TY - JOUR
A1 - Yang, Shih-Wei
A1 - Budarapu, Pattabhi Ramaiah
A1 - Mahapatra, D.R.
A1 - Bordas, Stéphane Pierre Alain
A1 - Zi, Goangseup
A1 - Rabczuk, Timon
T1 - A Meshless Adaptive Multiscale Method for Fracture
JF - Computational Materials Science
N2 - A Meshless Adaptive Multiscale Method for Fracture
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2015
SP - 382
EP - 395
ER -
TY - JOUR
A1 - Jia, Yue
A1 - Zhang, Yongjie
A1 - Rabczuk, Timon
T1 - A Novel Dynamic Multilevel Technique for Image Registration
JF - Computers and Mathematics with Applications
N2 - A Novel Dynamic Multilevel Technique for Image Registration
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2015
ER -
TY - JOUR
A1 - Areias, Pedro
A1 - Rabczuk, Timon
A1 - Cesar de Sa, J.M.
A1 - Jorge, R.N.
T1 - A semi-implicit _nite strain shell algorithm using in-plane strains based on least-squares
JF - Computational Mechanics
N2 - A semi-implicit _nite strain shell algorithm using in-plane strains based on least-squares
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2015
ER -
TY - JOUR
A1 - Jiang, Jin-Wu
A1 - Rabczuk, Timon
A1 - Park, Harold S.
T1 - 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
JF - Nanoscale
N2 - 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.
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2015
U6 - http://dx.doi.org/10.1039/C4NR07341J
ER -
TY - JOUR
A1 - Silani, Mohammad
A1 - Talebi, Hossein
A1 - Ziaei-Rad, S.
A1 - Hamouda, A.M.S.
A1 - Zi, Goangseup
A1 - Rabczuk, Timon
T1 - A three dimensional Extended Arlequin Method for Dynamic Fracture
JF - Computational Materials Science
N2 - A three dimensional Extended Arlequin Method for Dynamic Fracture
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2015
SP - 425
EP - 431
ER -
TY - JOUR
A1 - Vu-Bac, N.
A1 - Silani, Mohammad
A1 - Lahmer, Tom
A1 - Zhuang, Xiaoying
A1 - Rabczuk, Timon
T1 - A unified framework for stochastic predictions of Young's modulus of clay/epoxy nanocomposites (PCNs)
JF - Computational Materials Science
N2 - A unified framework for stochastic predictions of Young's modulus of clay/epoxy nanocomposites (PCNs)
KW - Angewandte Mathematik
KW - Stochastik
KW - Strukturmechanik
Y1 - 2015
SP - 520
EP - 535
ER -
TY - JOUR
A1 - Msekh, Mohammed Abdulrazzak
A1 - Sargado, M.
A1 - Jamshidian, M.
A1 - Areias, Pedro
A1 - Rabczuk, Timon
T1 - ABAQUS implementation of phase_field model for brittle fracture
JF - Computational Materials Science
N2 - ABAQUS implementation of phase_field model for brittle fracture
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2015
SP - 472
EP - 484
ER -
TY - THES
A1 - Budarapu, Pattabhi Ramaiah
T1 - Adaptive multiscale methods for fracture
T1 - Adaptive Multiskalen-Methoden zur Modellierung von Materialversagen
N2 - 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.
T3 - ISM-Bericht // Institut für Strukturmechanik, Bauhaus-Universität Weimar - 2015,1
KW - Material
KW - Strukturmechanik
KW - Materialversagen
KW - material failure
Y1 - 2015
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20150507-23918
ER -
TY - JOUR
A1 - Nguyen-Thanh, Nhon
A1 - Valizadeh, N.
A1 - Nguyen, Manh Hung
A1 - Nguyen-Xuan, Hung
A1 - Zhuang, Xiaoying
A1 - Areias, Pedro
A1 - Zi, Goangseup
A1 - Bazilevs, Yuri
A1 - De Lorenzis, Laura
A1 - Rabczuk, Timon
T1 - An extended isogeometric thin shell analysis based on Kirchhoff-Love theory
JF - Computer Methods in Applied Mechanics and Engineering
N2 - An extended isogeometric thin shell analysis based on Kirchho_-Love theory
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2015
SP - 265
EP - 291
ER -
TY - JOUR
A1 - Anitescu, C.
A1 - Jia, Yue
A1 - Zhang, Yongjie
A1 - Rabczuk, Timon
T1 - An isogeometric collocation method using superconvergent points
JF - Computer Methods in Applied Mechanics and Engineer-ing
N2 - An isogeometric collocation method using superconvergent points
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2015
SP - 1073
EP - 1097
ER -
TY - JOUR
A1 - Rabizadeh, E.
A1 - Saboor Bagherzadeh, Amir
A1 - Rabczuk, Timon
T1 - Application of goal-oriented error estimation and adaptive mesh refinement on thermo-mechanical multifield problems
JF - Computational Materials Science
N2 - Application of goal-oriented error estimation and adaptive mesh re_nement on thermo-mechanical multi_eld problems
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2015
SP - 27
EP - 44
ER -
TY - JOUR
A1 - Zhao, Jun-Hua
A1 - Jia, Yue
A1 - Wei, Ning
A1 - Rabczuk, Timon
T1 - Binding energy and mechanical stability of two parallel and crossing carbon nanotubes
JF - Journal of Applied Mechanics
N2 - Binding energy and mechanical stability of two parallel and crossing carbon nanotubes
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2015
ER -
TY - JOUR
A1 - Talebi, Hossein
A1 - Silani, Mohammad
A1 - Rabczuk, Timon
T1 - Concurrent Multiscale Modelling of Three Dimensional Crack and Dislocation Propagation
JF - Advances in Engineering Software
N2 - Concurrent Multiscale Modelling of Three Dimensional Crack and Dislocation Propagation
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2015
SP - 82
EP - 92
ER -
TY - JOUR
A1 - Zhao, Jun-Hua
A1 - Lu, Lixin
A1 - Zhang, Zhiliang
A1 - Guo, Wanlin
A1 - Rabczuk, Timon
T1 - Continuum modeling of the cohesive energy for the interfaces between _lms, spheres, coats and substrates
JF - Computational Materials Science
N2 - Continuum modeling of the cohesive energy for the interfaces between _lms, spheres, coats and substrates
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2015
SP - 432
EP - 438
ER -
TY - JOUR
A1 - Areias, Pedro
A1 - Rabczuk, Timon
A1 - Queiros de Melo, F. J. M.
A1 - Cesar de Sa, J.M.
T1 - Coulomb frictional contact by explicit projection in the cone for _nite displacement quasi-static problems
JF - Computational Mechanics
N2 - Coulomb frictional contact by explicit projection in the cone for _nite displacement quasi-static problems
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2015
SP - 57
EP - 72
ER -
TY - JOUR
A1 - Nanthakumar, S.S.
A1 - Lahmer, Tom
A1 - Zhuang, Xiaoying
A1 - Zi, Goangseup
A1 - Rabczuk, Timon
T1 - Detection of material interfaces using a regularized level set method in piezoelectric structures
JF - Inverse Problems in Science and Engineering
N2 - Detection of material interfaces using a regularized level set method in piezoelectric structures
KW - Angewandte Mathematik
KW - Stochastik
KW - Strukturmechanik
Y1 - 2015
ER -
TY - JOUR
A1 - Budarapu, Pattabhi Ramaiah
A1 - Narayana, T.S.S.
A1 - Rammohan, B.
A1 - Rabczuk, Timon
T1 - Directionality of sound radiation from rectangular panels
JF - Applied Acoustics
N2 - Directionality of sound radiation from rectangular panels
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2015
SP - 128
EP - 140
ER -
TY - JOUR
A1 - Areias, Pedro
A1 - Rabczuk, Timon
A1 - Cesar de Sa, J.M.
A1 - Garcao, J.E.
T1 - Finite strain quadrilateral shell using least-squares _t of relative Lagrangian in-plane strains
JF - Finite Elements in Analysis and Design
N2 - Finite strain quadrilateral shell using least-squares _t of relative Lagrangian in-plane strains
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2015
SP - 26
EP - 40
ER -
TY - JOUR
A1 - Ghasemi, Hamid
A1 - Kerfriden, Pierre
A1 - Bordas, Stéphane Pierre Alain
A1 - Muthu, Jacob
A1 - Zi, Goangseup
A1 - Rabczuk, Timon
T1 - Interfacial shear stress optimization in sandwich beams with polymeric core using nonuniform distribution of reinforcing ingredients
JF - Composite Structures
N2 - Interfacial shear stress optimization in sandwich beams with polymeric core using nonuniform distribution of reinforcing ingredients
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2015
SP - 221
EP - 230
ER -
TY - CHAP
ED - Gürlebeck, Klaus
ED - Lahmer, Tom
T1 - International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar
T1 - Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen : 20. bis 22.7. 2015, Bauhaus-Universität Weimar
T2 - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar
N2 - 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!
KW - Angewandte Informatik
KW - Angewandte Mathematik
KW - Computerunterstütztes Verfahren
KW - Building Information Modeling
KW - Optimization in engineering applications
KW - Data, information and knowledge modeling in civil engineering
KW - Function theoretic methods and PDE in engineering sciences
KW - Mathematical methods for (robotics and) computer vision
KW - Numerical modeling in engineering
Y1 - 2015
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20150828-24515
SN - 1611-4086
ER -
TY - JOUR
A1 - Thai, Chien H.
A1 - Nguyen-Xuan, Hung
A1 - Bordas, Stéphane Pierre Alain
A1 - Nguyen-Thanh, Nhon
A1 - Rabczuk, Timon
T1 - Isogeometric analysis of laminated composite plates using the higher-order shear deformation theory
JF - Mechanics of Advanced Materials and Structures
N2 - Isogeometric analysis of laminated composite plates using the higher-order shear deformation theory
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2015
SP - 451
EP - 469
ER -
TY - JOUR
A1 - Mortazavi, Bohayra
A1 - Cuniberti, G.
A1 - Rabczuk, Timon
T1 - Mechanical properties and thermal conductivity of graphitic carbon nitride: A molecular dynamics study
JF - Computational Materials Science
N2 - Mechanical properties and thermal conductivity of graphitic carbon nitride: A molecular dynamics study
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2015
SP - 285
EP - 289
ER -
TY - THES
A1 - Jia, Yue
T1 - Methods based on B-splines for model representation, numerical analysis and image registration
N2 - The thesis consists of inter-connected parts for modeling and analysis using newly developed isogeometric methods. The main parts are reproducing kernel triangular B-splines, extended isogeometric analysis for solving weakly discontinuous problems, collocation methods using superconvergent points, and B-spline basis in image registration applications.
Each topic is oriented towards application of isogeometric analysis basis functions to ease the process of integrating the modeling and analysis phases of simulation.
First, we develop reproducing a kernel triangular B-spline-based FEM for solving PDEs. We review the triangular B-splines and their properties. By definition, the triangular basis function is very flexible in modeling complicated domains. However, instability results when it is applied for analysis. We modify the triangular B-spline by a reproducing kernel technique, calculating a correction term for the triangular kernel function from the chosen surrounding basis. The improved triangular basis is capable to obtain the results with higher accuracy and almost optimal convergence rates.
Second, we propose an extended isogeometric analysis for dealing with weakly discontinuous problems such as material interfaces. The original IGA is combined with XFEM-like enrichments which are continuous functions themselves but with discontinuous derivatives. Consequently, the resulting solution space can approximate solutions with weak discontinuities. The method is also applied to curved material interfaces, where the inverse mapping and the curved triangular elements are considered.
Third, we develop an IGA collocation method using superconvergent points. The collocation methods are efficient because no numerical integration is needed. In particular when higher polynomial basis applied, the method has a lower computational cost than Galerkin methods. However, the positions of the collocation points are crucial for the accuracy of the method, as they affect the convergent rate significantly. The proposed IGA collocation method uses superconvergent points instead of the traditional Greville abscissae points. The numerical results show the proposed method can have better accuracy and optimal convergence rates, while the traditional IGA collocation has optimal convergence only for even polynomial degrees.
Lastly, we propose a novel dynamic multilevel technique for handling image registration. It is application of the B-spline functions in image processing. The procedure considered aims to align a target image from a reference image by a spatial transformation. The method starts with an energy function which is the same as a FEM-based image registration. However, we simplify the solving procedure, working on the energy function directly. We dynamically solve for control points which are coefficients of B-spline basis functions. The new approach is more simple and fast. Moreover, it is also enhanced by a multilevel technique in order to prevent instabilities. The numerical testing consists of two artificial images, four real bio-medical MRI brain and CT heart images, and they show our registration method is accurate, fast and efficient, especially for large deformation problems.
KW - Finite-Elemente-Methode
KW - isogeometric methods
Y1 - 2015
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20151210-24849
ER -
TY - JOUR
A1 - Kumar, S.
A1 - Singh, I.
A1 - Mishra, B.K.
A1 - Rabczuk, Timon
T1 - Modeling and Simulation of Kinked Cracks by Virtual Node XFEM
JF - Computer Methods in Applied Mechanics and Engineering
N2 - Modeling and Simulation of Kinked Cracks by Virtual Node XFEM
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2015
SP - 1425
EP - 1466
ER -
TY - JOUR
A1 - Mortazavi, Bohayra
A1 - Pereira, Luiz Felipe C.
A1 - Jiang, Jin-Wu
A1 - Rabczuk, Timon
T1 - Modelling heat conduction in polycrystalline hexagonal boron-nitride films
JF - Scientific Reports
N2 - We conducted extensive molecular dynamics simulations to investigate the thermal conductivity of polycrystalline hexagonal boron-nitride (h-BN) films. To this aim, we constructed large atomistic models of polycrystalline h-BN sheets with random and uniform grain configuration. By performing equilibrium molecular dynamics (EMD) simulations, we investigated the influence of the average grain size on the thermal conductivity of polycrystalline h-BN films at various temperatures. Using the EMD results, we constructed finite element models of polycrystalline h-BN sheets to probe the thermal conductivity of samples with larger grain sizes. Our multiscale investigations not only provide a general viewpoint regarding the heat conduction in h-BN films but also propose that polycrystalline h-BN sheets present high thermal conductivity comparable to monocrystalline sheets.
KW - Wärmeleitfähigkeit
KW - Bornitrid
KW - Finite-Elemente-Methode
Y1 - 2015
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170425-31534
ER -
TY - JOUR
A1 - Ilyani Akmar, A.B.
A1 - Kramer, O.
A1 - Rabczuk, Timon
T1 - Multi-objective evolutionary optimization of sandwich structures: An evaluation by elitist non-dominated sorting evolution strategy
JF - American Journal of Engineering and Applied Sciences
N2 - In this study, an application of evolutionary multi-objective optimization algorithms on the optimization of sandwich structures is presented. The solution strategy is known as Elitist Non-Dominated Sorting Evolution Strategy (ENSES) wherein Evolution Strategies (ES) as Evolutionary Algorithm (EA) in the elitist Non-dominated Sorting Genetic algorithm (NSGA-II) procedure. Evolutionary algorithm seems a compatible approach to resolve multi-objective optimization problems because it is inspired by natural evolution, which closely linked to Artificial Intelligence (AI) techniques and elitism has shown an important factor for improving evolutionary multi-objective search. In order to evaluate the notion of performance by ENSES, the well-known study case of sandwich structures are reconsidered. For Case 1, the goals of the multi-objective optimization are minimization of the deflection and the weight of the sandwich structures. The length, the core and skin thicknesses are the design variables of Case 1. For Case 2, the objective functions are the fabrication cost, the beam weight and the end deflection of the sandwich structures. There are four design variables i.e., the weld height, the weld length, the beam depth and the beam width in Case 2. Numerical results are presented in terms of Paretooptimal solutions for both evaluated cases.
KW - Optimierung
KW - Stahlbau
KW - Multi-objective Evolutionary Optimization, Elitist Non- Dominated Sorting Evolution Strategy (ENSES), Sandwich Structure, Pareto-Optimal Solutions, Evolutionary Algorithm
Y1 - 2015
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170418-31402
SP - 185
EP - 201
ER -
TY - JOUR
A1 - Mortazavi, Bohayra
A1 - Rabczuk, Timon
T1 - Multiscale modeling of heat conduction in graphene laminates
JF - Carbon
N2 - Multiscale modeling of heat conduction in graphene laminates
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2015
SP - 1
EP - 7
ER -
TY - JOUR
A1 - Arash, Behrouz
A1 - Rabczuk, Timon
A1 - Jiang, Jin-Wu
T1 - Nanoresonators and their applications: a state of the art review
JF - Applied Physics Reviews
N2 - Nanoresonators and their applications: a state of the art review
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2015
ER -
TY - JOUR
A1 - Ghasemi, Hamid
A1 - Brighenti, Roberto
A1 - Zhuang, Xiaoying
A1 - Muthu, Jacob
A1 - Rabczuk, Timon
T1 - Optimum fiber content and distribution in fiber-reinforced solids using a reliability and NURBS based sequential optimization approach
JF - Structural and Multidisciplinary Optimization
N2 - Optimum _ber content and distribution in _ber-reinforced solids using a reliability and NURBS based sequential optimization approach
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2015
SP - 99
EP - 112
ER -
TY - CHAP
A1 - Nguyen-Tuan, Long
A1 - Lahmer, Tom
A1 - Datcheva, Maria
A1 - Stoimenova, Eugenia
A1 - Schanz, Tom
ED - Gürlebeck, Klaus
ED - Lahmer, Tom
T1 - PARAMETER IDENTIFICATION APPLYING IN COMPLEX THERMO-HYDRO-MECHANICAL PROBLEMS LIKE THE DESIGN OF BUFFER ELEMENTS
T2 - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar
N2 - 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.
KW - Angewandte Informatik
KW - Angewandte Mathematik
KW - Building Information Modeling
KW - Computerunterstütztes Verfahren
KW - Data, information and knowledge modeling in civil engineering; Function theoretic methods and PDE in engineering sciences; Mathematical methods for (robotics and) computer vision; Numerical modeling in engineering; Optimization in engineering applications
Y1 - 2015
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-28162
SN - 1611-4086
ER -
TY - JOUR
A1 - Hamdia, K.
A1 - Lahmer, Tom
A1 - Nguyen-Thoi, T.
A1 - Rabczuk, Timon
T1 - Predicting The Fracture Toughness of PNCs: A Stochastic Approach Based on ANN and ANFIS
JF - Computational Materials Science
N2 - Predicting The Fracture Toughness of PNCs: A Stochastic Approach Based on ANN and ANFIS
KW - Angewandte Mathematik
KW - Stochastik
KW - Strukturmechanik
Y1 - 2015
SP - 304
EP - 313
ER -
TY - CHAP
A1 - Tan, Fengjie
A1 - Lahmer, Tom
A1 - Siddappa, Manju Gyaraganahalll
ED - Gürlebeck, Klaus
ED - Lahmer, Tom
T1 - SECTION OPTIMIZATION AND RELIABILITY ANALYSIS OF ARCH-TYPE DAMS INCLUDING COUPLED MECHANICAL-THERMAL AND HYDRAULIC FIELDS
T2 - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar
N2 - 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.
KW - Angewandte Informatik
KW - Angewandte Mathematik
KW - Building Information Modeling
KW - Computerunterstütztes Verfahren
KW - Data, information and knowledge modeling in civil engineering; Function theoretic methods and PDE in engineering sciences; Mathematical methods for (robotics and) computer vision; Numerical modeling in engineering; Optimization in engineering applications
Y1 - 2015
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-28212
SN - 1611-4086
ER -
TY - THES
A1 - Almasi, Ashkan
T1 - Stochastic Analysis of Interfacial Effects on the Polymeric Nanocomposites
N2 - The polymeric clay nanocomposites are a new class of materials of which recently have become the centre of attention due to their superior mechanical and physical properties. Several studies have been performed on the mechanical characterisation of these nanocomposites; however most of those studies have neglected the effect of the interfacial region between the clays and the matrix despite of its significant influence on the mechanical performance of the nanocomposites.
There are different analytical methods to calculate the overall elastic material properties of the composites. In this study we use the Mori-Tanaka method to determine the overall stiffness of the composites for simple inclusion geometries of cylinder and sphere. Furthermore, the effect of interphase layer on the overall properties of composites is calculated. Here, we intend to get ounds for the effective mechanical properties to compare with the analytical results. Hence, we use linear displacement boundary conditions (LD) and uniform traction boundary conditions (UT) accordingly. Finally, the analytical results are compared with numerical results and they are in a good agreement.
The next focus of this dissertation is a computational approach with a hierarchical multiscale method on the mesoscopic level. In other words, in this study we use the stochastic analysis and computational homogenization method to analyse the effect of thickness and stiffness of the interfacial region on the overall elastic properties of the clay/epoxy nanocomposites. The results show that the increase in interphase thickness, reduces the stiffness of the clay/epoxy naocomposites and this decrease becomes significant in higher clay contents. The results of the sensitivity analysis prove that the stiffness of the interphase layer has more significant effect on the final stiffness of nanocomposites. We also validate the results with the available experimental results from the literature which show good agreement.
KW - Homogenization
KW - Multiscale modeling
KW - Nanocomposite materials
KW - Stochastic analysis
Y1 - 2015
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20150709-24339
ER -
TY - THES
A1 - Vu, Bac Nam
T1 - Stochastic uncertainty quantification for multiscale modeling of polymeric nanocomposites
N2 - 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.
KW - Polymere
KW - nanocomposite
KW - Nanoverbundstruktur
KW - stochastic
KW - multiscale
Y1 - 2015
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20160322-25551
ER -
TY - JOUR
A1 - Ghorashi, Seyed Shahram
A1 - Valizadeh, N.
A1 - Mohammadi, S.
A1 - Rabczuk, Timon
T1 - T-spline based XIGA for Fracture Analysis of Orthotropic Media
JF - Computers & Structures
N2 - T-spline based XIGA for Fracture Analysis of Orthotropic Media
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2015
SP - 138
EP - 146
ER -
TY - JOUR
A1 - Ben, S.
A1 - Zhao, Jun-Hua
A1 - Zhang, Yancheng
A1 - Rabczuk, Timon
T1 - The interface strength and debonding for composite structures: review and recent developments
JF - Composite Structures
N2 - The interface strength and debonding for composite structures: review and recent developments
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2015
ER -
TY - JOUR
A1 - Zhao, Jiyun
A1 - Lu, Lixin
A1 - Rabczuk, Timon
T1 - The tensile and shear failure behavior dependence on chain length and temperature in amorphous polymers
JF - Computational Materials Science
N2 - The tensile and shear failure behavior dependence on chain length and temperature in amorphous polymers
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2015
SP - 567
EP - 572
ER -
TY - CHAP
A1 - Jaouadi, Zouhour
A1 - Lahmer, Tom
ED - Gürlebeck, Klaus
ED - Lahmer, Tom
T1 - Topology optimization of structures subjected to multiple load cases by introducing the Epsilon constraint method
T2 - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar
N2 - 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.
KW - Angewandte Informatik
KW - Angewandte Mathematik
KW - Building Information Modeling
KW - Computerunterstütztes Verfahren
KW - Data, information and knowledge modeling in civil engineering; Function theoretic methods and PDE in engineering sciences; Mathematical methods for (robotics and) computer vision; Numerical modeling in engineering; Optimization in engineering applications
Y1 - 2015
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-28042
SN - 1611-4086
ER -
TY - JOUR
A1 - Vu-Bac, N.
A1 - Rafiee, Roham
A1 - Zhuang, Xiaoying
A1 - Lahmer, Tom
A1 - Rabczuk, Timon
T1 - Uncertainty quantification for multiscale modeling of polymer nanocomposites with correlated parameters
JF - Composites Part B: Engineering
N2 - Uncertainty quantification for multiscale modeling of polymer nanocomposites with correlated parameters
KW - Angewandte Mathematik
KW - Stochastik
KW - Strukturmechanik
Y1 - 2015
SP - 446
EP - 464
ER -
TY - JOUR
A1 - Lahmer, Tom
A1 - Ilg, J.
A1 - Lerch, Reinhard
T1 - Variance-based sensitivity analyses of piezoelectric models
JF - Computer Modeling in Engineering & Sciences
N2 - Variance-based sensitivity analyses of piezoelectric models
KW - Angewandte Mathematik
KW - Stochastik
KW - Strukturmechanik
Y1 - 2015
SP - 105
EP - 126
ER -