = {Why twisting angles are diverse in graphene Moir'e patterns?}, series = {Journal of Applied Physics}, journal = {Journal of Applied Physics}, abstract = {Why twisting angles are diverse in graphene Moir'e patterns?}, subject = {Angewandte Mathematik}, language = {en} } @article{JiangZhaoZhouetal., author = {Jiang, Jin-Wu and Zhao, Jun-Hua and Zhou, K. and Rabczuk, Timon}, title = {Superior thermal conductivity and extremely high mechanical strength in polyethylene chains from ab initio calculation}, series = {Journal of Applied Physics}, journal = {Journal of Applied Physics}, doi = {10.1063/1.4729489}, abstract = {The upper limit of the thermal conductivity and the mechanical strength are predicted for the polyethylene chain, by performing the ab initio calculation and applying the quantum mechanical non-equilibrium Green's function approach. Specially, there are two main findings from our calculation: (1) the thermal conductivity can reach a high value of 310 Wm-1 K-1 in a 100 nm polyethylene chain at room temperature and the thermal conductivity increases with the length of the chain; (2) the Young's modulus in the polyethylene chain is as high as 374.5 GPa, and the polyethylene chain can sustain 32.85\%±0.05\% (ultimate) strain before undergoing structural phase transition into gaseous ethylene.}, subject = {Angewandte Mathematik}, language = {en} } @article{LutherKoenke, author = {Luther, Torsten and K{\"o}nke, Carsten}, title = {Coupled cohesive zone representations from 3D quasicontinuum simulation on aluminum grain boundaries}, series = {International Journal for Multiscale Computational Engineering}, journal = {International Journal for Multiscale Computational Engineering}, abstract = {Coupled cohesive zone representations from 3D quasicontinuum simulation on aluminum grain boundaries}, subject = {Angewandte Mathematik}, language = {en} } @phdthesis{Mai, author = {Mai, Luu}, title = {Structural Control Systems in High-speed Railway Bridges}, issn = {1610-7381}, doi = {10.25643/bauhaus-universitaet.2339}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20141223-23391}, school = {Bauhaus-Universit{\"a}t Weimar}, pages = {147}, abstract = {Structural vibration control of high-speed railway bridges using tuned mass dampers, semi-active tuned mass dampers, fluid viscous dampers and magnetorheological dampers to reduce resonant structural vibrations is studied. In this work, the addressed main issues include modeling of the dynamic interaction of the structures, optimization of the parameters of the dampers and comparison of their efficiency. A new approach to optimize multiple tuned mass damper systems on an uncertain model is proposed based on the H-infinity optimization criteria and the DK iteration procedure with norm-bounded uncertainties in frequency domain. The parameters of tuned mass dampers are optimized directly and simultaneously on different modes contributing significantly to the multi-resonant peaks to explore the different possible combinations of parameters. The effectiveness of the present method is also evaluated through comparison with a previous method. In the case of semi-active tuned mass dampers, an optimization algorithm is derived to control the magnetorheological damper in these semi-active damping systems. The use of the proposed algorithm can generate various combinations of control gains and state variables. This can lead to the improvement of the ability of MR dampers to track the desired control forces. An uncertain model to reduce detuning effects is also considered in this work. Next, for fluid viscous dampers, in order to tune the optimal parameters of fluid viscous dampers to the vicinity of the exact values, analytical formulae which can include structural damping are developed based on the perturbation method. The proposed formulae can also be considered as an improvement of the previous analytical formulae, especially for bridge beams with large structural damping. Finally, a new combination of magnetorheological dampers and a double-beam system to improve the performance of the primary structure vibration is proposed. An algorithm to control magnetorheological dampers in this system is developed by using standard linear matrix inequality techniques. Weight functions as a loop shaping procedure are also introduced in the feedback controllers to improve the tracking ability of magnetorheological damping forces. To this end, the effectiveness of magnetorheological dampers controlled by the proposed scheme, along with the effects of the uncertain and time-delay parameters on the models, are evaluated through numerical simulations. Additionally, a comparison of the dampers based on their performance is also considered in this work.}, subject = {High-speed railway bridge}, language = {en} } @article{AreiasRabczukBarbosa, author = {Areias, Pedro and Rabczuk, Timon and Barbosa, J.I.}, title = {The extended unsymmetric frontal solution for multiple-point constraints}, series = {Engineering Computations}, journal = {Engineering Computations}, abstract = {The extended unsymmetric frontal solution for multiple-point constraints}, subject = {Angewandte Mathematik}, language = {en} } @article{UngerTeughelsDeRoeck, author = {Unger, J{\"o}rg F. and Teughels, A. and De Roeck, G.}, title = {Damage detection of a prestressed concrete beam using modal strains}, series = {Journal of Structural Engineering}, journal = {Journal of Structural Engineering}, pages = {1456 -- 1463}, abstract = {Damage detection of a prestressed concrete beam using modal strains}, subject = {Angewandte Mathematik}, language = {en} } @article{VuBacSilaniLahmeretal., author = {Vu-Bac, N. and Silani, Mohammad and Lahmer, Tom and Zhuang, Xiaoying and Rabczuk, Timon}, title = {A unified framework for stochastic predictions of Young's modulus of clay/epoxy nanocomposites (PCNs)}, series = {Computational Materials Science}, journal = {Computational Materials Science}, pages = {520 -- 535}, abstract = {A unified framework for stochastic predictions of Young's modulus of clay/epoxy nanocomposites (PCNs)}, subject = {Angewandte Mathematik}, language = {en} } @article{NanthakumarLahmerZhuangetal., author = {Nanthakumar, S.S. and Lahmer, Tom and Zhuang, Xiaoying and Zi, Goangseup and Rabczuk, Timon}, title = {Detection of material interfaces using a regularized level set method in piezoelectric structures}, series = {Inverse Problems in Science and Engineering}, journal = {Inverse Problems in Science and Engineering}, abstract = {Detection of material interfaces using a regularized level set method in piezoelectric structures}, subject = {Angewandte Mathematik}, language = {en} } @article{VuBacRafieeZhuangetal., author = {Vu-Bac, N. and Rafiee, Roham and Zhuang, Xiaoying and Lahmer, Tom and Rabczuk, Timon}, title = {Uncertainty quantification for multiscale modeling of polymer nanocomposites with correlated parameters}, series = {Composites Part B: Engineering}, journal = {Composites Part B: Engineering}, pages = {446 -- 464}, abstract = {Uncertainty quantification for multiscale modeling of polymer nanocomposites with correlated parameters}, subject = {Angewandte Mathematik}, language = {en} } @article{VuBacLahmerZhangetal., author = {Vu-Bac, N. and Lahmer, Tom and Zhang, Yancheng and Zhuang, Xiaoying and Rabczuk, Timon}, title = {Stochastic predictions of interfacial characteristic of polymeric nanocomposites (PNCs)}, series = {Composites Part B Engineering}, journal = {Composites Part B Engineering}, pages = {80 -- 95}, abstract = {Stochastic predictions of interfacial characteristic of polymeric nanocomposites (PNCs)}, subject = {Angewandte Mathematik}, language = {en} } @inproceedings{JaouadiLahmer, author = {Jaouadi, Zouhour and Lahmer, Tom}, title = {Topology optimization of structures subjected to multiple load cases by introducing the Epsilon constraint method}, series = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar}, booktitle = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar}, editor = {G{\"u}rlebeck, Klaus and Lahmer, Tom}, organization = {Bauhaus-Universit{\"a}t Weimar}, issn = {1611-4086}, doi = {10.25643/bauhaus-universitaet.2804}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28042}, pages = {7}, abstract = {A topology optimization method has been developed for structures subjected to multiple load cases (Example of a bridge pier subjected to wind loads, traffic, superstructure...). We formulate the problem as a multi-criterial optimization problem, where the compliance is computed for each load case. Then, the Epsilon constraint method (method proposed by Chankong and Haimes, 1971) is adapted. The strategy of this method is based on the concept of minimizing the maximum compliance resulting from the critical load case while the other remaining compliances are considered in the constraints. In each iteration, the compliances of all load cases are computed and only the maximum one is minimized. The topology optimization process is switching from one load to another according to the variation of the resulting compliance. In this work we will motivate and explain the proposed methodology and provide some numerical examples.}, subject = {Angewandte Informatik}, language = {en} } @article{ZhangRen, author = {Zhang, Yongzheng and Ren, Huilong}, title = {Implicit implementation of the nonlocal operator method: an open source code}, series = {Engineering with computers}, volume = {2022}, journal = {Engineering with computers}, publisher = {Springer}, address = {London}, doi = {10.1007/s00366-021-01537-x}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220216-45930}, pages = {1 -- 35}, abstract = {In this paper, we present an open-source code for the first-order and higher-order nonlocal operator method (NOM) including a detailed description of the implementation. The NOM is based on so-called support, dual-support, nonlocal operators, and an operate energy functional ensuring stability. The nonlocal operator is a generalization of the conventional differential operators. Combined with the method of weighed residuals and variational principles, NOM establishes the residual and tangent stiffness matrix of operate energy functional through some simple matrix without the need of shape functions as in other classical computational methods such as FEM. NOM only requires the definition of the energy drastically simplifying its implementation. The implementation in this paper is focused on linear elastic solids for sake of conciseness through the NOM can handle more complex nonlinear problems. The NOM can be very flexible and efficient to solve partial differential equations (PDEs), it's also quite easy for readers to use the NOM and extend it to solve other complicated physical phenomena described by one or a set of PDEs. Finally, we present some classical benchmark problems including the classical cantilever beam and plate-with-a-hole problem, and we also make an extension of this method to solve complicated problems including phase-field fracture modeling and gradient elasticity material.}, subject = {Strukturmechanik}, language = {en} } @article{JoshiHildebrandAloraieretal., author = {Joshi, Suraj and Hildebrand, J{\"o}rg and Aloraier, Abdulkareem S. and Rabczuk, Timon}, title = {Characterization of material properties and heat source parameters in welding simulation of two overlapping beads on a substrate plate}, series = {Computational Materials Science}, journal = {Computational Materials Science}, doi = {10.1016/j.commatsci.2012.11.029}, pages = {559 -- 565}, abstract = {This paper presents several aspects of characterization of welding heat source parameters in Goldak's double ellipsoidal model using Sysweld simulation of welding of two overlapping beads on a substrate steel plate. The overlap percentages ranged from 40\% to 80\% in increments of 10\%. The new material properties of the fused metal were characterized using Weldware and their continuous cooling transformation curves. The convective and radiative heat transfer coefficients as well as the cooling time t8/5 were estimated using numerical formulations from relevant standards. The effects of the simulation geometry and mesh discretization were evaluated in terms of the factor F provided in Sysweld. Eventually, the parameters of Goldak's double ellipsoidal heat source model were determined for the welding simulation of overlapping beads on the plate and the simulated bead geometry, extent of the molten pool and the HAZ were compared with the macrographs of cross-sections of the experimental weldments. The results showed excellent matching, thus verifying this methodology for determination of welding heat source parameters.}, subject = {Angewandte Mathematik}, language = {en} } @article{Zhang, author = {Zhang, Yongzheng}, title = {Nonlocal dynamic Kirchhoff plate formulation based on nonlocal operator method}, series = {Engineering with Computers}, volume = {2022}, journal = {Engineering with Computers}, publisher = {Springer}, address = {London}, doi = {10.1007/s00366-021-01587-1}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220209-45849}, pages = {1 -- 35}, abstract = {In this study, we propose a nonlocal operator method (NOM) for the dynamic analysis of (thin) Kirchhoff plates. The nonlocal Hessian operator is derived based on a second-order Taylor series expansion. The NOM does not require any shape functions and associated derivatives as 'classical' approaches such as FEM, drastically facilitating the implementation. Furthermore, NOM is higher order continuous, which is exploited for thin plate analysis that requires C1 continuity. The nonlocal dynamic governing formulation and operator energy functional for Kirchhoff plates are derived from a variational principle. The Verlet-velocity algorithm is used for the time discretization. After confirming the accuracy of the nonlocal Hessian operator, several numerical examples are simulated by the nonlocal dynamic Kirchhoff plate formulation.}, subject = {Angewandte Mathematik}, language = {en} } @article{JiangRabczuk, author = {Jiang, Jin-Wu and Rabczuk, Timon}, title = {Mechanical Oscillation of Kinked Silicon Nanowires: a Natural Nanoscale Spring}, series = {Applied Physics Letters}, journal = {Applied Physics Letters}, abstract = {Mechanical Oscillation of Kinked Silicon Nanowires: a Natural Nanoscale Spring}, subject = {Angewandte Mathematik}, language = {en} } @phdthesis{Vu, author = {Vu, Bac Nam}, title = {Stochastic uncertainty quantification for multiscale modeling of polymeric nanocomposites}, doi = {10.25643/bauhaus-universitaet.2555}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20160322-25551}, school = {Bauhaus-Universit{\"a}t Weimar}, pages = {265}, abstract = {Nanostructured materials are extensively applied in many fields of material science for new industrial applications, particularly in the automotive, aerospace industry due to their exceptional physical and mechanical properties. Experimental testing of nanomaterials is expensive, timeconsuming,challenging and sometimes unfeasible. Therefore,computational simulations have been employed as alternative method to predict macroscopic material properties. The behavior of polymeric nanocomposites (PNCs) are highly complex. The origins of macroscopic material properties reside in the properties and interactions taking place on finer scales. It is therefore essential to use multiscale modeling strategy to properly account for all large length and time scales associated with these material systems, which across many orders of magnitude. Numerous multiscale models of PNCs have been established, however, most of them connect only two scales. There are a few multiscale models for PNCs bridging four length scales (nano-, micro-, meso- and macro-scales). In addition, nanomaterials are stochastic in nature and the prediction of macroscopic mechanical properties are influenced by many factors such as fine-scale features. The predicted mechanical properties obtained by traditional approaches significantly deviate from the measured values in experiments due to neglecting uncertainty of material features. This discrepancy is indicated that the effective macroscopic properties of materials are highly sensitive to various sources of uncertainty, such as loading and boundary conditions and material characteristics, etc., while very few stochastic multiscale models for PNCs have been developed. Therefore, it is essential to construct PNC models within the framework of stochastic modeling and quantify the stochastic effect of the input parameters on the macroscopic mechanical properties of those materials. This study aims to develop computational models at four length scales (nano-, micro-, meso- and macro-scales) and hierarchical upscaling approaches bridging length scales from nano- to macro-scales. A framework for uncertainty quantification (UQ) applied to predict the mechanical properties of the PNCs in dependence of material features at different scales is studied. Sensitivity and uncertainty analysis are of great helps in quantifying the effect of input parameters, considering both main and interaction effects, on the mechanical properties of the PNCs. To achieve this major goal, the following tasks are carried out: At nano-scale, molecular dynamics (MD) were used to investigate deformation mechanism of glassy amorphous polyethylene (PE) in dependence of temperature and strain rate. Steered molecular dynamics (SMD)were also employed to investigate interfacial characteristic of the PNCs. At mico-scale, we developed an atomistic-based continuum model represented by a representative volume element (RVE) in which the SWNT's properties and the SWNT/polymer interphase are modeled at nano-scale, the surrounding polymer matrix is modeled by solid elements. Then, a two-parameter model was employed at meso-scale. A hierarchical multiscale approach has been developed to obtain the structure-property relations at one length scale and transfer the effect to the higher length scales. In particular, we homogenized the RVE into an equivalent fiber. The equivalent fiber was then employed in a micromechanical analysis (i.e. Mori-Tanaka model) to predict the effective macroscopic properties of the PNC. Furthermore, an averaging homogenization process was also used to obtain the effective stiffness of the PCN at meso-scale. Stochastic modeling and uncertainty quantification consist of the following ingredients: - Simple random sampling, Latin hypercube sampling, Sobol' quasirandom sequences, Iman and Conover's method (inducing correlation in Latin hypercube sampling) are employed to generate independent and dependent sample data, respectively. - Surrogate models, such as polynomial regression, moving least squares (MLS), hybrid method combining polynomial regression and MLS, Kriging regression, and penalized spline regression, are employed as an approximation of a mechanical model. The advantage of the surrogate models is the high computational efficiency and robust as they can be constructed from a limited amount of available data. - Global sensitivity analysis (SA) methods, such as variance-based methods for models with independent and dependent input parameters, Fourier-based techniques for performing variance-based methods and partial derivatives, elementary effects in the context of local SA, are used to quantify the effects of input parameters and their interactions on the mechanical properties of the PNCs. A bootstrap technique is used to assess the robustness of the global SA methods with respect to their performance. In addition, the probability distribution of mechanical properties are determined by using the probability plot method. The upper and lower bounds of the predicted Young's modulus according to 95 \% prediction intervals were provided. The above-mentioned methods study on the behaviour of intact materials. Novel numerical methods such as a node-based smoothed extended finite element method (NS-XFEM) and an edge-based smoothed phantom node method (ES-Phantom node) were developed for fracture problems. These methods can be used to account for crack at macro-scale for future works. The predicted mechanical properties were validated and verified. They show good agreement with previous experimental and simulations results.}, subject = {Polymere}, language = {en} } @inproceedings{OPUS4-2451, title = {International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar}, series = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar}, booktitle = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar}, editor = {G{\"u}rlebeck, Klaus and Lahmer, Tom}, organization = {Bauhaus-Universit{\"a}t Weimar}, issn = {1611-4086}, doi = {10.25643/bauhaus-universitaet.2451}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20150828-24515}, pages = {230}, abstract = {The 20th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering will be held at the Bauhaus University Weimar from 20th till 22nd July 2015. Architects, computer scientists, mathematicians, and engineers from all over the world will meet in Weimar for an interdisciplinary exchange of experiences, to report on their results in research, development and practice and to discuss. The conference covers a broad range of research areas: numerical analysis, function theoretic methods, partial differential equations, continuum mechanics, engineering applications, coupled problems, computer sciences, and related topics. Several plenary lectures in aforementioned areas will take place during the conference. We invite architects, engineers, designers, computer scientists, mathematicians, planners, project managers, and software developers from business, science and research to participate in the conference!}, subject = {Angewandte Informatik}, language = {en} } @article{NguyenTuanLahmerDatchevaetal., author = {Nguyen-Tuan, Long and Lahmer, Tom and Datcheva, Maria and Schanz, Tom}, title = {Global and local sensitivity analyses for coupled thermo-hydro-mechanical problems}, series = {International Journal for Numerical and Analytical Methods in Geomechanics}, journal = {International Journal for Numerical and Analytical Methods in Geomechanics}, abstract = {Global and local sensitivity analyses for coupled thermo-hydro-mechanical problems}, subject = {Angewandte Mathematik}, language = {en} } @article{JiangParkRabczuk, author = {Jiang, Jin-Wu and Park, Harold S. and Rabczuk, Timon}, title = {Enhancing the mass sensitivity of graphene nanoresonators via nonlinear oscillations: The effective strain mechanism}, series = {Nanotechnology}, journal = {Nanotechnology}, abstract = {Enhancing the mass sensitivity of graphene nanoresonators via nonlinear oscillations: The effective strain mechanism}, subject = {Angewandte Mathematik}, language = {en} } @article{MsekhSargadoJamshidianetal., author = {Msekh, Mohammed Abdulrazzak and Sargado, M. and Jamshidian, M. and Areias, Pedro and Rabczuk, Timon}, title = {ABAQUS implementation of phase_field model for brittle fracture}, series = {Computational Materials Science}, journal = {Computational Materials Science}, pages = {472 -- 484}, abstract = {ABAQUS implementation of phase_field model for brittle fracture}, subject = {Angewandte Mathematik}, language = {en} } @phdthesis{Zhang, author = {Zhang, Yongzheng}, title = {A Nonlocal Operator Method for Quasi-static and Dynamic Fracture Modeling}, doi = {10.25643/bauhaus-universitaet.4732}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20221026-47321}, school = {Bauhaus-Universit{\"a}t Weimar}, abstract = {Material failure can be tackled by so-called nonlocal models, which introduce an intrinsic length scale into the formulation and, in the case of material failure, restore the well-posedness of the underlying boundary value problem or initial boundary value problem. Among nonlocal models, peridynamics (PD) has attracted a lot of attention as it allows the natural transition from continuum to discontinue and thus allows modeling of discrete cracks without the need to describe and track the crack topology, which has been a major obstacle in traditional discrete crack approaches. This is achieved by replacing the divergence of the Cauchy stress tensor through an integral over so-called bond forces, which account for the interaction of particles. A quasi-continuum approach is then used to calibrate the material parameters of the bond forces, i.e., equating the PD energy with the energy of a continuum. One major issue for the application of PD to general complex problems is that they are limited to fairly simple material behavior and pure mechanical problems based on explicit time integration. PD has been extended to other applications but losing simultaneously its simplicity and ease in modeling material failure. Furthermore, conventional PD suffers from instability and hourglass modes that require stabilization. It also requires the use of constant horizon sizes, which drastically reduces its computational efficiency. The latter issue was resolved by the so-called dual-horizon peridynamics (DH-PD) formulation and the introduction of the duality of horizons. Within the nonlocal operator method (NOM), the concept of nonlocality is further extended and can be considered a generalization of DH-PD. Combined with the energy functionals of various physical models, the nonlocal forms based on the dual-support concept can be derived. In addition, the variation of the energy functional allows implicit formulations of the nonlocal theory. While traditional integral equations are formulated in an integral domain, the dual-support approaches are based on dual integral domains. One prominent feature of NOM is its compatibility with variational and weighted residual methods. The NOM yields a direct numerical implementation based on the weighted residual method for many physical problems without the need for shape functions. Only the definition of the energy or boundary value problem is needed to drastically facilitate the implementation. The nonlocal operator plays an equivalent role to the derivatives of the shape functions in meshless methods and finite element methods (FEM). Based on the variational principle, the residual and the tangent stiffness matrix can be obtained with ease by a series of matrix multiplications. In addition, NOM can be used to derive many nonlocal models in strong form. The principal contributions of this dissertation are the implementation and application of NOM, and also the development of approaches for dealing with fractures within the NOM, mostly for dynamic fractures. The primary coverage and results of the dissertation are as follows: -The first/higher-order implicit NOM and explicit NOM, including a detailed description of the implementation, are presented. The NOM is based on so-called support, dual-support, nonlocal operators, and an operate energy functional ensuring stability. The nonlocal operator is a generalization of the conventional differential operators. Combining with the method of weighted residuals and variational principles, NOM establishes the residual and tangent stiffness matrix of operate energy functional through some simple matrix without the need of shape functions as in other classical computational methods such as FEM. NOM only requires the definition of the energy drastically simplifying its implementation. For the sake of conciseness, the implementation in this chapter is focused on linear elastic solids only, though the NOM can handle more complex nonlinear problems. An explicit nonlocal operator method for the dynamic analysis of elasticity solid problems is also presented. The explicit NOM avoids the calculation of the tangent stiffness matrix as in the implicit NOM model. The explicit scheme comprises the Verlet-velocity algorithm. The NOM can be very flexible and efficient for solving partial differential equations (PDEs). It's also quite easy for readers to use the NOM and extend it to solve other complicated physical phenomena described by one or a set of PDEs. Several numerical examples are presented to show the capabilities of this method. -A nonlocal operator method for the dynamic analysis of (thin) Kirchhoff plates is proposed. The nonlocal Hessian operator is derived from a second-order Taylor series expansion. NOM is higher-order continuous, which is exploited for thin plate analysis that requires \$C^1\$ continuity. The nonlocal dynamic governing formulation and operator energy functional for Kirchhoff plates are derived from a variational principle. The Verlet-velocity algorithm is used for time discretization. After confirming the accuracy of the nonlocal Hessian operator, several numerical examples are simulated by the nonlocal dynamic Kirchhoff plate formulation. -A nonlocal fracture modeling is developed and applied to the simulation of quasi-static and dynamic fractures using the NOM. The phase field's nonlocal weak and associated strong forms are derived from a variational principle. The NOM requires only the definition of energy. We present both a nonlocal implicit phase field model and a nonlocal explicit phase field model for fracture; the first approach is better suited for quasi-static fracture problems, while the key application of the latter one is dynamic fracture. To demonstrate the performance of the underlying approach, several benchmark examples for quasi-static and dynamic fracture are solved.}, subject = {Variationsprinzip}, language = {en} } @article{RabczukGuoZhuangetal., author = {Rabczuk, Timon and Guo, Hongwei and Zhuang, Xiaoying and Chen, Pengwan and Alajlan, Naif}, title = {Stochastic deep collocation method based on neural architecture search and transfer learning for heterogeneous porous media}, series = {Engineering with Computers}, volume = {2022}, journal = {Engineering with Computers}, publisher = {Springer}, address = {London}, doi = {10.1007/s00366-021-01586-2}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220209-45835}, pages = {1 -- 26}, abstract = {We present a stochastic deep collocation method (DCM) based on neural architecture search (NAS) and transfer learning for heterogeneous porous media. We first carry out a sensitivity analysis to determine the key hyper-parameters of the network to reduce the search space and subsequently employ hyper-parameter optimization to finally obtain the parameter values. The presented NAS based DCM also saves the weights and biases of the most favorable architectures, which is then used in the fine-tuning process. We also employ transfer learning techniques to drastically reduce the computational cost. The presented DCM is then applied to the stochastic analysis of heterogeneous porous material. Therefore, a three dimensional stochastic flow model is built providing a benchmark to the simulation of groundwater flow in highly heterogeneous aquifers. The performance of the presented NAS based DCM is verified in different dimensions using the method of manufactured solutions. We show that it significantly outperforms finite difference methods in both accuracy and computational cost.}, subject = {Maschinelles Lernen}, language = {en} } @article{ZhaoLuRabczuk, author = {Zhao, Jiyun and Lu, Lixin and Rabczuk, Timon}, title = {The tensile and shear failure behavior dependence on chain length and temperature in amorphous polymers}, series = {Computational Materials Science}, journal = {Computational Materials Science}, pages = {567 -- 572}, abstract = {The tensile and shear failure behavior dependence on chain length and temperature in amorphous polymers}, subject = {Angewandte Mathematik}, language = {en} } @article{HiguchiMacke, author = {Higuchi, Shoko and Macke, M.}, title = {Cost-benefit based optimization of maintenance interventions for deteriorating structures}, series = {Doboku Gakkai Ronbunshuu A}, journal = {Doboku Gakkai Ronbunshuu A}, pages = {727 -- 743}, abstract = {Cost-benefit based optimization of maintenance interventions for deteriorating structures}, subject = {Angewandte Mathematik}, language = {en} } @article{HaefnerEckardtLutheretal., author = {H{\"a}fner, Stefan and Eckardt, Stefan and Luther, Torsten and K{\"o}nke, Carsten}, title = {Mesoscale modeling of concrete: Geometry and numerics}, series = {Computers and Structures}, journal = {Computers and Structures}, pages = {450 -- 461}, abstract = {Mesoscale modeling of concrete: Geometry and numerics}, subject = {Angewandte Mathematik}, language = {en} } @article{HauckLahmerKaltenbacher, author = {Hauck, A. and Lahmer, Tom and Kaltenbacher, Manfred}, title = {Enhanced homogenization technique for magnetomechanical systems using the generalized finite element method}, series = {COMPEL: The international journal for computation and mathematics in electrical and electronic engineering}, journal = {COMPEL: The international journal for computation and mathematics in electrical and electronic engineering}, pages = {935 -- 947}, abstract = {Enhanced homogenization technique for magnetomechanical systems using the generalized finite element method}, subject = {Angewandte Mathematik}, language = {en} } @article{KaltenbacherLahmerMohretal., author = {Kaltenbacher, Barbara and Lahmer, Tom and Mohr, Marcus and Kaltenbacher, Manfred}, title = {PDE based determination of piezoelectric material tensors}, series = {European Journal of Applied Mathematics}, journal = {European Journal of Applied Mathematics}, doi = {10.25643/bauhaus-universitaet.3595}, pages = {383 -- 416}, abstract = {PDE based determination of piezoelectric material tensors.}, subject = {Angewandte Mathematik}, language = {en} } @article{LahmerKoenkeBettzieche, author = {Lahmer, Tom and K{\"o}nke, Carsten and Bettzieche, Volker}, title = {Optimale Positionierung von Messeinrichtungen an Staumauern zur Bauwerks{\"u}berwachung}, series = {WASSERWIRTSCHAFT}, journal = {WASSERWIRTSCHAFT}, pages = {16 -- 16}, abstract = {Optimale Positionierung von Messeinrichtungen an Staumauern zur Bauwerks{\"u}berwachung}, subject = {Angewandte Mathematik}, language = {de} } @article{LahmerKoenkeBettzieche, author = {Lahmer, Tom and K{\"o}nke, Carsten and Bettzieche, Volker}, title = {Optimal positioning of sensors for the monitoring of water dams}, series = {WASSERWIRTSCHAFT}, journal = {WASSERWIRTSCHAFT}, pages = {16 -- 19}, abstract = {Optimal positioning of sensors for the monitoring of water dams}, subject = {Angewandte Mathematik}, language = {de} } @inproceedings{TanLahmerSiddappa, author = {Tan, Fengjie and Lahmer, Tom and Siddappa, Manju Gyaraganahalll}, title = {SECTION OPTIMIZATION AND RELIABILITY ANALYSIS OF ARCH-TYPE DAMS INCLUDING COUPLED MECHANICAL-THERMAL AND HYDRAULIC FIELDS}, series = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar}, booktitle = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar}, editor = {G{\"u}rlebeck, Klaus and Lahmer, Tom}, organization = {Bauhaus-Universit{\"a}t Weimar}, issn = {1611-4086}, doi = {10.25643/bauhaus-universitaet.2821}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28212}, pages = {8}, abstract = {From the design experiences of arch dams in the past, it has significant practical value to carry out the shape optimization of arch dams, which can fully make use of material characteristics and reduce the cost of constructions. Suitable variables need to be chosen to formulate the objective function, e.g. to minimize the total volume of the arch dam. Additionally a series of constraints are derived and a reasonable and convenient penalty function has been formed, which can easily enforce the characteristics of constraints and optimal design. For the optimization method, a Genetic Algorithm is adopted to perform a global search. Simultaneously, ANSYS is used to do the mechanical analysis under the coupling of thermal and hydraulic loads. One of the constraints of the newly designed dam is to fulfill requirements on the structural safety. Therefore, a reliability analysis is applied to offer a good decision supporting for matters concerning predictions of both safety and service life of the arch dam. By this, the key factors which would influence the stability and safety of arch dam significantly can be acquired, and supply a good way to take preventive measures to prolong ate the service life of an arch dam and enhances the safety of structure.}, subject = {Angewandte Informatik}, language = {en} } @article{NguyenThoiPhungVanRabczuketal., author = {Nguyen-Thoi, T. and Phung-Van, P. and Rabczuk, Timon and Nguyen-Xuan, Hung and Le-Van, C.}, title = {An application of the ES-FEM in solid domain for dynamic analysis of 2D fluid-solid interaction problems}, series = {International Journal of Computational Methods}, journal = {International Journal of Computational Methods}, abstract = {An application of the ES-FEM in solid domain for dynamic analysis of 2D fluid-solid interaction problems}, subject = {Angewandte Mathematik}, language = {en} } @article{MarzbanLahmer, author = {Marzban, Samira and Lahmer, Tom}, title = {Conceptual implementation of the variance-based sensitivity analysis for the calculation of the first-order effects}, series = {Journal of Statistical Theory and Practice}, journal = {Journal of Statistical Theory and Practice}, pages = {589 -- 611}, abstract = {Conceptual implementation of the variance-based sensitivity analysis for the calculation of the first-order effects}, subject = {Angewandte Mathematik}, language = {en} } @article{NanthakumarLahmerRabczuk, author = {Nanthakumar, S.S. and Lahmer, Tom and Rabczuk, Timon}, title = {Detection of multiple flaws in piezoelectric structures using XFEM and level sets}, series = {International Journal for Numerical Methods in Engineering}, journal = {International Journal for Numerical Methods in Engineering}, pages = {960}, abstract = {Detection of multiple flaws in piezoelectric structures using XFEM and level sets}, subject = {Angewandte Mathematik}, language = {en} } @article{AnitescuJiaZhangetal., author = {Anitescu, Cosmin and Jia, Yue and Zhang, Yongjie and Rabczuk, Timon}, title = {An isogeometric collocation method using superconvergent points}, series = {Computer Methods in Applied Mechanics and Engineer-ing}, journal = {Computer Methods in Applied Mechanics and Engineer-ing}, pages = {1073 -- 1097}, abstract = {An isogeometric collocation method using superconvergent points}, subject = {Angewandte Mathematik}, language = {en} } @article{ChakrabortyAnitescuZhuangetal., author = {Chakraborty, Ayan and Anitescu, Cosmin and Zhuang, Xiaoying and Rabczuk, Timon}, title = {Domain adaptation based transfer learning approach for solving PDEs on complex geometries}, series = {Engineering with Computers}, volume = {2022}, journal = {Engineering with Computers}, doi = {10.1007/s00366-022-01661-2}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220811-46776}, pages = {1 -- 20}, abstract = {In machine learning, if the training data is independently and identically distributed as the test data then a trained model can make an accurate predictions for new samples of data. Conventional machine learning has a strong dependence on massive amounts of training data which are domain specific to understand their latent patterns. In contrast, Domain adaptation and Transfer learning methods are sub-fields within machine learning that are concerned with solving the inescapable problem of insufficient training data by relaxing the domain dependence hypothesis. In this contribution, this issue has been addressed and by making a novel combination of both the methods we develop a computationally efficient and practical algorithm to solve boundary value problems based on nonlinear partial differential equations. We adopt a meshfree analysis framework to integrate the prevailing geometric modelling techniques based on NURBS and present an enhanced deep collocation approach that also plays an important role in the accuracy of solutions. We start with a brief introduction on how these methods expand upon this framework. We observe an excellent agreement between these methods and have shown that how fine-tuning a pre-trained network to a specialized domain may lead to an outstanding performance compare to the existing ones. As proof of concept, we illustrate the performance of our proposed model on several benchmark problems.}, subject = {Maschinelles Lernen}, language = {en} } @article{ZhaoJiangJiaetal., author = {Zhao, Jun-Hua and Jiang, Jin-Wu and Jia, Yue and Guo, Wanlin and Rabczuk, Timon}, title = {A theoretical analysis of cohesive energy between carbon nanotubes, graphene and substrates}, series = {Carbon}, journal = {Carbon}, doi = {10.1016/j.carbon.2013.01.041}, pages = {108 -- 119}, abstract = {Explicit solutions for the cohesive energy between carbon nanotubes, graphene and substrates are obtained through continuum modeling of the van der Waals interaction between them. The dependence of the cohesive energy on their size, spacing and crossing angles is analyzed. Checking against full atom molecular dynamics calculations and available experimental results shows that the continuum solution has high accuracy. The equilibrium distances between the nanotubes, graphene and substrates with minimum cohesive energy are also provided explicitly. The obtained analytical solution should be of great help for understanding the interaction between the nanostructures and substrates, and designing composites and nanoelectromechanical systems.}, subject = {Angewandte Mathematik}, language = {en} } @article{LeNguyenXuanAskesetal., author = {Le, C.V. and Nguyen-Xuan, Hung and Askes, H. and Rabczuk, Timon and Nguyen-Thoi, T.}, title = {Computation of limit load using edge-based smoothed finite element method and second-order cone programming}, series = {International Journal of Computational Methods}, journal = {International Journal of Computational Methods}, abstract = {Computation of limit load using edge-based smoothed finite element method and second-order cone programming}, subject = {Angewandte Mathematik}, language = {en} } @article{NguyenThanhKiendlNguyenXuanetal., author = {Nguyen-Thanh, Nhon and Kiendl, J. and Nguyen-Xuan, Hung and W{\"u}chner, R. and Bletzinger, Kai-Uwe and Bazilevs, Yuri and Rabczuk, Timon}, title = {Rotation free isogeometric thin shell analysis using PHT-splines}, series = {Computer Methods in Applied Mechanics and Engineering}, journal = {Computer Methods in Applied Mechanics and Engineering}, pages = {3410 -- 3424}, abstract = {Rotation free isogeometric thin shell analysis using PHT-splines}, subject = {Angewandte Mathematik}, language = {en} } @article{SchraderKoenke, author = {Schrader, Kai and K{\"o}nke, Carsten}, title = {Distributed computing for the nonlinear analysis of multiphase composites}, series = {Advances in Engineering Software}, journal = {Advances in Engineering Software}, pages = {20 -- 32}, abstract = {Distributed computing for the nonlinear analysis of multiphase composites}, subject = {Angewandte Mathematik}, language = {en} } @inproceedings{TheilerKoenke, author = {Theiler, Michael and K{\"o}nke, Carsten}, title = {Damping in Bolted Joints}, series = {Proceedings of International Conference on Structural Engineering Dynamics (ICEDyn) 2013}, booktitle = {Proceedings of International Conference on Structural Engineering Dynamics (ICEDyn) 2013}, editor = {Maia, Nuno}, isbn = {978-989-96276-4-2}, doi = {10.25643/bauhaus-universitaet.1970}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20130701-19709}, pages = {8}, abstract = {With the help of modern CAE-based simulation processes, it is possible to predict the dynamic behavior of fatigue strength problems in order to improve products of many industries, e.g. the building, the machine construction or the automotive industry. Amongst others, it can be used to improve the acoustic design of automobiles in an early development stage. Nowadays, the acoustics of automobiles plays a crucial role in the process of vehicle development. Because of the advanced demand of comfort and due to statutory rules the manufacturers are faced with the challenge of optimizing their car's sound emissions. The optimization includes not only the reduction of noises. Lately with the trend to hybrid and electric cars, it has been shown that vehicles can become too quiet. Thus, the prediction of structural and acoustic properties based on FE-simulations is becoming increasingly important before any experimental prototype is examined. With the state of the art, qualitative comparisons between different implementations are possible. However, an accurate and reliable quantitative prediction is still a challenge. One aspect in the context of increasing the prediction quality of acoustic (or general oscillating) problems - especially in power-trains of automobiles - is the more accurate implementation of damping in joint structures. While material damping occurs globally and homogenous in a structural system, the damping due to joints is a very local problem, since energy is especially dissipated in the vicinity of joints. This paper focusses on experimental and numerical studies performed on a single (extracted) screw connection. Starting with experimental studies that are used to identify the underlying physical model of the energy loss, the locally influencing parameters (e.g. the damping factor) should be identified. In contrast to similar research projects, the approach tends to a more local consideration within the joint interface. Tangential stiffness and energy loss within the interface are spatially distributed and interactions between the influencing parameters are regarded. As a result, the damping matrix is no longer proportional to mass or stiffness matrix, since it is composed of the global material damping and the local joint damping. With this new approach, the prediction quality can be increased, since the local distribution of the physical parameters within the joint interface corresponds much closer to the reality.}, subject = {Damping}, language = {en} } @phdthesis{Luther2010, author = {Luther, Torsten}, title = {Adaptation of atomistic and continuum methods for multiscale simulation of quasi-brittle intergranular damage}, doi = {10.25643/bauhaus-universitaet.1436}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20101101-15245}, school = {Bauhaus-Universit{\"a}t Weimar}, year = {2010}, abstract = {The numerical simulation of damage using phenomenological models on the macroscale was state of the art for many decades. However, such models are not able to capture the complex nature of damage, which simultaneously proceeds on multiple length scales. Furthermore, these phenomenological models usually contain damage parameters, which are physically not interpretable. Consequently, a reasonable experimental determination of these parameters is often impossible. In the last twenty years, the ongoing advance in computational capacities provided new opportunities for more and more detailed studies of the microstructural damage behavior. Today, multiphase models with several million degrees of freedom enable for the numerical simulation of micro-damage phenomena in naturally heterogeneous materials. Therewith, the application of multiscale concepts for the numerical investigation of the complex nature of damage can be realized. The presented thesis contributes to a hierarchical multiscale strategy for the simulation of brittle intergranular damage in polycrystalline materials, for example aluminum. The numerical investigation of physical damage phenomena on an atomistic microscale and the integration of these physically based information into damage models on the continuum meso- and macroscale is intended. Therefore, numerical methods for the damage analysis on the micro- and mesoscale including the scale transfer are presented and the transition to the macroscale is discussed. The investigation of brittle intergranular damage on the microscale is realized by the application of the nonlocal Quasicontinuum method, which fully describes the material behavior by atomistic potential functions, but reduces the number of atomic degrees of freedom by introducing kinematic couplings. Since this promising method is applied only by a limited group of researchers for special problems, necessary improvements have been realized in an own parallelized implementation of the 3D nonlocal Quasicontinuum method. The aim of this implementation was to develop and combine robust and efficient algorithms for a general use of the Quasicontinuum method, and therewith to allow for the atomistic damage analysis in arbitrary grain boundary configurations. The implementation is applied in analyses of brittle intergranular damage in ideal and nonideal grain boundary models of FCC aluminum, considering arbitrary misorientations. From the microscale simulations traction separation laws are derived, which describe grain boundary decohesion on the mesoscale. Traction separation laws are part of cohesive zone models to simulate the brittle interface decohesion in heterogeneous polycrystal structures. 2D and 3D mesoscale models are presented, which are able to reproduce crack initiation and propagation along cohesive interfaces in polycrystals. An improved Voronoi algorithm is developed in 2D to generate polycrystal material structures based on arbitrary distribution functions of grain size. The new model is more flexible in representing realistic grain size distributions. Further improvements of the 2D model are realized by the implementation and application of an orthotropic material model with Hill plasticity criterion to grains. The 2D and 3D polycrystal models are applied to analyze crack initiation and propagation in statically loaded samples of aluminum on the mesoscale without the necessity of initial damage definition.}, subject = {Mechanik}, language = {en} } @phdthesis{Eckardt2009, author = {Eckardt, Stefan}, title = {Adaptive heterogeneous multiscale models for the nonlinear simulation of concrete}, doi = {10.25643/bauhaus-universitaet.1416}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20100317-15023}, school = {Bauhaus-Universit{\"a}t Weimar}, year = {2009}, abstract = {The nonlinear behavior of concrete can be attributed to the propagation of microcracks within the heterogeneous internal material structure. In this thesis, a mesoscale model is developed which allows for the explicit simulation of these microcracks. Consequently, the actual physical phenomena causing the complex nonlinear macroscopic behavior of concrete can be represented using rather simple material formulations. On the mesoscale, the numerical model explicitly resolves the components of the internal material structure. For concrete, a three-phase model consisting of aggregates, mortar matrix and interfacial transition zone is proposed. Based on prescribed grading curves, an efficient algorithm for the generation of three-dimensional aggregate distributions using ellipsoids is presented. In the numerical model, tensile failure of the mortar matrix is described using a continuum damage approach. In order to reduce spurious mesh sensitivities, introduced by the softening behavior of the matrix material, nonlocal integral-type material formulations are applied. The propagation of cracks at the interface between aggregates and mortar matrix is represented in a discrete way using a cohesive crack approach. The iterative solution procedure is stabilized using a new path following constraint within the framework of load-displacement-constraint methods which allows for an efficient representation of snap-back phenomena. In several examples, the influence of the randomly generated heterogeneous material structure on the stochastic scatter of the results is analyzed. Furthermore, the ability of mesoscale models to represent size effects is investigated. Mesoscale simulations require the discretization of the internal material structure. Compared to simulations on the macroscale, the numerical effort and the memory demand increases dramatically. Due to the complexity of the numerical model, mesoscale simulations are, in general, limited to small specimens. In this thesis, an adaptive heterogeneous multiscale approach is presented which allows for the incorporation of mesoscale models within nonlinear simulations of concrete structures. In heterogeneous multiscale models, only critical regions, i.e. regions in which damage develops, are resolved on the mesoscale, whereas undamaged or sparsely damage regions are modeled on the macroscale. A crucial point in simulations with heterogeneous multiscale models is the coupling of sub-domains discretized on different length scales. The sub-domains differ not only in the size of the finite elements but also in the constitutive description. In this thesis, different methods for the coupling of non-matching discretizations - constraint equations, the mortar method and the arlequin method - are investigated and the application to heterogeneous multiscale models is presented. Another important point is the detection of critical regions. An adaptive solution procedure allowing the transfer of macroscale sub-domains to the mesoscale is proposed. In this context, several indicators which trigger the model adaptation are introduced. Finally, the application of the proposed adaptive heterogeneous multiscale approach in nonlinear simulations of concrete structures is presented.}, subject = {Beton}, language = {en} } @phdthesis{Abeltshauser, author = {Abeltshauser, Rainer}, title = {Identification and separation of physical effects of coupled systems by using defined model abstractions}, doi = {10.25643/bauhaus-universitaet.2860}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28600}, school = {Bauhaus-Universit{\"a}t Weimar}, abstract = {The thesis investigates at the computer aided simulation process for operational vibration analysis of complex coupled systems. As part of the internal methods project "Absolute Values" of the BMW Group, the thesis deals with the analysis of the structural dynamic interactions and excitation interactions. The overarching aim of the methods project is to predict the operational vibrations of engines. Simulations are usually used to analyze technical aspects (e. g. operational vibrations, strength, ...) of single components in the industrial development. The boundary conditions of submodels are mostly based on experiences. So the interactions with neighboring components and systems are neglected. To get physically more realistic results but still efficient simulations, this work wants to support the engineer during the preprocessing phase by useful criteria. At first suitable abstraction levels based on the existing literature are defined to identify structural dynamic interactions and excitation interactions of coupled systems. So it is possible to separate different effects of the coupled subsystems. On this basis, criteria are derived to assess the influence of interactions between the considered systems. These criteria can be used during the preprocessing phase and help the engineer to build up efficient models with respect to the interactions with neighboring systems. The method was developed by using several models with different complexity levels. Furthermore, the method is proved for the application in the industrial environment by using the example of a current combustion engine.}, subject = {Strukturdynamik}, language = {en} } @phdthesis{Higuchi2007, author = {Higuchi, Shoko}, title = {Cost-Benefit Based Maintenance Optimization for Deteriorating Structures}, doi = {10.25643/bauhaus-universitaet.1288}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20080513-13616}, school = {Bauhaus-Universit{\"a}t Weimar}, year = {2007}, abstract = {In recent years increasingly consideration has been given to the lifetime extension of existing structures. This is based on the fact that a growing percentage of civil infrastructure as well as buildings is threatened by obsolescence and that due to simple monetary reasons this can no longer be countered by simply re-building everything anew. Hence maintenance interventions are required which allow partial or complete structural rehabilitation. However, maintenance interventions have to be economically reasonable, that is, maintenance expenditures have to be outweighed by expected future benefits. Is this not the case, then indeed the structure is obsolete - at least in its current functional, economic, technical, or social configuration - and innovative alternatives have to be evaluated. An optimization formulation for planning maintenance interventions based on cost-benefit criteria is proposed herein. The underlying formulation is as follows: (a) between maintenance interventions structural deterioration is described as a random process; (b) maintenance interventions can take place anytime throughout lifetime and comprise the rehabilitation of all deterioration states above a certain minimum level; and (c) maintenance interventions are optimized by taking into account all expected life-cycle costs (construction, failure, inspection and state-dependent repair costs) as well as state- or time-dependent benefit rates. The optimization is performed by an evolutionary algorithm. The proposed approach also allows to determine optimal lifetimes and acceptable failure rates. Numerical examples demonstrate the importance of defining benefit rates explicitly. It is shown, that the optimal solution to maintenance interventions requires to take action before reaching the acceptable failure rate or the zero expected net benefit rate level. Deferring decisions with respect to maintenance not only results, in general, in higher losses, but also results in overly hazardous structures.}, subject = {Kosten-Nutzen-Analyse}, language = {en} } @phdthesis{Will1999, author = {Will, Johannes}, title = {Beitrag zur Standsicherheitsberechnung im gekl{\"u}fteten Fels in der Kontinuums- und Diskontinuumsmechanik unter Verwendung impliziter und expliziter Berechnungsstrategien}, doi = {10.25643/bauhaus-universitaet.58}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20040310-613}, school = {Bauhaus-Universit{\"a}t Weimar}, year = {1999}, subject = {Staumauer}, language = {de} } @article{LahmerNguyenTuanKoenkeetal., author = {Lahmer, Tom and Nguyen-Tuan, Long and K{\"o}nke, Carsten and Bettzieche, Volker}, title = {Thermo-hydro-mechanische 3-D-Simulation von Staumauern-Modellierung und Validierung}, series = {WASSERWIRTSCHAFT}, journal = {WASSERWIRTSCHAFT}, pages = {27 -- 30}, abstract = {Thermo-hydro-mechanische 3-D-Simulation von Staumauern-Modellierung und Validierung}, subject = {Angewandte Mathematik}, language = {de} } @article{AreiasRabczukCesardeSaetal., author = {Areias, Pedro and Rabczuk, Timon and Cesar de Sa, J.M. and Garcao, J.E.}, title = {Finite strain quadrilateral shell using least-squares _t of relative Lagrangian in-plane strains}, series = {Finite Elements in Analysis and Design}, journal = {Finite Elements in Analysis and Design}, pages = {26 -- 40}, abstract = {Finite strain quadrilateral shell using least-squares _t of relative Lagrangian in-plane strains}, subject = {Angewandte Mathematik}, language = {en} } @article{LahmerKaltenbacherSchulz, author = {Lahmer, Tom and Kaltenbacher, Barbara and Schulz, V.}, title = {Optimal measurement selection for piezoelectric material tensor identification}, series = {Inverse Problems in Science and Engineering}, journal = {Inverse Problems in Science and Engineering}, doi = {10.25643/bauhaus-universitaet.3593}, pages = {369 -- 387}, abstract = {Optimal measurement selection for piezoelectric material tensor identification.}, subject = {Angewandte Mathematik}, language = {en} } @article{Lahmer, author = {Lahmer, Tom}, title = {Modified Landweber iterations in a multilevel algorithm applied to inverse problems in piezoelectricity}, series = {Journal of Inverse and Ill-posed Problems}, journal = {Journal of Inverse and Ill-posed Problems}, pages = {585 -- 593}, abstract = {Modified Landweber iterations in a multilevel algorithm applied to inverse problems in piezoelectricity}, subject = {Angewandte Mathematik}, language = {en} } @article{GhasemiKerfridenBordasetal., author = {Ghasemi, Hamid and Kerfriden, Pierre and Bordas, St{\´e}phane Pierre Alain and Muthu, Jacob and Zi, Goangseup and Rabczuk, Timon}, title = {Interfacial shear stress optimization in sandwich beams with polymeric core using nonuniform distribution of reinforcing ingredients}, series = {Composite Structures}, journal = {Composite Structures}, pages = {221 -- 230}, abstract = {Interfacial shear stress optimization in sandwich beams with polymeric core using nonuniform distribution of reinforcing ingredients}, subject = {Angewandte Mathematik}, language = {en} } @article{ZhaoKouJiangetal., author = {Zhao, Jun-Hua and Kou, Liangzhi and Jiang, Jin-Wu and Rabczuk, Timon}, title = {Tension-induced phase transition of single-layer molybdenum disulphide (MoS2) at low temperatures}, series = {Nanotechnology}, journal = {Nanotechnology}, doi = {10.1088/0957-4484/25/29/295701}, abstract = {Tension-induced phase transition of single-layer molybdenum disulphide (MoS2) at low temperatures}, subject = {Angewandte Mathematik}, language = {en} } @article{JiaZhangRabczuk, author = {Jia, Yue and Zhang, Yongjie and Rabczuk, Timon}, title = {A Novel Dynamic Multilevel Technique for Image Registration}, series = {Computers and Mathematics with Applications}, journal = {Computers and Mathematics with Applications}, abstract = {A Novel Dynamic Multilevel Technique for Image Registration}, subject = {Angewandte Mathematik}, language = {en} } @phdthesis{Schrader, author = {Schrader, Kai}, title = {Hybrid 3D simulation methods for the damage analysis of multiphase composites}, doi = {10.25643/bauhaus-universitaet.2059}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20131021-20595}, school = {Bauhaus-Universit{\"a}t Weimar}, pages = {174}, abstract = {Modern digital material approaches for the visualization and simulation of heterogeneous materials allow to investigate the behavior of complex multiphase materials with their physical nonlinear material response at various scales. However, these computational techniques require extensive hardware resources with respect to computing power and main memory to solve numerically large-scale discretized models in 3D. Due to a very high number of degrees of freedom, which may rapidly be increased to the two-digit million range, the limited hardware ressources are to be utilized in a most efficient way to enable an execution of the numerical algorithms in minimal computation time. Hence, in the field of computational mechanics, various methods and algorithms can lead to an optimized runtime behavior of nonlinear simulation models, where several approaches are proposed and investigated in this thesis. Today, the numerical simulation of damage effects in heterogeneous materials is performed by the adaption of multiscale methods. A consistent modeling in the three-dimensional space with an appropriate discretization resolution on each scale (based on a hierarchical or concurrent multiscale model), however, still contains computational challenges in respect to the convergence behavior, the scale transition or the solver performance of the weak coupled problems. The computational efficiency and the distribution among available hardware resources (often based on a parallel hardware architecture) can significantly be improved. In the past years, high-performance computing (HPC) and graphics processing unit (GPU) based computation techniques were established for the investigationof scientific objectives. Their application results in the modification of existing and the development of new computational methods for the numerical implementation, which enables to take advantage of massively clustered computer hardware resources. In the field of numerical simulation in material science, e.g. within the investigation of damage effects in multiphase composites, the suitability of such models is often restricted by the number of degrees of freedom (d.o.f.s) in the three-dimensional spatial discretization. This proves to be difficult for the type of implementation method used for the nonlinear simulation procedure and, simultaneously has a great influence on memory demand and computational time. In this thesis, a hybrid discretization technique has been developed for the three-dimensional discretization of a three-phase material, which is respecting the numerical efficiency of nonlinear (damage) simulations of these materials. The increase of the computational efficiency is enabled by the improved scalability of the numerical algorithms. Consequently, substructuring methods for partitioning the hybrid mesh were implemented, tested and adapted to the HPC computing framework using several hundred CPU (central processing units) nodes for building the finite element assembly. A memory-efficient iterative and parallelized equation solver combined with a special preconditioning technique for solving the underlying equation system was modified and adapted to enable combined CPU and GPU based computations. Hence, it is recommended by the author to apply the substructuring method for hybrid meshes, which respects different material phases and their mechanical behavior and which enables to split the structure in elastic and inelastic parts. However, the consideration of the nonlinear material behavior, specified for the corresponding phase, is limited to the inelastic domains only, and by that causes a decreased computing time for the nonlinear procedure. Due to the high numerical effort for such simulations, an alternative approach for the nonlinear finite element analysis, based on the sequential linear analysis, was implemented in respect to scalable HPC. The incremental-iterative procedure in finite element analysis (FEA) during the nonlinear step was then replaced by a sequence of linear FE analysis when damage in critical regions occured, known in literature as saw-tooth approach. As a result, qualitative (smeared) crack initiation in 3D multiphase specimens has efficiently been simulated.}, subject = {high-performance computing}, language = {en} } @article{AreiasRabczukQueirosdeMeloetal., author = {Areias, Pedro and Rabczuk, Timon and Queiros de Melo, F. J. M. and Cesar de Sa, J.M.}, title = {Coulomb frictional contact by explicit projection in the cone for _nite displacement quasi-static problems}, series = {Computational Mechanics}, journal = {Computational Mechanics}, pages = {57 -- 72}, abstract = {Coulomb frictional contact by explicit projection in the cone for _nite displacement quasi-static problems}, subject = {Angewandte Mathematik}, language = {en} } @article{SilaniTalebiZiaeiRadetal., author = {Silani, Mohammad and Talebi, Hossein and Ziaei-Rad, S. and Hamouda, A.M.S. and Zi, Goangseup and Rabczuk, Timon}, title = {A three dimensional Extended Arlequin Method for Dynamic Fracture}, series = {Computational Materials Science}, journal = {Computational Materials Science}, pages = {425 -- 431}, abstract = {A three dimensional Extended Arlequin Method for Dynamic Fracture}, subject = {Angewandte Mathematik}, language = {en} } @phdthesis{Nouri, author = {Nouri, Hamidreza}, title = {Mechanical Behavior of two dimensional sheets and polymer compounds based on molecular dynamics and continuum mechanics approach}, doi = {10.25643/bauhaus-universitaet.4670}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220713-46700}, school = {Bauhaus-Universit{\"a}t Weimar}, pages = {152}, abstract = {Compactly, this thesis encompasses two major parts to examine mechanical responses of polymer compounds and two dimensional materials: 1- Molecular dynamics approach is investigated to study transverse impact behavior of polymers, polymer compounds and two dimensional materials. 2- Large deflection of circular and rectangular membranes is examined by employing continuum mechanics approach. Two dimensional materials (2D), including, Graphene and molybdenum disulfide (MoS2), exhibited new and promising physical and chemical properties, opening new opportunities to be utilized alone or to enhance the performance of conventional materials. These 2D materials have attracted tremendous attention owing to their outstanding physical properties, especially concerning transverse impact loading. Polymers, with the backbone of carbon (organic polymers) or do not include carbon atoms in the backbone (inorganic polymers) like polydimethylsiloxane (PDMS), have extraordinary characteristics particularly their flexibility leads to various easy ways of forming and casting. These simple shape processing label polymers as an excellent material often used as a matrix in composites (polymer compounds). In this PhD work, Classical Molecular Dynamics (MD) is implemented to calculate transverse impact loading of 2D materials as well as polymer compounds reinforced with graphene sheets. In particular, MD was adopted to investigate perforation of the target and impact resistance force . By employing MD approach, the minimum velocity of the projectile that could create perforation and passes through the target is obtained. The largest investigation was focused on how graphene could enhance the impact properties of the compound. Also the purpose of this work was to discover the effect of the atomic arrangement of 2D materials on the impact problem. To this aim, the impact properties of two different 2D materials, graphene and MoS2, are studied. The simulation of chemical functionalization was carried out systematically, either with covalently bonded molecules or with non-bonded ones, focusing the following efforts on the covalently bounded species, revealed as the most efficient linkers. To study transverse impact behavior by using classical MD approach , Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) software, that is well-known among most researchers, is employed. The simulation is done through predefined commands in LAMMPS. Generally these commands (atom style, pair style, angle style, dihedral style, improper style, kspace style, read data, fix, run, compute and so on) are used to simulate and run the model for the desired outputs. Depends on the particles and model types, suitable inter-atomic potentials (force fields) are considered. The ensembles, constraints and boundary conditions are applied depends upon the problem definition. To do so, atomic creation is needed. Python codes are developed to generate particles which explain atomic arrangement of each model. Each atomic arrangement introduced separately to LAMMPS for simulation. After applying constraints and boundary conditions, LAMMPS also include integrators like velocity-Verlet integrator or Brownian dynamics or other types of integrator to run the simulation and finally the outputs are emerged. The outputs are inspected carefully to appreciate the natural behavior of the problem. Appreciation of natural properties of the materials assist us to design new applicable materials. In investigation on the large deflection of circular and rectangular membranes, which is related to the second part of this thesis, continuum mechanics approach is implemented. Nonlinear F{\"o}ppl membrane theory, which carefully release nonlinear governing equations of motion, is considered to establish the non-linear partial differential equilibrium equations of the membranes under distributed and centric point loads. The Galerkin and energy methods are utilized to solve non-linear partial differential equilibrium equations of circular and rectangular plates respectively. Maximum deflection as well as stress through the film region, which are kinds of issue in many industrial applications, are obtained.}, subject = {Molekulardynamik}, language = {en} } @phdthesis{Jenabidehkordi, author = {Jenabidehkordi, Ali}, title = {An Efficient Adaptive PD Formulation for Complex Microstructures}, doi = {10.25643/bauhaus-universitaet.4742}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20221124-47422}, school = {Bauhaus-Universit{\"a}t Weimar}, pages = {118}, abstract = {The computational costs of newly developed numerical simulation play a critical role in their acceptance within both academic use and industrial employment. Normally, the refinement of a method in the area of interest reduces the computational cost. This is unfortunately not true for most nonlocal simulation, since refinement typically increases the size of the material point neighborhood. Reducing the discretization size while keep- ing the neighborhood size will often require extra consideration. Peridy- namic (PD) is a newly developed numerical method with nonlocal nature. Its straightforward integral form equation of motion allows simulating dy- namic problems without any extra consideration required. The formation of crack and its propagation is known as natural to peridynamic. This means that discontinuity is a result of the simulation and does not demand any post-processing. As with other nonlocal methods, PD is considered an expensive method. The refinement of the nodal spacing while keeping the neighborhood size (i.e., horizon radius) constant, emerges to several nonphysical phenomena. This research aims to reduce the peridynamic computational and imple- mentation costs. A novel refinement approach is introduced. The pro- posed approach takes advantage of the PD flexibility in choosing the shape of the horizon by introducing multiple domains (with no intersections) to the nodes of the refinement zone. It will be shown that no ghost forces will be created when changing the horizon sizes in both subdomains. The approach is applied to both bond-based and state-based peridynamic and verified for a simple wave propagation refinement problem illustrating the efficiency of the method. Further development of the method for higher dimensions proves to have a direct relationship with the mesh sensitivity of the PD. A method for solving the mesh sensitivity of the PD is intro- duced. The application of the method will be examined by solving a crack propagation problem similar to those reported in the literature. New software architecture is proposed considering both academic and in- dustrial use. The available simulation tools for employing PD will be collected, and their advantages and drawbacks will be addressed. The challenges of implementing any node base nonlocal methods while max- imizing the software flexibility to further development and modification will be discussed and addressed. A software named Relation-Based Sim- ulator (RBS) is developed for examining the proposed architecture. The exceptional capabilities of RBS will be explored by simulating three dis- tinguished models. RBS is available publicly and open to further develop- ment. The industrial acceptance of the RBS will be tested by targeting its performance on one Mac and two Linux distributions.}, subject = {Peridynamik}, language = {en} } @phdthesis{Hanna, author = {Hanna, John}, title = {Computational Fracture Modeling and Design of Encapsulation-Based Self-Healing Concrete Using XFEM and Cohesive Surface Technique}, doi = {10.25643/bauhaus-universitaet.4746}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20221124-47467}, school = {Bauhaus-Universit{\"a}t Weimar}, pages = {125}, abstract = {Encapsulation-based self-healing concrete (SHC) is the most promising technique for providing a self-healing mechanism to concrete. This is due to its capacity to heal fractures effectively without human interventions, extending the operational life and lowering maintenance costs. The healing mechanism is created by embedding capsules containing the healing agent inside the concrete. The healing agent will be released once the capsules are fractured and the healing occurs in the vicinity of the damaged part. The healing efficiency of the SHC is still not clear and depends on several factors; in the case of microcapsules SHC the fracture of microcapsules is the most important aspect to release the healing agents and hence heal the cracks. This study contributes to verifying the healing efficiency of SHC and the fracture mechanism of the microcapsules. Extended finite element method (XFEM) is a flexible, and powerful discrete crack method that allows crack propagation without the requirement for re-meshing and has been shown high accuracy for modeling fracture in concrete. In this thesis, a computational fracture modeling approach of Encapsulation-based SHC is proposed based on the XFEM and cohesive surface technique (CS) to study the healing efficiency and the potential of fracture and debonding of the microcapsules or the solidified healing agents from the concrete matrix as well. The concrete matrix and a microcapsule shell both are modeled by the XFEM and combined together by CS. The effects of the healed-crack length, the interfacial fracture properties, and microcapsule size on the load carrying capability and fracture pattern of the SHC have been studied. The obtained results are compared to those obtained from the zero thickness cohesive element approach to demonstrate the significant accuracy and the validity of the proposed simulation. The present fracture simulation is developed to study the influence of the capsular clustering on the fracture mechanism by varying the contact surface area of the CS between the microcapsule shell and the concrete matrix. The proposed fracture simulation is expanded to 3D simulations to validate the 2D computational simulations and to estimate the accuracy difference ratio between 2D and 3D simulations. In addition, a proposed design method is developed to design the size of the microcapsules consideration of a sufficient volume of healing agent to heal the expected crack width. This method is based on the configuration of the unit cell (UC), Representative Volume Element (RVE), Periodic Boundary Conditions (PBC), and associated them to the volume fraction (Vf) and the crack width as variables. The proposed microcapsule design is verified through computational fracture simulations.}, subject = {Beton}, language = {en} } @article{EckardtKoenke, author = {Eckardt, Stefan and K{\"o}nke, Carsten}, title = {Adaptive damage simulation of concrete using heterogeneous multiscale models}, series = {Journal of Algorithms \& Computational Technology}, journal = {Journal of Algorithms \& Computational Technology}, pages = {275 -- 297}, abstract = {Adaptive damage simulation of concrete using heterogeneous multiscale models}, subject = {Angewandte Mathematik}, language = {en} } @inproceedings{UngerKoenke, author = {Unger, J{\"o}rg F. and K{\"o}nke, Carsten}, title = {DISCRETE CRACK SIMULATION OF CONCRETE USING THE EXTENDED FINITE ELEMENTMETHOD}, editor = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten}, organization = {Bauhaus-Universit{\"a}t Weimar}, doi = {10.25643/bauhaus-universitaet.3030}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170327-30303}, pages = {12}, abstract = {The extended finite element method (XFEM) offers an elegant tool to model material discontinuities and cracks within a regular mesh, so that the element edges do not necessarily coincide with the discontinuities. This allows the modeling of propagating cracks without the requirement to adapt the mesh incrementally. Using a regular mesh offers the advantage, that simple refinement strategies based on the quadtree data structure can be used to refine the mesh in regions, that require a high mesh density. An additional benefit of the XFEM is, that the transmission of cohesive forces through a crack can be modeled in a straightforward way without introducing additional interface elements. Finally different criteria for the determination of the crack propagation angle are investigated and applied to numerical tests of cracked concrete specimens, which are compared with experimental results.}, subject = {Architektur }, language = {en} }