@article{ZhangWangLahmeretal., author = {Zhang, Chao and Wang, Cuixia and Lahmer, Tom and He, Pengfei and Rabczuk, Timon}, title = {A dynamic XFEM formulation for crack identification}, series = {International Journal of Mechanics and Materials in Design}, journal = {International Journal of Mechanics and Materials in Design}, pages = {427 -- 448}, abstract = {A dynamic XFEM formulation for crack identification}, subject = {Angewandte Mathematik}, language = {en} } @article{ZhangNanthakumarLahmeretal., author = {Zhang, Chao and Nanthakumar, S.S. and Lahmer, Tom and Rabczuk, Timon}, title = {Multiple cracks identification for piezoelectric structures}, series = {International Journal of Fracture}, journal = {International Journal of Fracture}, pages = {1 -- 19}, abstract = {Multiple cracks identification for piezoelectric structures}, subject = {Angewandte Mathematik}, language = {en} } @article{NanthakumarLahmerZhuangetal., author = {Nanthakumar, S.S. and Lahmer, Tom and Zhuang, Xiaoying and Park, Harold S. and Rabczuk, Timon}, title = {Topology optimization of piezoelectric nanostructures}, series = {Journal of the Mechanics and Physics of Solids}, journal = {Journal of the Mechanics and Physics of Solids}, pages = {316 -- 335}, abstract = {Topology optimization of piezoelectric nanostructures}, subject = {Angewandte Mathematik}, language = {en} } @article{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{GhorashiLahmerBagherzadehetal., author = {Ghorashi, Seyed Shahram and Lahmer, Tom and Bagherzadeh, Amir Saboor and Zi, Goangseup and Rabczuk, Timon}, title = {A stochastic computational method based on goal-oriented error estimation for heterogeneous geological materials}, series = {Engineering Geology}, journal = {Engineering Geology}, abstract = {A stochastic computational method based on goal-oriented error estimation for heterogeneous geological materials}, subject = {Angewandte Mathematik}, language = {en} } @article{NanthakumarLahmerZhuangetal., author = {Nanthakumar, S.S. and Lahmer, Tom and Zhuang, Xiaoying and Zi, Goangseup and Rabczuk, Timon}, title = {Detection of material interfaces using a regularized level set method in piezoelectric structures}, series = {Inverse Problems in Science and Engineering}, journal = {Inverse Problems in Science and Engineering}, pages = {153 -- 176}, abstract = {Detection of material interfaces using a regularized level set method in piezoelectric structures}, subject = {Angewandte Mathematik}, language = {en} } @article{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{ZhaoLuZhangetal., author = {Zhao, Jun-Hua and Lu, Lixin and Zhang, Zhiliang and Guo, Wanlin and Rabczuk, Timon}, title = {Continuum modeling of the cohesive energy for the interfaces between _lms, spheres, coats and substrates}, series = {Computational Materials Science}, journal = {Computational Materials Science}, pages = {432 -- 438}, abstract = {Continuum modeling of the cohesive energy for the interfaces between _lms, spheres, coats and substrates}, subject = {Angewandte Mathematik}, language = {en} } @article{BenZhaoZhangetal., author = {Ben, S. and Zhao, Jun-Hua and Zhang, Yancheng and Rabczuk, Timon}, title = {The interface strength and debonding for composite structures: review and recent developments}, series = {Composite Structures}, journal = {Composite Structures}, abstract = {The interface strength and debonding for composite structures: review and recent developments}, subject = {Angewandte Mathematik}, language = {en} } @article{ZhaoJiaWeietal., author = {Zhao, Jun-Hua and Jia, Yue and Wei, Ning and Rabczuk, Timon}, title = {Binding energy and mechanical stability of two parallel and crossing carbon nanotubes}, series = {Journal of Applied Mechanics}, journal = {Journal of Applied Mechanics}, abstract = {Binding energy and mechanical stability of two parallel and crossing carbon nanotubes}, subject = {Angewandte Mathematik}, language = {en} } @article{KumarSinghMishraetal., author = {Kumar, S. and Singh, I. and Mishra, B.K. and Rabczuk, Timon}, title = {Modeling and Simulation of Kinked Cracks by Virtual Node XFEM}, series = {Computer Methods in Applied Mechanics and Engineering}, journal = {Computer Methods in Applied Mechanics and Engineering}, pages = {1425 -- 1466}, abstract = {Modeling and Simulation of Kinked Cracks by Virtual Node XFEM}, subject = {Angewandte Mathematik}, language = {en} } @article{NanthakumarLahmerRabczuk, author = {Nanthakumar, S.S. and Lahmer, Tom and Rabczuk, Timon}, title = {Detection of flaws in piezoelectric structures using extended FEM}, series = {International Journal for Numerical Methods in Engineering}, journal = {International Journal for Numerical Methods in Engineering}, pages = {373 -- 389}, abstract = {Detection of flaws in piezoelectric structures using extended FEM}, subject = {Angewandte Mathematik}, language = {en} } @article{ZhaoWeiFanetal., author = {Zhao, Jun-Hua and Wei, Ning and Fan, Z. and Jiang, Jin-Wu and Rabczuk, Timon}, title = {Mechanical properties of three types of carbon allotropes}, series = {Nanotechnology}, journal = {Nanotechnology}, abstract = {Mechanical properties of three types of carbon allotropes}, subject = {Angewandte Mathematik}, language = {en} } @article{AreiasRabczukDiasdaCostaetal., author = {Areias, Pedro and Rabczuk, Timon and Dias-da-Costa, D. and Piresh, E.B.}, title = {Implicit solutions with consistent additive and multiplicative components}, series = {Finite Elements in Analysis and Design}, journal = {Finite Elements in Analysis and Design}, doi = {10.1016/j.finel.2012.03.007}, pages = {15 -- 31}, abstract = {This work describes an algorithm and corresponding software for incorporating general nonlinear multiple-point equality constraints in a implicit sparse direct solver. It is shown that direct addressing of sparse matrices is possible in general circumstances, circumventing the traditional linear or binary search for introducing (generalized) constituents to a sparse matrix. Nested and arbitrarily interconnected multiple-point constraints are introduced by processing of multiplicative constituents with a built-in topological ordering of the resulting directed graph. A classification of discretization methods is performed and some re-classified problems are described and solved under this proposed perspective. The dependence relations between solution methods, algorithms and constituents becomes apparent. Fracture algorithms can be naturally casted in this framework. Solutions based on control equations are also directly incorporated as equality constraints. We show that arbitrary constituents can be used as long as the resulting directed graph is acyclic. It is also shown that graph partitions and orderings should be performed in the innermost part of the algorithm, a fact with some peculiar consequences. The core of our implicit code is described, specifically new algorithms for direct access of sparse matrices (by means of the clique structure) and general constituent processing. It is demonstrated that the graph structure of the second derivatives of the equality constraints are cliques (or pseudo-elements) and are naturally included as such. A complete algorithm is presented which allows a complete automation of equality constraints, avoiding the need of pre-sorting. Verification applications in four distinct areas are shown: single and multiple rigid body dynamics, solution control and computational fracture.}, subject = {Angewandte Mathematik}, language = {en} } @article{JiangRabczukPark, author = {Jiang, Jin-Wu and Rabczuk, Timon and Park, Harold S.}, title = {A Stillinger-Weber Potential for Single-Layer Black Phosphorus, and the Importance of Cross-Pucker Interactions for Negative Poisson's Ratio and Edge Stress-Induced Bending}, series = {Nanoscale}, journal = {Nanoscale}, doi = {10.1039/C4NR07341J}, abstract = {The distinguishing structural feature of single-layered black phosphorus is its puckered structure, which leads to many novel physical properties. In this work, we first present a new parameterization of the Stillinger-Weber potential for single-layered black phosphorus. In doing so, we reveal the importance of a cross-pucker interaction term in capturing its unique mechanical properties, such as a negative Poisson's ratio. In particular, we show that the cross-pucker interaction enables the pucker to act as a re-entrant hinge, which expands in the lateral direction when it is stretched in the longitudinal direction. As a consequence, single-layered black phosphorus has a negative Poisson's ratio in the direction perpendicular to the atomic plane. As an additional demonstration of the impact of the cross-pucker interaction, we show that it is also the key factor that enables capturing the edge stress-induced bending of single-layered black phosphorus that has been reported in ab initio calculations.}, subject = {Angewandte Mathematik}, language = {en} } @article{TalebiSilaniRabczuk, author = {Talebi, Hossein and Silani, Mohammad and Rabczuk, Timon}, title = {Concurrent Multiscale Modelling of Three Dimensional Crack and Dislocation Propagation}, series = {Advances in Engineering Software}, journal = {Advances in Engineering Software}, pages = {82 -- 92}, abstract = {Concurrent Multiscale Modelling of Three Dimensional Crack and Dislocation Propagation}, subject = {Angewandte Mathematik}, language = {en} } @article{XuMourrainGalligoetal., author = {Xu, G. and Mourrain, B. and Galligo, A. and Rabczuk, Timon}, title = {High-quality construction of analysis-suitable trivariate NURBS solids by reparameterization methods}, series = {Computational Mechanics}, journal = {Computational Mechanics}, abstract = {High-quality construction of analysis-suitable trivariate NURBS solids by reparameterization methods}, subject = {Angewandte Mathematik}, language = {en} } @article{PhanDaoNguyenXuanThaiHoangetal., author = {Phan-Dao, H. and Nguyen-Xuan, Hung and Thai-Hoang, C. and Nguyen-Thoi, T. and Rabczuk, Timon}, title = {An edge-based smoothed finite element method for analysis of laminated composite plates}, series = {International Journal of Computational Methods}, journal = {International Journal of Computational Methods}, abstract = {An edge-based smoothed finite element method for analysis of laminated composite plates}, subject = {Angewandte Mathematik}, language = {en} } @article{SilaniZiaeiRadTalebietal., author = {Silani, Mohammad and Ziaei-Rad, S. and Talebi, Hossein and Rabczuk, Timon}, title = {A Semi-Concurrent Multiscale Approach for Modeling Damage in Nanocomposites}, series = {Theoretical and Applied Fracture Mechanics}, journal = {Theoretical and Applied Fracture Mechanics}, abstract = {A Semi-Concurrent Multiscale Approach for Modeling Damage in Nanocomposites}, subject = {Angewandte Mathematik}, language = {en} } @article{AmaniBagherzadehRabczuk, author = {Amani, Jafar and Bagherzadeh, Amir Saboor and Rabczuk, Timon}, title = {Error estimate and adaptive refinement in Mixed Discrete Least Squares Meshless method}, series = {Mathematical Problems in Engineering}, journal = {Mathematical Problems in Engineering}, abstract = {Error estimate and adaptive refinement in Mixed Discrete Least Squares Meshless method}, subject = {Angewandte Mathematik}, language = {en} }