@article{NguyenXuanNguyenBordasetal., author = {Nguyen-Xuan, Hung and Nguyen, Hiep Vinh and Bordas, St{\´e}phane Pierre Alain and Rabczuk, Timon and Duflot, Marc}, title = {A cell-based smoothed finite element method for three dimensional solid structures}, series = {KSCE Journal of Civil Engineering}, journal = {KSCE Journal of Civil Engineering}, doi = {10.1007/s12205-012-1515-7}, pages = {1230 -- 1242}, abstract = {This paper extends further the strain smoothing technique in finite elements to 8-noded hexahedral elements (CS-FEM-H8). The idea behind the present method is similar to the cell-based smoothed 4-noded quadrilateral finite elements (CS-FEM-Q4). In CSFEM, the smoothing domains are created based on elements, and each element can be further subdivided into 1 or several smoothing cells. It is observed that: 1) The CS-FEM using a single smoothing cell can produce higher stress accuracy, but insufficient rank and poor displacement accuracy; 2) The CS-FEM using several smoothing cells has proper rank, good displacement accuracy, but lower stress accuracy, especially for nearly incompressible and bending dominant problems. We therefore propose 1) an extension of strain smoothing to 8-noded hexahedral elements and 2) an alternative CS-FEM form, which associates the single smoothing cell issue with multi-smoothing cell one via a stabilization technique. Several numerical examples are provided to show the reliability and accuracy of the present formulation.}, subject = {Angewandte Mathematik}, language = {en} } @article{ZhaoWangJiangetal., author = {Zhao, Jun-Hua and Wang, L. and Jiang, Jin-Wu and Wang, Z. and Guo, Wanlin and Rabczuk, Timon}, title = {A comparative study of two molecular mechanics models based on harmonic potentials}, series = {Journal of Applied Physics}, journal = {Journal of Applied Physics}, abstract = {A comparative study of two molecular mechanics models based on harmonic potentials}, subject = {Angewandte Mathematik}, language = {en} } @article{BucherMost, author = {Bucher, Christian and Most, Thomas}, title = {A comparison of approximate response functions in structural reliability analysis}, series = {Probabilistic Engineering Mechanics}, journal = {Probabilistic Engineering Mechanics}, pages = {154 -- 163}, abstract = {A comparison of approximate response functions in structural reliability analysis}, subject = {Angewandte Mathematik}, language = {en} } @article{TalebiSilaniBordasetal., author = {Talebi, Hossein and Silani, Mohammad and Bordas, St{\´e}phane Pierre Alain and Kerfriden, Pierre and Rabczuk, Timon}, title = {A computational library for multiscale modeling of material failure}, series = {Computational Mechanics}, journal = {Computational Mechanics}, abstract = {A computational library for multiscale modeling of material failure}, subject = {Angewandte Mathematik}, language = {en} } @article{ZhuangHuangRabczuketal., author = {Zhuang, Xiaoying and Huang, Runqiu and Rabczuk, Timon and Liang, C.}, title = {A coupled thermo-hydro-mechanical model of jointed hard rock for compressed air energy storage}, series = {Mathematical Problems in Engineering}, journal = {Mathematical Problems in Engineering}, abstract = {A coupled thermo-hydro-mechanical model of jointed hard rock for compressed air energy storage}, subject = {Angewandte Mathematik}, language = {en} } @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{YangBudarapuMahapatraetal., author = {Yang, Shih-Wei and Budarapu, Pattabhi Ramaiah and Mahapatra, D.R. and Bordas, St{\´e}phane Pierre Alain and Zi, Goangseup and Rabczuk, Timon}, title = {A Meshless Adaptive Multiscale Method for Fracture}, series = {Computational Materials Science}, journal = {Computational Materials Science}, pages = {382 -- 395}, abstract = {A Meshless Adaptive Multiscale Method for Fracture}, subject = {Angewandte Mathematik}, language = {en} } @article{MostBucher, author = {Most, Thomas and Bucher, Christian}, title = {A moving least squares weighting function for the element-free Galerkin method which almost fulfills essential boundary conditions}, series = {Structural Engineering and Mechanics}, journal = {Structural Engineering and Mechanics}, pages = {315 -- 332}, abstract = {A moving least squares weighting function for the element-free Galerkin method which almost fulfills essential boundary conditions}, subject = {Angewandte Mathematik}, language = {en} } @article{Most, author = {Most, Thomas}, title = {A natural neighbour-based moving least-squares approach for the element-free Galerkin method}, series = {International Journal for Numerical Methods in Engineering}, journal = {International Journal for Numerical Methods in Engineering}, pages = {224 -- 252}, abstract = {A natural neighbour-based moving least-squares approach for the element-free Galerkin method}, subject = {Angewandte Mathematik}, language = {en} } @article{NguyenXuanRabczukNguyenThanhetal., author = {Nguyen-Xuan, Hung and Rabczuk, Timon and Nguyen-Thanh, Nhon and Nguyen-Thoi, T. and Bordas, St{\´e}phane Pierre Alain}, title = {A node-based smoothed finite element method (NS-FEM) for analysis of Reissner-Mindlin plates}, series = {Computational Mechanics}, journal = {Computational Mechanics}, pages = {679 -- 701}, abstract = {A node-based smoothed finite element method (NS-FEM) for analysis of Reissner-Mindlin plates}, 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} } @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{KerfridenGouryRabczuketal., author = {Kerfriden, Pierre and Goury, O. and Rabczuk, Timon and Bordas, St{\´e}phane Pierre Alain}, title = {A partitioned model order reduction approach to rationalise computational expenses in nonlinear fracture mechanics}, series = {Computer Methods in Applied Mechanics and Engineering}, journal = {Computer Methods in Applied Mechanics and Engineering}, pages = {169 -- 188}, abstract = {A partitioned model order reduction approach to rationalise computational expenses in nonlinear fracture mechanics}, subject = {Angewandte Mathematik}, language = {en} } @article{DoeringHoffmeyerSeegeretal., author = {D{\"o}ring, R. and Hoffmeyer, J. and Seeger, T. and Vormwald, Michael}, title = {A plasticity model for calculating stress-strain sequences under multiaxial nonproportional cyclic loading}, series = {Computational Materials Science}, journal = {Computational Materials Science}, pages = {587 -- 596}, abstract = {A plasticity model for calculating stress-strain sequences under multiaxial nonproportional cyclic loading}, 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{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{TalebiZiSilanietal., author = {Talebi, Hossein and Zi, Goangseup and Silani, Mohammad and Samaniego, Esteban and Rabczuk, Timon}, title = {A simple circular cell method for multilevel finite element analysis}, series = {Journal of Applied Mathematics}, journal = {Journal of Applied Mathematics}, doi = {10.1155/2012/526846}, abstract = {A simple multiscale analysis framework for heterogeneous solids based on a computational homogenization technique is presented. The macroscopic strain is linked kinematically to the boundary displacement of a circular or spherical representative volume which contains the microscopic information of the material. The macroscopic stress is obtained from the energy principle between the macroscopic scale and the microscopic scale. This new method is applied to several standard examples to show its accuracy and consistency of the method proposed.}, subject = {Angewandte Mathematik}, language = {en} } @article{NguyenThanhThaiHoangNguyenXuanetal., author = {Nguyen-Thanh, Nhon and Thai-Hoang, C. and Nguyen-Xuan, Hung and Rabczuk, Timon}, title = {A smoothed finite element method for the static and free vibration analysis of shells}, series = {Journal of Civil Engineering and Architecture}, journal = {Journal of Civil Engineering and Architecture}, pages = {13 -- 25}, abstract = {A smoothed finite element method for the static and free vibration analysis of shells}, 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{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{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{JiangParkGalletal., author = {Jiang, Jin-Wu and Park, Harold S. and Gall, K. and Leach, A. and Rabczuk, Timon}, title = {A Surface Stacking Fault Energy Approach to Predicting Defect Nucleation in Surface-Dominated Nanostructures}, series = {Journal of the Mechanics and Physics of Solids}, journal = {Journal of the Mechanics and Physics of Solids}, abstract = {A Surface Stacking Fault Energy Approach to Predicting Defect Nucleation in Surface-Dominated Nanostructures}, subject = {Angewandte Mathematik}, 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{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} } @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{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} } @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{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} } @phdthesis{Budarapu, author = {Budarapu, Pattabhi Ramaiah}, title = {Adaptive multiscale methods for fracture}, doi = {10.25643/bauhaus-universitaet.2391}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20150507-23918}, school = {Bauhaus-Universit{\"a}t Weimar}, abstract = {One major research focus in the Material Science and Engineering Community in the past decade has been to obtain a more fundamental understanding on the phenomenon 'material failure'. Such an understanding is critical for engineers and scientists developing new materials with higher strength and toughness, developing robust designs against failure, or for those concerned with an accurate estimate of a component's design life. Defects like cracks and dislocations evolve at nano scales and influence the macroscopic properties such as strength, toughness and ductility of a material. In engineering applications, the global response of the system is often governed by the behaviour at the smaller length scales. Hence, the sub-scale behaviour must be computed accurately for good predictions of the full scale behaviour. Molecular Dynamics (MD) simulations promise to reveal the fundamental mechanics of material failure by modeling the atom to atom interactions. Since the atomistic dimensions are of the order of Angstroms ( A), approximately 85 billion atoms are required to model a 1 micro- m^3 volume of Copper. Therefore, pure atomistic models are prohibitively expensive with everyday engineering computations involving macroscopic cracks and shear bands, which are much larger than the atomistic length and time scales. To reduce the computational effort, multiscale methods are required, which are able to couple a continuum description of the structure with an atomistic description. In such paradigms, cracks and dislocations are explicitly modeled at the atomistic scale, whilst a self-consistent continuum model elsewhere. Many multiscale methods for fracture are developed for "fictitious" materials based on "simple" potentials such as the Lennard-Jones potential. Moreover, multiscale methods for evolving cracks are rare. Efficient methods to coarse grain the fine scale defects are missing. However, the existing multiscale methods for fracture do not adaptively adjust the fine scale domain as the crack propagates. Most methods, therefore only "enlarge" the fine scale domain and therefore drastically increase computational cost. Adaptive adjustment requires the fine scale domain to be refined and coarsened. One of the major difficulties in multiscale methods for fracture is to up-scale fracture related material information from the fine scale to the coarse scale, in particular for complex crack problems. Most of the existing approaches therefore were applied to examples with comparatively few macroscopic cracks. Key contributions The bridging scale method is enhanced using the phantom node method so that cracks can be modeled at the coarse scale. To ensure self-consistency in the bulk, a virtual atom cluster is devised providing the response of the intact material at the coarse scale. A molecular statics model is employed in the fine scale where crack propagation is modeled by naturally breaking the bonds. The fine scale and coarse scale models are coupled by enforcing the displacement boundary conditions on the ghost atoms. An energy criterion is used to detect the crack tip location. Adaptive refinement and coarsening schemes are developed and implemented during the crack propagation. The results were observed to be in excellent agreement with the pure atomistic simulations. The developed multiscale method is one of the first adaptive multiscale method for fracture. A robust and simple three dimensional coarse graining technique to convert a given atomistic region into an equivalent coarse region, in the context of multiscale fracture has been developed. The developed method is the first of its kind. The developed coarse graining technique can be applied to identify and upscale the defects like: cracks, dislocations and shear bands. The current method has been applied to estimate the equivalent coarse scale models of several complex fracture patterns arrived from the pure atomistic simulations. The upscaled fracture pattern agree well with the actual fracture pattern. The error in the potential energy of the pure atomistic and the coarse grained model was observed to be acceptable. A first novel meshless adaptive multiscale method for fracture has been developed. The phantom node method is replaced by a meshless differential reproducing kernel particle method. The differential reproducing kernel particle method is comparatively more expensive but allows for a more "natural" coupling between the two scales due to the meshless interpolation functions. The higher order continuity is also beneficial. The centro symmetry parameter is used to detect the crack tip location. The developed multiscale method is employed to study the complex crack propagation. Results based on the meshless adaptive multiscale method were observed to be in excellent agreement with the pure atomistic simulations. The developed multiscale methods are applied to study the fracture in practical materials like Graphene and Graphene on Silicon surface. The bond stretching and the bond reorientation were observed to be the net mechanisms of the crack growth in Graphene. The influence of time step on the crack propagation was studied using two different time steps. Pure atomistic simulations of fracture in Graphene on Silicon surface are presented. Details of the three dimensional multiscale method to study the fracture in Graphene on Silicon surface are discussed.}, subject = {Material}, language = {en} } @article{BudarapuGracieBordasetal., author = {Budarapu, Pattabhi Ramaiah and Gracie, Robert and Bordas, St{\´e}phane Pierre Alain and Rabczuk, Timon}, title = {An adaptive multiscale method for quasi-static crack growth}, series = {Computational Mechanics}, journal = {Computational Mechanics}, doi = {10.1007/s00466-013-0952-6}, pages = {1129 -- 1148}, abstract = {This paper proposes an adaptive atomistic- continuum numerical method for quasi-static crack growth. The phantom node method is used to model the crack in the continuum region and a molecular statics model is used near the crack tip. To ensure self-consistency in the bulk, a virtual atom cluster is used to model the material of the coarse scale. The coupling between the coarse scale and fine scale is realized through ghost atoms. The ghost atom positions are interpolated from the coarse scale solution and enforced as boundary conditions on the fine scale. The fine scale region is adaptively enlarged as the crack propagates and the region behind the crack tip is adaptively coarsened. An energy criterion is used to detect the crack tip location. The triangular lattice in the fine scale region corresponds to the lattice structure of the (111) plane of an FCC crystal. The Lennard-Jones potential is used to model the atom-atom interactions. The method is implemented in two dimensions. The results are compared to pure atomistic simulations; they show excellent agreement.}, subject = {Angewandte Mathematik}, language = {en} } @article{NguyenXuanLiuBordasetal., author = {Nguyen-Xuan, Hung and Liu, G.R. and Bordas, St{\´e}phane Pierre Alain and Natarajan, S. and Rabczuk, Timon}, title = {An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order}, series = {Computer Methods in Applied Mechanics and Engineering}, journal = {Computer Methods in Applied Mechanics and Engineering}, pages = {252 -- 273}, abstract = {An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order}, subject = {Angewandte Mathematik}, language = {en} } @article{NguyenThanhMuthuZhuangetal., author = {Nguyen-Thanh, Nhon and Muthu, Jacob and Zhuang, Xiaoying and Rabczuk, Timon}, title = {An adaptive three-dimensional RHT-splines formulation in linear elasto-statics and elasto-dynamics}, series = {Computational Mechanics}, journal = {Computational Mechanics}, pages = {369 -- 385}, abstract = {An adaptive three-dimensional RHT-splines formulation in linear elasto-statics and elasto-dynamics}, subject = {Angewandte Mathematik}, language = {en} } @article{NguyenThanhRabczukNguyenXuanetal., author = {Nguyen-Thanh, Nhon and Rabczuk, Timon and Nguyen-Xuan, Hung and Bordas, St{\´e}phane Pierre Alain}, title = {An alternative alpha finite element method (A?FEM) free and forced vibration analysis of solids using triangular meshes}, series = {Journal of Computational and Applied Mathematics}, journal = {Journal of Computational and Applied Mathematics}, pages = {2112 -- 2135}, abstract = {An alternative alpha finite element method (A?FEM) free and forced vibration analysis of solids using triangular meshes}, subject = {Angewandte Mathematik}, language = {en} } @article{NguyenThanhRabczukNguyenXuanetal., author = {Nguyen-Thanh, Nhon and Rabczuk, Timon and Nguyen-Xuan, Hung and Bordas, St{\´e}phane Pierre Alain}, title = {An alternative alpha finite element method with stabilized discrete shear gap technique for analysis of Mindlin-Reissner plates}, series = {Finite Elements in Analysis \& Design}, journal = {Finite Elements in Analysis \& Design}, pages = {519 -- 535}, abstract = {An alternative alpha finite element method with stabilized discrete shear gap technique for analysis of Mindlin-Reissner plates}, subject = {Angewandte Mathematik}, language = {en} } @article{AreiasPintodaCostaRabczuketal., author = {Areias, Pedro and Pinto da Costa, A. and Rabczuk, Timon and Queiros de Melo, F. J. M. and Dias-da-Costa, D.}, title = {An alternative formulation for quasi-static frictional and cohesive contact problems}, series = {Computational Mechanics}, journal = {Computational Mechanics}, pages = {807 -- 824}, abstract = {An alternative formulation for quasi-static frictional and cohesive contact problems}, subject = {Angewandte Mathematik}, language = {en} } @article{ZhaoGuoRabczuk, author = {Zhao, Jun-Hua and Guo, Wanlin and Rabczuk, Timon}, title = {An analytical molecular mechanics model for the elastic properties of crystalline polyethylene}, series = {Journal of Applied Physics}, journal = {Journal of Applied Physics}, doi = {10.1063/1.4745035}, abstract = {We present an analytical model to relate the elastic properties of crystalline polyethylene based on a molecular mechanics approach. Along the polymer chains direction, the united-atom (UA) CH2-CH2 bond stretching, angle bending potentials are replaced with equivalent Euler-Bernoulli beams. Between any two polymer chains, the explicit formulae are derived for the van der Waals interaction represented by the linear springs of different stiffness. Then, the nine independent elastic constants are evaluated systematically using the formulae. The analytical model is finally validated by present united-atom molecular dynamics (MD) simulations and against available all-atom molecular dynamics results in the literature. The established analytical model provides an efficient route for mechanical characterization of crystalline polymers and related materials.}, subject = {Angewandte Mathematik}, language = {en} } @article{ZhangZhaoJiaetal., author = {Zhang, Yancheng and Zhao, Jun-Hua and Jia, Yue and Mabrouki, Tarek and Gong, Yadong and Wei, Ning and Rabczuk, Timon}, title = {An analytical solution on the interface debonding for large diameter carbon nanotube-reinforced composite with functionally graded variation interphase}, series = {Composite Structures}, journal = {Composite Structures}, pages = {261 -- 269}, abstract = {An analytical solution on the interface debonding for large diameter carbon nanotube-reinforced composite with functionally graded variation interphase}, subject = {Angewandte Mathematik}, language = {en} } @article{Zabel, author = {Zabel, Volkmar}, title = {An application of discrete wavelet analysis and connection coefficients to parametric system identification}, series = {Structural Health Monitoring}, journal = {Structural Health Monitoring}, pages = {5 -- 18}, abstract = {An application of discrete wavelet analysis and connection coefficients to parametric system identification}, subject = {Angewandte Mathematik}, 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{BrehmZabelBucher, author = {Brehm, Maik and Zabel, Volkmar and Bucher, Christian}, title = {An automatic mode pairing strategy using an enhanced modal assurance citerion based on modal strain energies}, series = {Journal of Sound and Vibration}, journal = {Journal of Sound and Vibration}, doi = {10.1016/j.jsv.2010.07.006}, pages = {5375 -- 5392}, abstract = {In the context of finite element model updating using output-only vibration test data, natural frequencies and mode shapes are used as validation criteria. Consequently, the correct pairing of experimentally obtained and numerically derived natural frequencies and mode shapes is important. In many cases, only limited spatial information is available and noise is present in the measurements. Therefore, the automatic selection of the most likely numerical mode shape corresponding to a particular experimentally identified mode shape can be a difficult task. The most common criterion for indicating corresponding mode shapes is the modal assurance criterion. Unfortunately, this criterion fails in certain cases and is not reliable for automatic approaches. In this paper, the purely mathematical modal assurance criterion will be enhanced by additional physical information from the numerical model in terms of modal strain energies. A numerical example and a benchmark study with experimental data are presented to show the advantages of the proposed energy-based criterion in comparison to the traditional modal assurance criterion.}, 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{NguyenThanhValizadehNguyenetal., author = {Nguyen-Thanh, Nhon and Valizadeh, Navid and Nguyen, Manh Hung and Nguyen-Xuan, Hung and Zhuang, Xiaoying and Areias, Pedro and Zi, Goangseup and Bazilevs, Yuri and De Lorenzis, Laura and Rabczuk, Timon}, title = {An extended isogeometric thin shell analysis based on Kirchhoff-Love theory}, series = {Computer Methods in Applied Mechanics and Engineering}, journal = {Computer Methods in Applied Mechanics and Engineering}, pages = {265 -- 291}, abstract = {An extended isogeometric thin shell analysis based on Kirchho_-Love theory}, subject = {Angewandte Mathematik}, language = {en} } @article{SimpsonBordasTrevelyanetal., author = {Simpson, R. and Bordas, St{\´e}phane Pierre Alain and Trevelyan, J. and Kerfriden, Pierre and Rabczuk, Timon}, title = {An Isogeometric Boundary Element Method for elastostatic analysis}, series = {Computer Methods in Applied Mechanics and Engineering}, journal = {Computer Methods in Applied Mechanics and Engineering}, doi = {10.1016/j.cma.2011.08.008}, abstract = {The concept of isogeometric analysis, where functions that are used to describe geometry in CAD software are used to approximate the unknown fields in numerical simulations, has received great attention in recent years. The method has the potential to have profound impact on engineering design, since the task of meshing, which in some cases can add significant overhead, has been circumvented. Much of the research effort has been focused on finite element implementations of the isogeometric concept, but at present, little has been seen on the application to the Boundary Element Method. The current paper proposes an Isogeometric Boundary Element Method (BEM), which we term IGABEM, applied to two-dimensional elastostatic problems using Non-Uniform Rational B-Splines (NURBS). We find it is a natural fit with the isogeometric concept since both the NURBS approximation and BEM deal with quantities entirely on the boundary. The method is verified against analytical solutions where it is seen that superior accuracies are achieved over a conventional quadratic isoparametric BEM implementation.}, 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{RabizadehSaboorBagherzadehRabczuk, author = {Rabizadeh, Ehsan and Saboor Bagherzadeh, Amir and Rabczuk, Timon}, title = {Application of goal-oriented error estimation and adaptive mesh refinement on thermo-mechanical multifield problems}, series = {Computational Materials Science}, journal = {Computational Materials Science}, pages = {27 -- 44}, abstract = {Application of goal-oriented error estimation and adaptive mesh re_nement on thermo-mechanical multi_eld problems}, subject = {Angewandte Mathematik}, language = {en} } @article{AreiasRabczukDiasdaCosta, author = {Areias, Pedro and Rabczuk, Timon and Dias-da-Costa, D.}, title = {Assumed-metric spherically-interpolated quadrilateral shell element}, series = {Finite Elements in Analysis and Design}, journal = {Finite Elements in Analysis and Design}, pages = {53 -- 67}, abstract = {Assumed-metric spherically-interpolated quadrilateral shell element}, subject = {Angewandte Mathematik}, language = {en} } @article{AreiasRabczukDiasdaCosta, author = {Areias, Pedro and Rabczuk, Timon and Dias-da-Costa, D.}, title = {Asymmetric Shell Elements Based on a Corrected Updated-Lagrangian Approach}, series = {CMES: Computer Modeling in Engineering and Sciences}, journal = {CMES: Computer Modeling in Engineering and Sciences}, abstract = {Asymmetric Shell Elements Based on a Corrected Updated-Lagrangian Approach}, subject = {Angewandte Mathematik}, language = {en} } @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{ZhaoLuRabczuk, author = {Zhao, Jun-Hua and Lu, Lixin and Rabczuk, Timon}, title = {Binding energy and mechanical stability of single- and multi-walled carbon nanotube serpentines}, series = {The Journal of Chemical Physics}, journal = {The Journal of Chemical Physics}, doi = {10.1063/1.4878115}, abstract = {Binding energy and mechanical stability of single- and multi-walled carbon nanotube serpentines}, 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{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{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{ReichertOlneyLahmer, author = {Reichert, Ina and Olney, Peter and Lahmer, Tom}, title = {Combined approach for optimal sensor placement and experimental verification in the context of tower-like structures}, series = {Journal of Civil Structural Health Monitoring}, volume = {2021}, journal = {Journal of Civil Structural Health Monitoring}, number = {volume 11}, publisher = {Heidelberg}, address = {Springer}, doi = {10.1007/s13349-020-00448-7}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20210804-44701}, pages = {223 -- 234}, abstract = {When it comes to monitoring of huge structures, main issues are limited time, high costs and how to deal with the big amount of data. In order to reduce and manage them, respectively, methods from the field of optimal design of experiments are useful and supportive. Having optimal experimental designs at hand before conducting any measurements is leading to a highly informative measurement concept, where the sensor positions are optimized according to minimal errors in the structures' models. For the reduction of computational time a combined approach using Fisher Information Matrix and mean-squared error in a two-step procedure is proposed under the consideration of different error types. The error descriptions contain random/aleatoric and systematic/epistemic portions. Applying this combined approach on a finite element model using artificial acceleration time measurement data with artificially added errors leads to the optimized sensor positions. These findings are compared to results from laboratory experiments on the modeled structure, which is a tower-like structure represented by a hollow pipe as the cantilever beam. Conclusively, the combined approach is leading to a sound experimental design that leads to a good estimate of the structure's behavior and model parameters without the need of preliminary measurements for model updating.}, subject = {Strukturmechanik}, language = {en} } @article{NguyenXuanRabczukNguyenThoietal., author = {Nguyen-Xuan, Hung and Rabczuk, Timon and Nguyen-Thoi, T. and Tran, T. and Nguyen-Thanh, Nhon}, title = {Computation of limit and shakedown loads using a node-based smoothed finite element method}, series = {International Journal for Numerical Methods in Engineering}, journal = {International Journal for Numerical Methods in Engineering}, doi = {10.1002/nme.3317}, pages = {287 -- 310}, abstract = {This paper presents a novel numerical procedure for computing limit and shakedown loads of structures using a node-based smoothed FEM in combination with a primal-dual algorithm. An associated primal-dual form based on the von Mises yield criterion is adopted. The primal-dual algorithm together with a Newton-like iteration are then used to solve this associated primal-dual form to determine simultaneously both approximate upper and quasi-lower bounds of the plastic collapse limit and the shakedown limit. The present formulation uses only linear approximations and its implementation into finite element programs is quite simple. Several numerical examples are given to show the reliability, accuracy, and generality of the present formulation compared with other available methods.}, 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{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{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{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{HiguchiMacke, author = {Higuchi, Shoko and Macke, M.}, title = {Cost-benefit analysis for the optimal rehabilitation of deteriorating structures}, series = {Structural Safety}, journal = {Structural Safety}, pages = {291 -- 306}, abstract = {Cost-benefit analysis for the optimal rehabilitation of deteriorating structures}, 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{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{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{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} } @article{UngerKoenke, author = {Unger, J{\"o}rg F. and K{\"o}nke, Carsten}, title = {Coupling of scales in a multiscale simulation using neural networks}, series = {Computers \& Structures}, journal = {Computers \& Structures}, abstract = {Coupling of scales in a multiscale simulation using neural networks}, subject = {Angewandte Mathematik}, language = {en} } @article{Lahmer, author = {Lahmer, Tom}, title = {Crack identification in hydro-mechanical systems with applications to gravity water dams}, series = {Inverse Problems in Science and Engineering}, journal = {Inverse Problems in Science and Engineering}, pages = {1083 -- 1101}, abstract = {Crack identification in hydro-mechanical systems with applications to gravity water dams}, 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{AlaladeNguyenTuanWuttkeetal., author = {Alalade, Muyiwa and Nguyen-Tuan, Long and Wuttke, Frank and Lahmer, Tom}, title = {Damage identification in gravity dams using dynamic coupled hydro-mechanical XFEM}, series = {International Journal of Mechanics and Materials in Design}, journal = {International Journal of Mechanics and Materials in Design}, doi = {10.25643/bauhaus-universitaet.3596}, pages = {1 -- 19}, abstract = {Damage identification in gravity dams using dynamic coupled hydro-mechanical XFEM.}, subject = {Angewandte Mathematik}, language = {en} } @phdthesis{Vollmering, author = {Vollmering, Max}, title = {Damage Localization of Mechanical Structures by Subspace Identification and Krein Space Based H-infinity Estimation}, doi = {10.25643/bauhaus-universitaet.3772}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20180730-37728}, school = {Bauhaus-Universit{\"a}t Weimar}, pages = {205}, abstract = {This dissertation is devoted to the theoretical development and experimental laboratory verification of a new damage localization method: The state projection estimation error (SP2E). This method is based on the subspace identification of mechanical structures, Krein space based H-infinity estimation and oblique projections. To explain method SP2E, several theories are discussed and laboratory experiments have been conducted and analysed. A fundamental approach of structural dynamics is outlined first by explaining mechanical systems based on first principles. Following that, a fundamentally different approach, subspace identification, is comprehensively explained. While both theories, first principle and subspace identification based mechanical systems, may be seen as widespread methods, barely known and new techniques follow up. Therefore, the indefinite quadratic estimation theory is explained. Based on a Popov function approach, this leads to the Krein space based H-infinity theory. Subsequently, a new method for damage identification, namely SP2E, is proposed. Here, the introduction of a difference process, the analysis by its average process power and the application of oblique projections is discussed in depth. Finally, the new method is verified in laboratory experiments. Therefore, the identification of a laboratory structure at Leipzig University of Applied Sciences is elaborated. Then structural alterations are experimentally applied, which were localized by SP2E afterwards. In the end four experimental sensitivity studies are shown and discussed. For each measurement series the structural alteration was increased, which was successfully tracked by SP2E. The experimental results are plausible and in accordance with the developed theories. By repeating these experiments, the applicability of SP2E for damage localization is experimentally proven.}, subject = {Strukturmechanik}, language = {en} } @article{ZabelBrehm, author = {Zabel, Volkmar and Brehm, Maik}, title = {Das dynamische Verhalten von Eisenbahnbr{\"u}cken mit kurzer Spannweite - numerische und experimentelle Untersuchungen}, series = {Bauingenieur, D-A-CH-Mitteilungsblatt}, journal = {Bauingenieur, D-A-CH-Mitteilungsblatt}, abstract = {Das dynamische Verhalten von Eisenbahnbr{\"u}cken mit kurzer Spannweite - numerische und experimentelle Untersuchungen}, subject = {Angewandte Mathematik}, language = {de} } @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{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{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{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{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 = {Computer Methods in Applied Mechanics and Engineering}, journal = {Computer Methods in Applied Mechanics and Engineering}, pages = {98 -- 112}, abstract = {Detection of multiple flaws in piezoelectric structures using XFEM and level sets}, subject = {Angewandte Mathematik}, language = {en} } @article{KhosravaniRabczuk, author = {Khosravani, M.R. and Rabczuk, Timon}, title = {Determiniation of shear modulus for double and multi-walled Carbon Nanotubes}, series = {Mechanics of Composite Materials}, journal = {Mechanics of Composite Materials}, abstract = {Determiniation of shear modulus for double and multi-walled Carbon Nanotubes}, subject = {Angewandte Mathematik}, language = {en} } @article{BudarapuNarayanaRammohanetal., author = {Budarapu, Pattabhi Ramaiah and Narayana, T.S.S. and Rammohan, B. and Rabczuk, Timon}, title = {Directionality of sound radiation from rectangular panels}, series = {Applied Acoustics}, journal = {Applied Acoustics}, pages = {128 -- 140}, abstract = {Directionality of sound radiation from rectangular panels}, subject = {Angewandte Mathematik}, language = {en} } @article{MostIshiiGengetal., author = {Most, Thomas and Ishii, H. and Geng, X. and Bolzern, P. and Colaneri, P. and De Nicolao, G.}, title = {Discussion on Almost sure stability of stochastic linear systems with ergodic parameters}, series = {European Journal of Control}, journal = {European Journal of Control}, pages = {124 -- 130}, abstract = {Discussion on Almost sure stability of stochastic linear systems with ergodic parameters}, 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} } @article{MostBucherSchorling, author = {Most, Thomas and Bucher, Christian and Schorling, York}, title = {Dynamic stability analysis of non-linear structures with geometrical imperfections under random loading}, series = {Journal of Sound and Vibration}, journal = {Journal of Sound and Vibration}, pages = {381 -- 400}, abstract = {Dynamic stability analysis of non-linear structures with geometrical imperfections under random loading}, subject = {Angewandte Mathematik}, language = {en} } @article{ZhangZhaoWeietal., author = {Zhang, Yancheng and Zhao, Jiyun and Wei, Ning and Jiang, Jin-Wu and Rabczuk, Timon}, title = {Effects of the dispersion of polymer wrapped two neighbouring single walled carbon nanotubes (SWNTs) on nanoengineering load transfer}, series = {Composites Part B: Engineering}, journal = {Composites Part B: Engineering}, pages = {1714 -- 1721}, abstract = {Effects of the dispersion of polymer wrapped two neighbouring single walled carbon nanotubes (SWNTs) on nanoengineering load transfer}, subject = {Angewandte Mathematik}, language = {en} } @article{BudarapuGracieYangetal., author = {Budarapu, Pattabhi Ramaiah and Gracie, Robert and Yang, Shih-Wei and Zhuang, Xiaoying and Rabczuk, Timon}, title = {Efficient Coarse Graining in Multiscale Modeling of Fracture}, series = {Theoretical and Applied Fracture Mechanics}, journal = {Theoretical and Applied Fracture Mechanics}, pages = {126 -- 143}, abstract = {Efficient Coarse Graining in Multiscale Modeling of Fracture}, subject = {Angewandte Mathematik}, language = {en} } @article{MostBucher, author = {Most, Thomas and Bucher, Christian}, title = {Energy-based simulation of concrete cracking using an improved mixed-mode cohesive crack model within a meshless discretization}, series = {International Journal for Numerical and Analytical Methods in Geomechanics}, journal = {International Journal for Numerical and Analytical Methods in Geomechanics}, pages = {285 -- 305}, abstract = {Energy-based simulation of concrete cracking using an improved mixed-mode cohesive crack model within a meshless discretization}, 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{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{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{KeitelKarakiLahmeretal., author = {Keitel, Holger and Karaki, Ghada and Lahmer, Tom and Nikulla, Susanne and Zabel, Volkmar}, title = {Evaluation of coupled partial models in structural engineering using graph theory and sensitivity analysis}, series = {Engineering structures}, journal = {Engineering structures}, pages = {3726 -- 3736}, abstract = {Evaluation of coupled partial models in structural engineering using graph theory and sensitivity analysis}, subject = {Angewandte Mathematik}, language = {en} } @article{SavaidisSavaidisSchliebneretal., author = {Savaidis, G. and Savaidis, A. and Schliebner, R. and Vormwald, Michael}, title = {Evaluation of fatigue of fillet welded joints in vehicle components under multiaxial service loads}, series = {European Structural Integrity Society}, journal = {European Structural Integrity Society}, pages = {23 -- 42}, abstract = {Evaluation of fatigue of fillet welded joints in vehicle components under multiaxial service loads}, subject = {Angewandte Mathematik}, language = {en} } @article{ChenNguyenThanhNguyenXuanetal., author = {Chen, Lei and Nguyen-Thanh, Nhon and Nguyen-Xuan, Hung and Rabczuk, Timon and Bordas, St{\´e}phane Pierre Alain and Limbert, Georges}, title = {Explicit finite deformation analysis of isogeometric membranes}, series = {Computer Methods in Applied Mechanics and Engineering}, journal = {Computer Methods in Applied Mechanics and Engineering}, pages = {104 -- 130}, abstract = {Explicit finite deformation analysis of isogeometric membranes}, 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{ChenRabczukLiuetal., author = {Chen, Lei and Rabczuk, Timon and Liu, G.R. and Zeng, K.Y. and Kerfriden, Pierre and Bordas, St{\´e}phane Pierre Alain}, title = {Extended finite element method with edge-based strain smoothing (ESm-XFEM) for linear elastic crack growth}, series = {Computer Methods in Applied Mechanics and Engineering}, journal = {Computer Methods in Applied Mechanics and Engineering}, doi = {10.1016/j.cma.2011.08.013}, abstract = {This paper presents a strain smoothing procedure for the extended finite element method (XFEM). The resulting "edge-based" smoothed extended finite element method (ESm-XFEM) is tailored to linear elastic fracture mechanics and, in this context, to outperform the standard XFEM. In the XFEM, the displacement-based approximation is enriched by the Heaviside and asymptotic crack tip functions using the framework of partition of unity. This eliminates the need for the mesh alignment with the crack and re-meshing, as the crack evolves. Edge-based smoothing (ES) relies on a generalized smoothing operation over smoothing domains associated with edges of simplex meshes, and produces a softening effect leading to a close-to-exact stiffness, "super-convergence" and "ultra-accurate" solutions. The present method takes advantage of both the ES-FEM and the XFEM. Thanks to the use of strain smoothing, the subdivision of elements intersected by discontinuities and of integrating the (singular) derivatives of the approximation functions is suppressed via transforming interior integration into boundary integration. Numerical examples show that the proposed method improves significantly the accuracy of stress intensity factors and achieves a near optimal convergence rate in the energy norm even without geometrical enrichment or blending correction.}, subject = {Angewandte Mathematik}, language = {en} } @article{JiaAnitescuGhorashietal., author = {Jia, Yue and Anitescu, Cosmin and Ghorashi, Seyed Shahram and Rabczuk, Timon and Dias-da-Costa, D.}, title = {Extended Isogeometric Analysis for Material Interface Problems}, series = {Journal of Applied Mathematics}, journal = {Journal of Applied Mathematics}, abstract = {Extended Isogeometric Analysis for Material Interface Problems}, subject = {Angewandte Mathematik}, language = {en} } @article{LahmerKaltenbacherKaltenbacheretal., author = {Lahmer, Tom and Kaltenbacher, Manfred and Kaltenbacher, Barbara and Lerch, Reinhard and Leder, Erich}, title = {Fem-based determination of real and complex elastic, dielectric, and piezoelectric moduli in piezoceramic materials}, series = {IEEE transactions on ultrasonics, ferroelectrics, and frequency control}, journal = {IEEE transactions on ultrasonics, ferroelectrics, and frequency control}, doi = {10.25643/bauhaus-universitaet.3594}, abstract = {Fem-based determination of real and complex elastic, dielectric, and piezoelectric moduli in piezoceramic materials.}, subject = {Angewandte Mathematik}, language = {en} } @article{AreiasRabczukCamanho, author = {Areias, Pedro and Rabczuk, Timon and Camanho, P.P.}, title = {Finite strain fracture of 2D problems with injected anisotropic softening elements}, series = {Theoretical and Applied Fracture Mechanics}, journal = {Theoretical and Applied Fracture Mechanics}, abstract = {Finite strain fracture of 2D problems with injected anisotropic softening elements}, 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{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{NguyenThoiPhungVanRabczuketal., author = {Nguyen-Thoi, T. and Phung-Van, P. and Rabczuk, Timon and Nguyen-Xuan, Hung and Le-Van, C.}, title = {Free and forced vibration analysis using the n-sided polygonal cell-based smoothed finite element method (nCS-FEM)}, series = {International Journal of Computational Methods}, journal = {International Journal of Computational Methods}, abstract = {Free and forced vibration analysis using the n-sided polygonal cell-based smoothed finite element method (nCS-FEM)}, subject = {Angewandte Mathematik}, language = {en} } @article{NguyenThoiRabczukLamPhatetal., author = {Nguyen-Thoi, T. and Rabczuk, Timon and Lam-Phat, T. and Ho-Huu, V. and Phung-Van, P.}, title = {Free vibration analysis of cracked Mindlin plate using an extended cell-based smoothed discrete shear gap method (XCS-DSG3)}, series = {Theoretical and Applied Fracture Mechanics}, journal = {Theoretical and Applied Fracture Mechanics}, abstract = {Free vibration analysis of cracked Mindlin plate using an extended cell-based smoothed discrete shear gap method (XCS-DSG3)}, subject = {Angewandte Mathematik}, 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{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{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} }