@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{ZhangZhuangMuthuetal.,
  author    = {Zhang, Yancheng and Zhuang, Xiaoying and Muthu, Jacob and Mabrouki, Tarek and Fontaine, Micha{\"e}l and Gong, Yadong and Rabczuk, Timon},
  title     = {Load transfer of graphene/carbon nanotube/polyethylene hybrid nanocomposite by molecular dynamics simulation},
  series = {Composites Part B Engineering},
  journal   = {Composites Part B Engineering},
  pages     = {27 -- 33},
  abstract  = {Load transfer of graphene/carbon nanotube/polyethylene hybrid nanocomposite by molecular dynamics simulation},
  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{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{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{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}
}
@phdthesis{ZHANG2018,
  author    = {ZHANG, CHAO},
  title     = {Crack Identification using Dynamic Extended Finite Element Method and Thermal Conductivity Engineering for Nanomaterials},
  doi       = {10.25643/bauhaus-universitaet.3847},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20190119-38478},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  year      = {2018},
  abstract  = {Identification of flaws in structures is a critical element in the management of maintenance and quality assurance processes in engineering. Nondestructive testing (NDT) techniques based on a wide range of physical principles have been developed and are used in common practice for structural health monitoring. However, basic NDT techniques are usually limited in their ability to provide the accurate information on locations, dimensions and shapes of flaws. One alternative to extract additional information from the results of NDT is to append it with a computational model that provides detailed analysis of the physical process involved and enables the accurate identification of the flaw parameters. The aim here is to develop the strategies to uniquely identify cracks in two-dimensional 2D) structures under dynamic loadings. A local NDT technique combined eXtended Finite Element Method (XFEM) with dynamic loading in order to identify the cracks in the structures quickly and accurately is developed in this dissertation. The Newmark-b time integration method with Rayleigh damping is used for the time integration. We apply Nelder-Mead (NM)and Quasi-Newton (QN) methods for identifying the crack tip in plate. The inverse problem is solved iteratively, in which XFEM is used for solving the forward problem in each iteration. For a timeharmonic excitation with a single frequency and a short-duration signal measured along part of the external boundary, the crack is detected through the solution of an inverse time-dependent problem. Compared to the static load, we show that the dynamic loads are more effective for crack detection problems. Moreover, we tested different dynamic loads and find that NM method works more efficient under the harmonic load than the pounding load while the QN method achieves almost the same results for both load types. A global strategy, Multilevel Coordinate Search (MCS) with XFEM (XFEM-MCS) methodology under the dynamic electric load, to detect multiple cracks in 2D piezoelectric plates is proposed in this dissertation. The Newmark-b method is employed for the time integration and in each iteration the forward problem is solved by XFEM for various cracks. The objective functional is minimized by using a global search algorithm MCS. The test problems show that the XFEM-MCS algorithm under the dynamic electric load can be effectively employed for multiple cracks detection in piezoelectric materials, and it proves to be robust in identifying defects in piezoelectric structures. Fiber-reinforced composites (FRCs) are extensively applied in practical engineering since they have high stiffness and strength. Experiments reveal a so-called interphase zone, i.e. the space between the outside interface of the fiber and the inside interface of the matrix. The interphase strength between the fiber and the matrix strongly affects the mechanical properties as a result of the large ratio of interface/volume. For the purpose of understanding the mechanical properties of FRCs with functionally graded interphase (FGI), a closed-form expression of the interface strength between a fiber and a matrix is obtained in this dissertation using a continuum modeling approach according to the ver derWaals (vdW) forces. Based on the interatomic potential, we develop a new modified nonlinear cohesive law, which is applied to study the interface delamination of FRCs with FGI under different loadings. The analytical solutions show that the delamination behavior strongly depends on the interphase thickness, the fiber radius, the Young's moduli and Poisson's ratios of the fiber and the matrix. Thermal conductivity is the property of a material to conduct heat. With the development and deep research of 2D materials, especially graphene and molybdenum disulfide (MoS2), the thermal conductivity of 2D materials attracts wide attentions. The thermal conductivity of graphene nanoribbons (GNRs) is found to appear a tendency of decreasing under tensile strain by classical molecular dynamics (MD) simulations. Hence, the strain effects of graphene can play a key role in the continuous tunability and applicability of its thermal conductivity property at nanoscale, and the dissipation of thermal conductivity is an obstacle for the applications of thermal management. Up to now, the thermal conductivity of graphene under shear deformation has not been investigated yet. From a practical point of view, good thermal managements of GNRs have significantly potential applications of future GNR-based thermal nanodevices, which can greatly improve performances of the nanosized devices due to heat dissipations. Meanwhile, graphene is a thin membrane structure, it is also important to understand the wrinkling behavior under shear deformation. MoS2 exists in the stable semiconducting 1H phase (1H-MoS2) while the metallic 1T phase (1T-MoS2) is unstable at ambient conditions. As it's well known that much attention has been focused on studying the nonlinear optical properties of the 1H-MoS2. In a very recent research, the 1T-type monolayer crystals of TMDCs, MX2 (MoS2, WS2 ...) was reported having an intrinsic in-plane negative Poisson's ratio. Luckily, nearly at the same time, unprecedented long-term (>3months) air stability of the 1T-MoS2 can be achieved by using the donor lithium hydride (LiH). Therefore, it's very important to study the thermal conductivity of 1T-MoS2. The thermal conductivity of graphene under shear strain is systematically studied in this dissertation by MD simulations. The results show that, in contrast to the dramatic decrease of thermal conductivity of graphene under uniaxial tensile, the thermal conductivity of graphene is not sensitive to the shear strain, and the thermal conductivity decreases only 12-16\%. The wrinkle evolves when the shear strain is around 5\%-10\%, but the thermal conductivity barely changes. The thermal conductivities of single-layer 1H-MoS2(1H-SLMoS2) and single-layer 1T-MoS2 (1T-SLMoS2) with different sample sizes, temperatures and strain rates have been studied systematically in this dissertation. We find that the thermal conductivities of 1H-SLMoS2 and 1T-SLMoS2 in both the armchair and the zigzag directions increase with the increasing of the sample length, while the increase of the width of the sample has minor effect on the thermal conductions of these two structures. The thermal conductivity of 1HSLMoS2 is smaller than that of 1T-SLMoS2 under size effect. Furthermore, the temperature effect results show that the thermal conductivities of both 1H-SLMoS2 and 1T-SLMoS2 decrease with the increasing of the temperature. The thermal conductivities of 1HSLMoS2 and 1T-SLMoS2 are nearly the same (difference <6\%) in both of the chiral orientations under corresponding temperatures, especially in the armchair direction (difference <2.8\%). Moreover, we find that the strain effects on the thermal conductivity of 1HSLMoS2 and 1T-SLMoS2 are different. More specifically, the thermal conductivity decreases with the increasing tensile strain rate for 1T-SLMoS2, while fluctuates with the growth of the strain for 1HSLMoS2. Finally, we find that the thermal conductivity of same sized 1H-SLMoS2 is similar with that of the strained 1H-SLMoS2 structure.},
  subject      = {crack},
  language  = {en}
}
@article{ZerbstVormwaldAnderschetal.,
  author    = {Zerbst, U. and Vormwald, Michael and Andersch, C. and M{\"a}dler, K. and Pfuff, M.},
  title     = {The development of a damage tolerance concept for railway components and its demonstration for a railway axle},
  series = {Engineering Fracture Mechanics},
  journal   = {Engineering Fracture Mechanics},
  pages     = {209 -- 239},
  abstract  = {The development of a damage tolerance concept for railway components and its demonstration for a railway axle},
  subject      = {Angewandte Mathematik},
  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{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{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{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{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{VuBacRafieeZhuangetal.,
  author    = {Vu-Bac, N. and Rafiee, Roham and Zhuang, Xiaoying and Lahmer, Tom and Rabczuk, Timon},
  title     = {Uncertainty quantification for multiscale modeling of polymer nanocomposites with correlated parameters},
  series = {Composites Part B: Engineering},
  journal   = {Composites Part B: Engineering},
  pages     = {446 -- 464},
  abstract  = {Uncertainty quantification for multiscale modeling of polymer nanocomposites with correlated parameters},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{VuBacLahmerZhangetal.,
  author    = {Vu-Bac, N. and Lahmer, Tom and Zhang, Yancheng and Zhuang, Xiaoying and Rabczuk, Timon},
  title     = {Stochastic predictions of interfacial characteristic of polymeric nanocomposites (PNCs)},
  series = {Composites Part B Engineering},
  journal   = {Composites Part B Engineering},
  pages     = {80 -- 95},
  abstract  = {Stochastic predictions of interfacial characteristic of polymeric nanocomposites (PNCs)},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@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{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{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{UngerTeughelsDeRoeck,
  author    = {Unger, J{\"o}rg F. and Teughels, A. and De Roeck, G.},
  title     = {System identification and damage detection of a prestressed concrete beam},
  series = {Journal of Structural Engineering},
  journal   = {Journal of Structural Engineering},
  pages     = {1691 -- 1698},
  abstract  = {System identification and damage detection of a prestressed concrete beam},
  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{UngerEckardtKoenke,
  author    = {Unger, J{\"o}rg F. and Eckardt, Stefan and K{\"o}nke, Carsten},
  title     = {Modelling of cohesive crack growth in concrete structures with the extended finite element method},
  series = {Computer Methods in Applied Mechanics and Engineering},
  journal   = {Computer Methods in Applied Mechanics and Engineering},
  pages     = {4087 -- 4100},
  abstract  = {Modelling of cohesive crack growth in concrete structures with the extended finite element method},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{ThumserBergmannVormwald,
  author    = {Thumser, Rayk and Bergmann, Joachim W. and Vormwald, Michael},
  title     = {Residual stress fields and fatigue analysis of autofrettaged parts},
  series = {International Journal of Pressure Vessels and Piping},
  journal   = {International Journal of Pressure Vessels and Piping},
  pages     = {113 -- 117},
  abstract  = {Residual stress fields and fatigue analysis of autofrettaged parts},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{ThaiNguyenXuanNguyenThanhetal.,
  author    = {Thai, Chien H. and Nguyen-Xuan, Hung and Nguyen-Thanh, Nhon and Le, T.H. and Nguyen-Thoi, T. and Rabczuk, Timon},
  title     = {Static, free vibration and buckling analysis of laminated composite Reissner-Mindlin plates using NURBS-based isogeometric approach},
  series = {International Journal for Numerical Methods in Engineering},
  journal   = {International Journal for Numerical Methods in Engineering},
  doi       = {10.1002/nme.4282},
  pages     = {571 -- 603},
  abstract  = {This paper presents a novel numerical procedure based on the framework of isogeometric analysis for static, free vibration, and buckling analysis of laminated composite plates using the first-order shear deformation theory. The isogeometric approach utilizes non-uniform rational B-splines to implement for the quadratic, cubic, and quartic elements. Shear locking problem still exists in the stiffness formulation, and hence, it can be significantly alleviated by a stabilization technique. Several numerical examples are presented to show the performance of the method, and the results obtained are compared with other available ones.},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{ThaiNguyenXuanBordasetal.,
  author    = {Thai, Chien H. and Nguyen-Xuan, Hung and Bordas, St{\´e}phane Pierre Alain and Nguyen-Thanh, Nhon and Rabczuk, Timon},
  title     = {Isogeometric analysis of laminated composite plates using the higher-order shear deformation theory},
  series = {Mechanics of Advanced Materials and Structures},
  journal   = {Mechanics of Advanced Materials and Structures},
  pages     = {451 -- 469},
  abstract  = {Isogeometric analysis of laminated composite plates using the higher-order shear deformation theory},
  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{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{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},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170426-31639},
  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      = {Finite-Elemente-Methode},
  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{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{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{TalebiSamaniegoSamaniegoetal.,
  author    = {Talebi, Hossein and Samaniego, C. and Samaniego, Esteban and Rabczuk, Timon},
  title     = {On the numerical stability and mass-lumping schemes for explicit enriched meshfree methods},
  series = {International Journal for Numerical Methods in Engineering},
  journal   = {International Journal for Numerical Methods in Engineering},
  doi       = {10.1002/nme.3275},
  pages     = {1009 -- 1027},
  abstract  = {Meshfree methods (MMs) such as the element free Galerkin (EFG)method have gained popularity because of some advantages over other numerical methods such as the finite element method (FEM). A group of problems that have attracted a great deal of attention from the EFG method community includes the treatment of large deformations and dealing with strong discontinuities such as cracks. One efficient solution to model cracks is adding special enrichment functions to the standard shape functions such as extended FEM, within the FEM context, and the cracking particles method, based on EFG method. It is well known that explicit time integration in dynamic applications is conditionally stable. Furthermore, in enriched methods, the critical time step may tend to very small values leading to computationally expensive simulations. In this work, we study the stability of enriched MMs and propose two mass-lumping strategies. Then we show that the critical time step for enriched MMs based on lumped mass matrices is of the same order as the critical time step of MMs without enrichment. Moreover, we show that, in contrast to extended FEM, even with a consistent mass matrix, the critical time step does not vanish even when the crack directly crosses a node.},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{SteinLahmerBock,
  author    = {Stein, Peter and Lahmer, Tom and Bock, Sebastian},
  title     = {Synthese und Analyse von gekoppelten Modellen im konstruktiven Ingenieurbau},
  series = {Bautechnik},
  journal   = {Bautechnik},
  pages     = {8 -- 11},
  abstract  = {Synthese und Analyse von gekoppelten Modellen im konstruktiven Ingenieurbau},
  subject      = {Angewandte Mathematik},
  language  = {de}
}
@article{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{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{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{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{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{SchraderKoenke,
  author    = {Schrader, Kai and K{\"o}nke, Carsten},
  title     = {Hybrid computing models for large-scale heterogeneous 3d microstructures},
  series = {International Journal for Multiscale Computational Engineering},
  journal   = {International Journal for Multiscale Computational Engineering},
  pages     = {365 -- 377},
  abstract  = {Hybrid computing models for large-scale heterogeneous 3d microstructures},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{SavaidisVormwald,
  author    = {Savaidis, G. and Vormwald, Michael},
  title     = {Hot-spot stress evaluation of fatigue in welded structural connections supported by finite element analysis},
  series = {International Journal of Fatigue},
  journal   = {International Journal of Fatigue},
  pages     = {85 -- 91},
  abstract  = {Hot-spot stress evaluation of fatigue in welded structural connections supported by finite element analysis},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{SavaidisSchliebnerVormwald,
  author    = {Savaidis, G. and Schliebner, R. and Vormwald, Michael},
  title     = {Lebensdauerermittlung von geschweißten, mehrachsig belasteten Nutzfahrzeugkomponenten - Vergleich von Schwingfestigkeiten aus Rechnung und Versuch bei nichtproportionaler Beanspruchung},
  series = {Materialpr{\"u}fung},
  journal   = {Materialpr{\"u}fung},
  pages     = {381 -- 386},
  abstract  = {Lebensdauerermittlung von geschweißten, mehrachsig belasteten Nutzfahrzeugkomponenten - Vergleich von Schwingfestigkeiten aus Rechnung und Versuch bei nichtproportionaler Beanspruchung},
  subject      = {Angewandte Mathematik},
  language  = {de}
}
@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{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{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{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{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{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{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{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{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{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{NguyenTuanKoenkeBettziecheetal.,
  author    = {Nguyen-Tuan, Long and K{\"o}nke, Carsten and Bettzieche, Volker and Lahmer, Tom},
  title     = {Numerical modeling and validation for 3D coupled-nonlinear thermo-hydro-mechanical problems in masonry dams},
  series = {Computers \& Structures},
  journal   = {Computers \& Structures},
  pages     = {143 -- 154},
  abstract  = {Numerical modeling and validation for 3D coupled-nonlinear thermo-hydro-mechanical problems in masonry dams},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{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{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{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{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{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{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{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{NguyenThanhNguyenXuanBordasetal.,
  author    = {Nguyen-Thanh, Nhon and Nguyen-Xuan, Hung and Bordas, St{\´e}phane Pierre Alain and Rabczuk, Timon},
  title     = {Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids},
  series = {Computer Methods in Applied Mechanics and Engineering},
  journal   = {Computer Methods in Applied Mechanics and Engineering},
  pages     = {1892 -- 1908},
  abstract  = {Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids},
  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{NguyenThanhKiendlNguyenXuanetal.,
  author    = {Nguyen-Thanh, Nhon and Kiendl, J. and Nguyen-Xuan, Hung and W{\"u}chner, R. and Bletzinger, Kai-Uwe and Bazilevs, Yuri and Rabczuk, Timon},
  title     = {Rotation free isogeometric thin shell analysis using PHT-splines},
  series = {Computer Methods in Applied Mechanics and Engineering},
  journal   = {Computer Methods in Applied Mechanics and Engineering},
  pages     = {3410 -- 3424},
  abstract  = {Rotation free isogeometric thin shell analysis using PHT-splines},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{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{NatarajanChakrabortyThangaveletal.,
  author    = {Natarajan, S. and Chakraborty, S. and Thangavel, M. and Bordas, St{\´e}phane Pierre Alain and Rabczuk, Timon},
  title     = {Size dependent free flexural vibration behavior of functionally graded nanoplates},
  series = {Computational Materials Science},
  journal   = {Computational Materials Science},
  pages     = {74 -- 80},
  abstract  = {Size dependent free flexural vibration behavior of functionally graded nanoplates},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{NasserSchwedlerWuttkeetal.,
  author    = {Nasser, Mourad and Schwedler, Michael and Wuttke, Frank and K{\"o}nke, Carsten},
  title     = {Seismic analysis of structural response using simplified soil-structure interaction models},
  series = {Bauingenieur, D-A-CH-Mitteilungsblatt},
  journal   = {Bauingenieur, D-A-CH-Mitteilungsblatt},
  abstract  = {Seismic analysis of structural response using simplified soil-structure interaction models},
  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{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{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{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{MsekhSargadoJamshidianetal.,
  author    = {Msekh, Mohammed Abdulrazzak and Sargado, M. and Jamshidian, M. and Areias, Pedro and Rabczuk, Timon},
  title     = {ABAQUS implementation of phase_field model for brittle fracture},
  series = {Computational Materials Science},
  journal   = {Computational Materials Science},
  pages     = {472 -- 484},
  abstract  = {ABAQUS implementation of phase_field model for brittle fracture},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@phdthesis{Msekh,
  author    = {Msekh, Mohammed Abdulrazzak},
  title     = {Phase Field Modeling for Fracture with Applications to Homogeneous and Heterogeneous Materials},
  doi       = {10.25643/bauhaus-universitaet.3229},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170615-32291},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {190},
  abstract  = {The thesis presents an implementation including different applications of a variational-based approach for gradient type standard dissipative solids. Phase field model for brittle fracture is an application of the variational-based framework for gradient type solids. This model allows the prediction of different crack topologies and states. Of significant concern is the application of theoretical and numerical formulation of the phase field modeling into the commercial finite element software Abaqus in 2D and 3D. The fully coupled incremental variational formulation of phase field method is implemented by using the UEL and UMAT subroutines of Abaqus. The phase field method considerably reduces the implementation complexity of fracture problems as it removes the need for numerical tracking of discontinuities in the displacement field that are characteristic of discrete crack methods. This is accomplished by replacing the sharp discontinuities with a scalar damage phase field representing the diffuse crack topology wherein the amount of diffusion is controlled by a regularization parameter. The nonlinear coupled system consisting of the linear momentum equation and a diffusion type equation governing the phase field evolution is solved simultaneously via a Newton- Raphson approach. Post-processing of simulation results to be used as visualization module is performed via an additional UMAT subroutine implemented in the standard Abaqus viewer. In the same context, we propose a simple yet effective algorithm to initiate and propagate cracks in 2D geometries which is independent of both particular constitutive laws and specific element technology and dimension. It consists of a localization limiter in the form of the screened Poisson equation with, optionally, local mesh refinement. A staggered scheme for standard equilibrium and screened Cauchy equations is used. The remeshing part of the algorithm consists of a sequence of mesh subdivision and element erosion steps. Element subdivision is based on edge split operations using a given constitutive quantity (either damage or void fraction). Mesh smoothing makes use of edge contraction as function of a given constitutive quantity such as the principal stress or void fraction. To assess the robustness and accuracy of this algorithm, we use both quasi-brittle benchmarks and ductile tests. Furthermore, we introduce a computational approach regarding mechanical loading in microscale on an inelastically deforming composite material. The nanocomposites material of fully exfoliated clay/epoxy is shaped to predict macroscopic elastic and fracture related material parameters based on their fine-scale features. Two different configurations of polymer nanocomposites material (PNCs) have been studied. These configurations are fully bonded PNCs and PNCs with an interphase zone formation between the matrix and the clay reinforcement. The representative volume element of PNCs specimens with different clay weight contents, different aspect ratios, and different interphase zone thicknesses are generated by adopting Python scripting. Different constitutive models are employed for the matrix, the clay platelets, and the interphase zones. The brittle fracture behavior of the epoxy matrix and the interphase zones material are modeled using the phase field approach, whereas the stiff silicate clay platelets of the composite are designated as a linear elastic material. The comprehensive study investigates the elastic and fracture behavior of PNCs composites, in addition to predict Young's modulus, tensile strength, fracture toughness, surface energy dissipation, and cracks surface area in the composite for different material parameters, geometry, and interphase zones properties and thicknesses.},
  subject      = {Finite-Elemente-Methode},
  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{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{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{MostBucher,
  author    = {Most, Thomas and Bucher, Christian},
  title     = {New concepts for moving least squares: An interpolating non-singular weighting function and weighted nodal least squares},
  series = {Engineering Analysis with Boundary Elements},
  journal   = {Engineering Analysis with Boundary Elements},
  pages     = {461 -- 470},
  abstract  = {New concepts for moving least squares: An interpolating non-singular weighting function and weighted nodal least squares},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{MostBucher,
  author    = {Most, Thomas and Bucher, Christian},
  title     = {Probabilistic analysis of concrete cracking using neural networks and random fields},
  series = {Probabilistic Engineering Mechanics},
  journal   = {Probabilistic Engineering Mechanics},
  pages     = {219 -- 229},
  abstract  = {Probabilistic analysis of concrete cracking using neural networks and random fields},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{MostBucher,
  author    = {Most, Thomas and Bucher, Christian},
  title     = {Stochastic simulation of cracking in concrete structures using multi-parameter random fields},
  series = {International Journal of Reliability and Safety},
  journal   = {International Journal of Reliability and Safety},
  pages     = {168 -- 187},
  abstract  = {Stochastic simulation of cracking in concrete structures using multi-parameter random fields},
  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{MortazaviRabczuk,
  author    = {Mortazavi, Bohayra and Rabczuk, Timon},
  title     = {Multiscale modeling of heat conduction in graphene laminates},
  series = {Carbon},
  journal   = {Carbon},
  pages     = {1 -- 7},
  abstract  = {Multiscale modeling of heat conduction in graphene laminates},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{MortazaviCunibertiRabczuk,
  author    = {Mortazavi, Bohayra and Cuniberti, G. and Rabczuk, Timon},
  title     = {Mechanical properties and thermal conductivity of graphitic carbon nitride: A molecular dynamics study},
  series = {Computational Materials Science},
  journal   = {Computational Materials Science},
  pages     = {285 -- 289},
  abstract  = {Mechanical properties and thermal conductivity of graphitic carbon nitride: A molecular dynamics study},
  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{MackeHiguchi,
  author    = {Macke, M. and Higuchi, Shoko},
  title     = {Optimizing maintenance interventions for deteriorating structures using cost-benefit criteria},
  series = {Journal of Structural Engineering},
  journal   = {Journal of Structural Engineering},
  pages     = {925 -- 934},
  abstract  = {Optimizing maintenance interventions for deteriorating structures using cost-benefit criteria},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{LuuMartinezRodrigoZabeletal.,
  author    = {Luu, M. and Martinez-Rodrigo, M.D. and Zabel, Volkmar and K{\"o}nke, Carsten},
  title     = {H∞ optimization of fluid viscous dampers for reducing vibrations of high-speed railway bridges},
  series = {Journal of Sound and Vibration},
  journal   = {Journal of Sound and Vibration},
  pages     = {2421 -- 2442},
  abstract  = {H∞ optimization of fluid viscous dampers for reducing vibrations of high-speed railway bridges},
  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{LutherKoenke,
  author    = {Luther, Torsten and K{\"o}nke, Carsten},
  title     = {Polycrystal models for the analysis of intergranular crack growth in metallic materials},
  series = {Engineering Fracture Mechanics},
  journal   = {Engineering Fracture Mechanics},
  pages     = {2332 -- 2343},
  abstract  = {Polycrystal models for the analysis of intergranular crack growth in metallic materials},
  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{LahmerNguyenTuanKoenkeetal.,
  author    = {Lahmer, Tom and Nguyen-Tuan, Long and K{\"o}nke, Carsten and Bettzieche, Volker},
  title     = {Thermo-hydro-mechanische 3-D-Simulation von Staumauern-Modellierung und Validierung},
  series = {WASSERWIRTSCHAFT},
  journal   = {WASSERWIRTSCHAFT},
  pages     = {27 -- 30},
  abstract  = {Thermo-hydro-mechanische 3-D-Simulation von Staumauern-Modellierung und Validierung},
  subject      = {Angewandte Mathematik},
  language  = {de}
}