@article{GhasemiBrighentiZhuangetal., author = {Ghasemi, Hamid and Brighenti, Roberto and Zhuang, Xiaoying and Muthu, Jacob and Rabczuk, Timon}, title = {Optimization of fiber distribution in fiber reinforced composite by using NURBS functions}, series = {Computational Materials Science}, journal = {Computational Materials Science}, pages = {463 -- 473}, abstract = {Optimization of fiber distribution in fiber reinforced composite by using NURBS functions}, subject = {Angewandte Mathematik}, language = {en} } @article{JamshidianRabczuk, author = {Jamshidian, M. and Rabczuk, Timon}, title = {Phase field modelling of stressed grain growth: Analytical study and the effect of microstructural length scale}, series = {Journal of Computational Physics}, journal = {Journal of Computational Physics}, pages = {23 -- 35}, abstract = {Phase field modelling of stressed grain growth: Analytical study and the effect of microstructural length scale}, subject = {Angewandte Mathematik}, language = {en} } @article{ThaiFerreiraBordasetal., author = {Thai, Chien H. and Ferreira, A.J.M. and Bordas, St{\´e}phane Pierre Alain and Rabczuk, Timon and Nguyen-Xuan, Hung}, title = {Isogeometric analysis of laminated composite and sandwich plates using a new inverse trigonometric shear deformation theory}, series = {European Journal of Mechanics}, journal = {European Journal of Mechanics}, pages = {89 -- 108}, abstract = {Isogeometric analysis of laminated composite and sandwich plates using a new inverse trigonometric shear deformation theory}, subject = {Angewandte Mathematik}, language = {en} } @article{GhasemiBrighentiZhuangetal., author = {Ghasemi, Hamid and Brighenti, Roberto and Zhuang, Xiaoying and Muthu, Jacob and Rabczuk, Timon}, title = {Sequential reliability based optimization of fiber content and dispersion in fiber reinforced composite by using NURBS finite elements}, series = {Structural and Multidisciplinary Optimization}, journal = {Structural and Multidisciplinary Optimization}, abstract = {Sequential reliability based optimization of fiber content and dispersion in fiber reinforced composite by using NURBS finite elements}, 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{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{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{AmiriMillanShenetal., author = {Amiri, Fatemeh and Mill{\´a}n, D. and Shen, Y. and Rabczuk, Timon and Arroyo, M.}, title = {Phase-field modeling of fracture in linear thin shells}, series = {Theoretical and Applied Fracture Mechanics}, journal = {Theoretical and Applied Fracture Mechanics}, pages = {102 -- 109}, abstract = {Phase-field modeling of fracture in linear thin shells}, subject = {Angewandte Mathematik}, language = {en} } @article{JiangParkRabczuk, author = {Jiang, Jin-Wu and Park, Harold S. and Rabczuk, Timon}, title = {MoS2 nanoresonators: intrinsically better than graphene?}, series = {Nanoscale}, journal = {Nanoscale}, pages = {3618 -- 3625}, abstract = {MoS2 nanoresonators: intrinsically better than graphene?}, 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{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{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{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{BeexKerfridenRabczuketal., author = {Beex, L.A.A. and Kerfriden, Pierre and Rabczuk, Timon and Bordas, St{\´e}phane Pierre Alain}, title = {Quasicontinuum-based multiscale approaches for plate-like beam lattices experiencing in-plane and out-of-plane deformation}, series = {Computer Methods in Applied Mechanics and Engineering}, journal = {Computer Methods in Applied Mechanics and Engineering}, abstract = {Quasicontinuum-based multiscale approaches for plate-like beam lattices experiencing in-plane and out-of-plane deformation}, subject = {Angewandte Mathematik}, language = {en} } @article{NguyenKerfridenBordasetal., author = {Nguyen, V.P. and Kerfriden, Pierre and Bordas, St{\´e}phane Pierre Alain and Rabczuk, Timon}, title = {Isogeometric analysis suitable trivariate NURBS representation of composite panels with a new offset algorithm}, series = {Computer-Aided Design}, journal = {Computer-Aided Design}, abstract = {Isogeometric analysis suitable trivariate NURBS representation of composite panels with a new offset algorithm}, 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{IlyaniAkmarLahmerBordasetal., author = {Ilyani Akmar, A.B. and Lahmer, Tom and Bordas, St{\´e}phane Pierre Alain and Beex, L.A.A. and Rabczuk, Timon}, title = {Uncertainty quantification of dry woven fabrics: A sensitivity analysis on material properties}, series = {Composite Structures}, journal = {Composite Structures}, doi = {10.1016/j.compstruct.2014.04.014}, pages = {1 -- 17}, abstract = {Uncertainty quantification of dry woven fabrics: A sensitivity analysis on material properties}, 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{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{VuBacLahmerKeiteletal., author = {Vu-Bac, N. and Lahmer, Tom and Keitel, Holger and Zhao, Jun-Hua and Zhuang, Xiaoying and Rabczuk, Timon}, title = {Stochastic predictions of bulk properties of amorphous polyethylene based on molecular dynamics simulations}, series = {Mechanics of Materials}, journal = {Mechanics of Materials}, pages = {70 -- 84}, abstract = {Stochastic predictions of bulk properties of amorphous polyethylene based on molecular dynamics simulations}, 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{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{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{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{JiangWangRabczuk, author = {Jiang, Jin-Wu and Wang, Bing-Shen and Rabczuk, Timon}, title = {Why twisting angles are diverse in graphene Moir'e patterns?}, series = {Journal of Applied Physics}, journal = {Journal of Applied Physics}, abstract = {Why twisting angles are diverse in graphene Moir'e patterns?}, subject = {Angewandte Mathematik}, language = {en} } @article{JiangRabczuk, author = {Jiang, Jin-Wu and Rabczuk, Timon}, title = {Mechanical Oscillation of Kinked Silicon Nanowires: a Natural Nanoscale Spring}, series = {Applied Physics Letters}, journal = {Applied Physics Letters}, abstract = {Mechanical Oscillation of Kinked Silicon Nanowires: a Natural Nanoscale Spring}, subject = {Angewandte Mathematik}, language = {en} } @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{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{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{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{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{TalebiSilaniBordasetal., author = {Talebi, Hossein and Silani, Mohammad and Bordas, St{\´e}phane Pierre Alain and Kerfriden, Pierre and Rabczuk, Timon}, title = {Molecular Dynamics/XFEM Coupling by a Three-Dimensional Extended Bridging Domain with Applications to Dynamic Brittle Fracture}, series = {International Journal for Multiscale Computational Engineering}, journal = {International Journal for Multiscale Computational Engineering}, abstract = {Molecular Dynamics/XFEM Coupling by a Three-Dimensional Extended Bridging Domain with Applications to Dynamic Brittle Fracture}, 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{KerfridenSchmidtRabczuketal., author = {Kerfriden, Pierre and Schmidt, K.M. and Rabczuk, Timon and Bordas, St{\´e}phane Pierre Alain}, title = {Statistical extraction of process zones and representative subspaces in fracture of random composites}, series = {International Journal for Multiscale Computational Engineering}, journal = {International Journal for Multiscale Computational Engineering}, abstract = {Statistical extraction of process zones and representative subspaces in fracture of random composites}, subject = {Angewandte Mathematik}, language = {en} } @article{BakarKramerBordasetal., author = {Bakar, I. and Kramer, O. and Bordas, St{\´e}phane Pierre Alain and Rabczuk, Timon}, title = {Optimization of Elastic Properties and Weaving Patterns of Woven Composites}, series = {Composite Structures}, journal = {Composite Structures}, pages = {575 -- 591}, abstract = {Optimization of Elastic Properties and Weaving Patterns of Woven Composites}, 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{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{JiangZhaoRabczuk, author = {Jiang, Jin-Wu and Zhao, Jun-Hua and Rabczuk, Timon}, title = {Size-Sensitive Young's Modulus of Kinked Silicon Nanowires}, series = {Nanotechnology}, journal = {Nanotechnology}, doi = {10.1088/0957-4484/24/18/185702}, abstract = {We perform both classical molecular dynamics simulations and beam model calculations to investigate the Young's modulus of kinked silicon nanowires (KSiNWs). The Young's modulus is found to be highly sensitive to the arm length of the kink and is essentially inversely proportional to the arm length. The mechanism underlying the size dependence is found to be the interplay between the kink angle potential and the arm length potential, where we obtain an analytic relationship between the Young's modulus and the arm length of the KSiNW. Our results provide insight into the application of this novel building block in nanomechanical devices.}, 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{SilaniTalebiArnoldetal., author = {Silani, Mohammad and Talebi, Hossein and Arnold, Daniel and Ziaei-Rad, S. and Rabczuk, Timon}, title = {On the coupling of a commercial finite element package with lammps for multiscale modeling of materials}, series = {Steel Research International}, journal = {Steel Research International}, abstract = {On the coupling of a commercial finite element package with lammps for multiscale modeling of materials}, 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{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{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{JiangRabczuk, author = {Jiang, Jin-Wu and Rabczuk, Timon}, title = {Modulation of Thermal Conductivity in kinked Silicon Nanowires: Phonon interchanging and pinching effects or Reduction of thermal conductivity in kinked silicon nanowire superlattices}, series = {Nano Letters}, journal = {Nano Letters}, abstract = {Modulation of Thermal Conductivity in kinked Silicon Nanowires: Phonon interchanging and pinching effects or Reduction of thermal conductivity in kinked silicon nanowire superlattices}, subject = {Angewandte Mathematik}, language = {en} } @article{ZhangWeiZhaoetal., author = {Zhang, Yancheng and Wei, Ning and Zhao, Jun-Hua and Gong, Yadong and Rabczuk, Timon}, title = {Quasi-analytical solution for the stable system of the multi-layer folded graphene wrinkles}, series = {Journal of Applied Physics}, journal = {Journal of Applied Physics}, abstract = {Quasi-analytical solution for the stable system of the multi-layer folded graphene wrinkles}, subject = {Angewandte Mathematik}, language = {en} } @article{ValizadehNatarajanGonzalezEstradaetal., author = {Valizadeh, Navid and Natarajan, S. and Gonzalez-Estrada, O.A. and Rabczuk, Timon and Tinh Quoc, Bui and Bordas, St{\´e}phane Pierre Alain}, title = {NURBS-based finite element analysis of functionally graded plates: static bending, vibration, buckling and flutter}, series = {Composite Structures}, journal = {Composite Structures}, pages = {309 -- 326}, abstract = {NURBS-based finite element analysis of functionally graded plates: static bending, vibration, buckling and flutter}, 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{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{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} }