@inproceedings{GhorashiRabczukRodenasGarciaetal.,
  author    = {Ghorashi, Seyed Shahram and Rabczuk, Timon and R{\´o}denas Garc{\´i}a, Juan Jos{\´e} and Lahmer, Tom},
  title     = {T-SPLINE BASED XIGA FOR ADAPTIVE MODELING OF CRACKED BODIES},
  series = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar},
  booktitle = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar},
  editor    = {G{\"u}rlebeck, Klaus and Lahmer, Tom and Werner, Frank},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  issn      = {1611-4086},
  doi       = {10.25643/bauhaus-universitaet.2763},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-27637},
  pages     = {13},
  abstract  = {Safety operation of important civil structures such as bridges can be estimated by using fracture analysis. Since the analytical methods are not capable of solving many complicated engineering problems, numerical methods have been increasingly adopted. In this paper, a part of isotropic material which contains a crack is considered as a partial model and the proposed model quality is evaluated. EXtended IsoGeometric Analysis (XIGA) is a new developed numerical approach [1, 2] which benefits from advantages of its origins: eXtended Finite Element Method (XFEM) and IsoGeometric Analysis (IGA). It is capable of simulating crack propagation problems with no remeshing necessity and capturing singular field at the crack tip by using the crack tip enrichment functions. Also, exact representation of geometry is possible using only few elements. XIGA has also been successfully applied for fracture analysis of cracked orthotropic bodies [3] and for simulation of curved cracks [4]. XIGA applies NURBS functions for both geometry description and solution field approximation. The drawback of NURBS functions is that local refinement cannot be defined regarding that it is based on tensorproduct constructs unless multiple patches are used which has also some limitations. In this contribution, the XIGA is further developed to make the local refinement feasible by using Tspline basis functions. Adopting a recovery based error estimator in the proposed approach for evaluation of the model quality and performing the adaptive processes is in progress. Finally, some numerical examples with available analytical solutions are investigated by the developed scheme.},
  subject      = {Angewandte Informatik},
  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}
}
@article{VuBacLahmerZhuangetal.,
  author    = {Vu-Bac, N. and Lahmer, Tom and Zhuang, Xiaoying and Nguyen-Thoi, T. and Rabczuk, Timon},
  title     = {A software framework for probabilistic sensitivity analysis for computationally expensive models},
  series = {Advances in Engineering Software},
  journal   = {Advances in Engineering Software},
  pages     = {19 -- 31},
  abstract  = {A software framework for probabilistic sensitivity analysis for computationally expensive models},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{NanthakumarLahmerZhuangetal.,
  author    = {Nanthakumar, S.S. and Lahmer, Tom and Zhuang, Xiaoying and Park, Harold S. and Rabczuk, Timon},
  title     = {Topology optimization of piezoelectric nanostructures},
  series = {Journal of the Mechanics and Physics of Solids},
  journal   = {Journal of the Mechanics and Physics of Solids},
  pages     = {316 -- 335},
  abstract  = {Topology optimization of piezoelectric nanostructures},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{NguyenVinhBakarMsekhetal.,
  author    = {Nguyen-Vinh, H. and Bakar, I. and Msekh, Mohammed Abdulrazzak and Song, Jeong-Hoon and Muthu, Jacob and Zi, Goangseup and Le, P. and Bordas, St{\´e}phane Pierre Alain and Simpson, R. and Natarajan, S. and Lahmer, Tom and Rabczuk, Timon},
  title     = {Extended Finite Element Method for Dynamic Fracture of Piezo-Electric Materials},
  series = {Engineering Fracture Mechanics},
  journal   = {Engineering Fracture Mechanics},
  doi       = {10.1016/j.engfracmech.2012.04.025},
  pages     = {19 -- 31},
  abstract  = {We present an extended finite element formulation for dynamic fracture of piezo-electric materials. The method is developed in the context of linear elastic fracture mechanics. It is applied to mode I and mixed mode-fracture for quasi-steady cracks. An implicit time integration scheme is exploited. The results are compared to results obtained with the boundary element method and show excellent agreement.},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{GhorashiLahmerBagherzadehetal.,
  author    = {Ghorashi, Seyed Shahram and Lahmer, Tom and Bagherzadeh, Amir Saboor and Zi, Goangseup and Rabczuk, Timon},
  title     = {A stochastic computational method based on goal-oriented error estimation for heterogeneous geological materials},
  series = {Engineering Geology},
  journal   = {Engineering Geology},
  abstract  = {A stochastic computational method based on goal-oriented error estimation for heterogeneous geological materials},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{NanthakumarLahmerZhuangetal.,
  author    = {Nanthakumar, S.S. and Lahmer, Tom and Zhuang, Xiaoying and Zi, Goangseup and Rabczuk, Timon},
  title     = {Detection of material interfaces using a regularized level set method in piezoelectric structures},
  series = {Inverse Problems in Science and Engineering},
  journal   = {Inverse Problems in Science and Engineering},
  pages     = {153 -- 176},
  abstract  = {Detection of material interfaces using a regularized level set method in piezoelectric structures},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{AreiasRabczuk,
  author    = {Areias, Pedro and Rabczuk, Timon},
  title     = {Finite strain fracture of plates and shells with configurational forces and edge rotation},
  series = {International Journal for Numerical Methods in Engineering},
  journal   = {International Journal for Numerical Methods in Engineering},
  abstract  = {Finite strain fracture of plates and shells with configurational forces and edge rotation},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{BanihaniRabczukAlmomani,
  author    = {Banihani, Suleiman and Rabczuk, Timon and Almomani, Thakir},
  title     = {POD for real-time simulation of hyperelastic soft biological tissue using the point collocation method of finite spheres},
  series = {Mathematical Problems in Engineering},
  journal   = {Mathematical Problems in Engineering},
  doi       = {10.1155/2013/386501},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170413-31203},
  abstract  = {The point collocation method of finite spheres (PCMFS) is used to model the hyperelastic response of soft biological tissue in real time within the framework of virtual surgery simulation. The proper orthogonal decomposition (POD) model order reduction (MOR) technique was used to achieve reduced-order model of the problem, minimizing computational cost. The PCMFS is a physics-based meshfree numerical technique for real-time simulation of surgical procedures where the approximation functions are applied directly on the strong form of the boundary value problem without the need for integration, increasing computational efficiency. Since computational speed has a significant role in simulation of surgical procedures, the proposed technique was able to model realistic nonlinear behavior of organs in real time. Numerical results are shown to demonstrate the effectiveness of the new methodology through a comparison between full and reduced analyses for several nonlinear problems. It is shown that the proposed technique was able to achieve good agreement with the full model; moreover, the computational and data storage costs were significantly reduced.},
  subject      = {Chirurgie},
  language  = {en}
}
@article{ZhaoLuZhangetal.,
  author    = {Zhao, Jun-Hua and Lu, Lixin and Zhang, Zhiliang and Guo, Wanlin and Rabczuk, Timon},
  title     = {Continuum modeling of the cohesive energy for the interfaces between _lms, spheres, coats and substrates},
  series = {Computational Materials Science},
  journal   = {Computational Materials Science},
  pages     = {432 -- 438},
  abstract  = {Continuum modeling of the cohesive energy for the interfaces between _lms, spheres, coats and substrates},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{BenZhaoZhangetal.,
  author    = {Ben, S. and Zhao, Jun-Hua and Zhang, Yancheng and Rabczuk, Timon},
  title     = {The interface strength and debonding for composite structures: review and recent developments},
  series = {Composite Structures},
  journal   = {Composite Structures},
  abstract  = {The interface strength and debonding for composite structures: review and recent developments},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{ZhaoJiaWeietal.,
  author    = {Zhao, Jun-Hua and Jia, Yue and Wei, Ning and Rabczuk, Timon},
  title     = {Binding energy and mechanical stability of two parallel and crossing carbon nanotubes},
  series = {Journal of Applied Mechanics},
  journal   = {Journal of Applied Mechanics},
  abstract  = {Binding energy and mechanical stability of two parallel and crossing carbon nanotubes},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{KumarSinghMishraetal.,
  author    = {Kumar, S. and Singh, I. and Mishra, B.K. and Rabczuk, Timon},
  title     = {Modeling and Simulation of Kinked Cracks by Virtual Node XFEM},
  series = {Computer Methods in Applied Mechanics and Engineering},
  journal   = {Computer Methods in Applied Mechanics and Engineering},
  pages     = {1425 -- 1466},
  abstract  = {Modeling and Simulation of Kinked Cracks by Virtual Node XFEM},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{NanthakumarLahmerRabczuk,
  author    = {Nanthakumar, S.S. and Lahmer, Tom and Rabczuk, Timon},
  title     = {Detection of flaws in piezoelectric structures using extended FEM},
  series = {International Journal for Numerical Methods in Engineering},
  journal   = {International Journal for Numerical Methods in Engineering},
  pages     = {373 -- 389},
  abstract  = {Detection of flaws in piezoelectric structures using extended FEM},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{ZhaoWeiFanetal.,
  author    = {Zhao, Jun-Hua and Wei, Ning and Fan, Z. and Jiang, Jin-Wu and Rabczuk, Timon},
  title     = {Mechanical properties of three types of carbon allotropes},
  series = {Nanotechnology},
  journal   = {Nanotechnology},
  abstract  = {Mechanical properties of three types of carbon allotropes},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{AreiasRabczukDiasdaCostaetal.,
  author    = {Areias, Pedro and Rabczuk, Timon and Dias-da-Costa, D. and Piresh, E.B.},
  title     = {Implicit solutions with consistent additive and multiplicative components},
  series = {Finite Elements in Analysis and Design},
  journal   = {Finite Elements in Analysis and Design},
  doi       = {10.1016/j.finel.2012.03.007},
  pages     = {15 -- 31},
  abstract  = {This work describes an algorithm and corresponding software for incorporating general nonlinear multiple-point equality constraints in a implicit sparse direct solver. It is shown that direct addressing of sparse matrices is possible in general circumstances, circumventing the traditional linear or binary search for introducing (generalized) constituents to a sparse matrix. Nested and arbitrarily interconnected multiple-point constraints are introduced by processing of multiplicative constituents with a built-in topological ordering of the resulting directed graph. A classification of discretization methods is performed and some re-classified problems are described and solved under this proposed perspective. The dependence relations between solution methods, algorithms and constituents becomes apparent. Fracture algorithms can be naturally casted in this framework. Solutions based on control equations are also directly incorporated as equality constraints. We show that arbitrary constituents can be used as long as the resulting directed graph is acyclic. It is also shown that graph partitions and orderings should be performed in the innermost part of the algorithm, a fact with some peculiar consequences. The core of our implicit code is described, specifically new algorithms for direct access of sparse matrices (by means of the clique structure) and general constituent processing. It is demonstrated that the graph structure of the second derivatives of the equality constraints are cliques (or pseudo-elements) and are naturally included as such. A complete algorithm is presented which allows a complete automation of equality constraints, avoiding the need of pre-sorting. Verification applications in four distinct areas are shown: single and multiple rigid body dynamics, solution control and computational fracture.},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{JiangRabczukPark,
  author    = {Jiang, Jin-Wu and Rabczuk, Timon and Park, Harold S.},
  title     = {A Stillinger-Weber Potential for Single-Layer Black Phosphorus, and the Importance of Cross-Pucker Interactions for Negative Poisson's Ratio and Edge Stress-Induced Bending},
  series = {Nanoscale},
  journal   = {Nanoscale},
  doi       = {10.1039/C4NR07341J},
  abstract  = {The distinguishing structural feature of single-layered black phosphorus is its puckered structure, which leads to many novel physical properties. In this work, we first present a new parameterization of the Stillinger-Weber potential for single-layered black phosphorus. In doing so, we reveal the importance of a cross-pucker interaction term in capturing its unique mechanical properties, such as a negative Poisson's ratio. In particular, we show that the cross-pucker interaction enables the pucker to act as a re-entrant hinge, which expands in the lateral direction when it is stretched in the longitudinal direction. As a consequence, single-layered black phosphorus has a negative Poisson's ratio in the direction perpendicular to the atomic plane. As an additional demonstration of the impact of the cross-pucker interaction, we show that it is also the key factor that enables capturing the edge stress-induced bending of single-layered black phosphorus that has been reported in ab initio calculations.},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{TalebiSilaniRabczuk,
  author    = {Talebi, Hossein and Silani, Mohammad and Rabczuk, Timon},
  title     = {Concurrent Multiscale Modelling of Three Dimensional Crack and Dislocation Propagation},
  series = {Advances in Engineering Software},
  journal   = {Advances in Engineering Software},
  pages     = {82 -- 92},
  abstract  = {Concurrent Multiscale Modelling of Three Dimensional Crack and Dislocation Propagation},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{XuMourrainGalligoetal.,
  author    = {Xu, G. and Mourrain, B. and Galligo, A. and Rabczuk, Timon},
  title     = {High-quality construction of analysis-suitable trivariate NURBS solids by reparameterization methods},
  series = {Computational Mechanics},
  journal   = {Computational Mechanics},
  abstract  = {High-quality construction of analysis-suitable trivariate NURBS solids by reparameterization methods},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{PhanDaoNguyenXuanThaiHoangetal.,
  author    = {Phan-Dao, H. and Nguyen-Xuan, Hung and Thai-Hoang, C. and Nguyen-Thoi, T. and Rabczuk, Timon},
  title     = {An edge-based smoothed finite element method for analysis of laminated composite plates},
  series = {International Journal of Computational Methods},
  journal   = {International Journal of Computational Methods},
  abstract  = {An edge-based smoothed finite element method for analysis of laminated composite plates},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{SilaniZiaeiRadTalebietal.,
  author    = {Silani, Mohammad and Ziaei-Rad, S. and Talebi, Hossein and Rabczuk, Timon},
  title     = {A Semi-Concurrent Multiscale Approach for Modeling Damage in Nanocomposites},
  series = {Theoretical and Applied Fracture Mechanics},
  journal   = {Theoretical and Applied Fracture Mechanics},
  abstract  = {A Semi-Concurrent Multiscale Approach for Modeling Damage in Nanocomposites},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{AmaniBagherzadehRabczuk,
  author    = {Amani, Jafar and Bagherzadeh, Amir Saboor and Rabczuk, Timon},
  title     = {Error estimate and adaptive refinement in Mixed Discrete Least Squares Meshless method},
  series = {Mathematical Problems in Engineering},
  journal   = {Mathematical Problems in Engineering},
  abstract  = {Error estimate and adaptive refinement in Mixed Discrete Least Squares Meshless method},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{JiangWangRabczuk,
  author    = {Jiang, Jin-Wu and Wang, Bing-Shen and Rabczuk, Timon},
  title     = {Acoustic and breathing phonon modes in bilayer graphene with Moire-acute patterns},
  series = {Applied Physics Letters},
  journal   = {Applied Physics Letters},
  doi       = {10.1063/1.4735246},
  abstract  = {The lattice dynamics properties are investigated for twisting bilayer graphene. There are big jumps for the inter-layer potential at twisting angle θ=0° and 60°, implying the stability of Bernal-stacking and the instability of AA-stacking structures, while a long platform in [8,55]° indicates the ease of twisting bilayer graphene in this wide angle range. Significant frequency shifts are observed for the z breathing mode around θ=0° and 60°, while the frequency is a constant in a wide range [8,55]°. Using the z breathing mode, a mechanical nanoresonator is proposed to operate on a robust resonant frequency in terahertz range.},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{GhasemiBrighentiZhuangetal.,
  author    = {Ghasemi, Hamid and Brighenti, Roberto and Zhuang, Xiaoying and Muthu, Jacob and Rabczuk, Timon},
  title     = {Optimum fiber content and distribution in fiber-reinforced solids using a reliability and NURBS based sequential optimization approach},
  series = {Structural and Multidisciplinary Optimization},
  journal   = {Structural and Multidisciplinary Optimization},
  pages     = {99 -- 112},
  abstract  = {Optimum _ber content and distribution in _ber-reinforced solids using a reliability and NURBS based sequential optimization approach},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{AreiasRabczukCesardeSaetal.,
  author    = {Areias, Pedro and Rabczuk, Timon and Cesar de Sa, J.M. and Jorge, R.N.},
  title     = {A semi-implicit _nite strain shell algorithm using in-plane strains based on least-squares},
  series = {Computational Mechanics},
  journal   = {Computational Mechanics},
  abstract  = {A semi-implicit _nite strain shell algorithm using in-plane strains based on least-squares},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{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{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{JiangZhaoZhouetal.,
  author    = {Jiang, Jin-Wu and Zhao, Jun-Hua and Zhou, K. and Rabczuk, Timon},
  title     = {Superior thermal conductivity and extremely high mechanical strength in polyethylene chains from ab initio calculation},
  series = {Journal of Applied Physics},
  journal   = {Journal of Applied Physics},
  doi       = {10.1063/1.4729489},
  abstract  = {The upper limit of the thermal conductivity and the mechanical strength are predicted for the polyethylene chain, by performing the ab initio calculation and applying the quantum mechanical non-equilibrium Green's function approach. Specially, there are two main findings from our calculation: (1) the thermal conductivity can reach a high value of 310 Wm-1 K-1 in a 100 nm polyethylene chain at room temperature and the thermal conductivity increases with the length of the chain; (2) the Young's modulus in the polyethylene chain is as high as 374.5 GPa, and the polyethylene chain can sustain 32.85\%±0.05\% (ultimate) strain before undergoing structural phase transition into gaseous ethylene.},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{AreiasRabczukBarbosa,
  author    = {Areias, Pedro and Rabczuk, Timon and Barbosa, J.I.},
  title     = {The extended unsymmetric frontal solution for multiple-point constraints},
  series = {Engineering Computations},
  journal   = {Engineering Computations},
  abstract  = {The extended unsymmetric frontal solution for multiple-point constraints},
  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{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{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{JoshiHildebrandAloraieretal.,
  author    = {Joshi, Suraj and Hildebrand, J{\"o}rg and Aloraier, Abdulkareem S. and Rabczuk, Timon},
  title     = {Characterization of material properties and heat source parameters in welding simulation of two overlapping beads on a substrate plate},
  series = {Computational Materials Science},
  journal   = {Computational Materials Science},
  doi       = {10.1016/j.commatsci.2012.11.029},
  pages     = {559 -- 565},
  abstract  = {This paper presents several aspects of characterization of welding heat source parameters in Goldak's double ellipsoidal model using Sysweld simulation of welding of two overlapping beads on a substrate steel plate. The overlap percentages ranged from 40\% to 80\% in increments of 10\%. The new material properties of the fused metal were characterized using Weldware and their continuous cooling transformation curves. The convective and radiative heat transfer coefficients as well as the cooling time t8/5 were estimated using numerical formulations from relevant standards. The effects of the simulation geometry and mesh discretization were evaluated in terms of the factor F provided in Sysweld. Eventually, the parameters of Goldak's double ellipsoidal heat source model were determined for the welding simulation of overlapping beads on the plate and the simulated bead geometry, extent of the molten pool and the HAZ were compared with the macrographs of cross-sections of the experimental weldments. The results showed excellent matching, thus verifying this methodology for determination of welding heat source parameters.},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{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{JiangParkRabczuk,
  author    = {Jiang, Jin-Wu and Park, Harold S. and Rabczuk, Timon},
  title     = {Enhancing the mass sensitivity of graphene nanoresonators via nonlinear oscillations: The effective strain mechanism},
  series = {Nanotechnology},
  journal   = {Nanotechnology},
  abstract  = {Enhancing the mass sensitivity of graphene nanoresonators via nonlinear oscillations: The effective strain mechanism},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{MsekhSargadoJamshidianetal.,
  author    = {Msekh, Mohammed Abdulrazzak and Sargado, M. and Jamshidian, M. and Areias, Pedro and Rabczuk, Timon},
  title     = {ABAQUS implementation of phase_field model for brittle fracture},
  series = {Computational Materials Science},
  journal   = {Computational Materials Science},
  pages     = {472 -- 484},
  abstract  = {ABAQUS implementation of phase_field model for brittle fracture},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{RabczukGuoZhuangetal.,
  author    = {Rabczuk, Timon and Guo, Hongwei and Zhuang, Xiaoying and Chen, Pengwan and Alajlan, Naif},
  title     = {Stochastic deep collocation method based on neural architecture search and transfer learning for heterogeneous porous media},
  series = {Engineering with Computers},
  volume    = {2022},
  journal   = {Engineering with Computers},
  publisher = {Springer},
  address   = {London},
  doi       = {10.1007/s00366-021-01586-2},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220209-45835},
  pages     = {1 -- 26},
  abstract  = {We present a stochastic deep collocation method (DCM) based on neural architecture search (NAS) and transfer learning for heterogeneous porous media. We first carry out a sensitivity analysis to determine the key hyper-parameters of the network to reduce the search space and subsequently employ hyper-parameter optimization to finally obtain the parameter values. The presented NAS based DCM also saves the weights and biases of the most favorable architectures, which is then used in the fine-tuning process. We also employ transfer learning techniques to drastically reduce the computational cost. The presented DCM is then applied to the stochastic analysis of heterogeneous porous material. Therefore, a three dimensional stochastic flow model is built providing a benchmark to the simulation of groundwater flow in highly heterogeneous aquifers. The performance of the presented NAS based DCM is verified in different dimensions using the method of manufactured solutions. We show that it significantly outperforms finite difference methods in both accuracy and computational cost.},
  subject      = {Maschinelles Lernen},
  language  = {en}
}
@article{ZhaoLuRabczuk,
  author    = {Zhao, Jiyun and Lu, Lixin and Rabczuk, Timon},
  title     = {The tensile and shear failure behavior dependence on chain length and temperature in amorphous polymers},
  series = {Computational Materials Science},
  journal   = {Computational Materials Science},
  pages     = {567 -- 572},
  abstract  = {The tensile and shear failure behavior dependence on chain length and temperature in amorphous polymers},
  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{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{AnitescuJiaZhangetal.,
  author    = {Anitescu, Cosmin and Jia, Yue and Zhang, Yongjie and Rabczuk, Timon},
  title     = {An isogeometric collocation method using superconvergent points},
  series = {Computer Methods in Applied Mechanics and Engineer-ing},
  journal   = {Computer Methods in Applied Mechanics and Engineer-ing},
  pages     = {1073 -- 1097},
  abstract  = {An isogeometric collocation method using superconvergent points},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{ChakrabortyAnitescuZhuangetal.,
  author    = {Chakraborty, Ayan and Anitescu, Cosmin and Zhuang, Xiaoying and Rabczuk, Timon},
  title     = {Domain adaptation based transfer learning approach for solving PDEs on complex geometries},
  series = {Engineering with Computers},
  volume    = {2022},
  journal   = {Engineering with Computers},
  doi       = {10.1007/s00366-022-01661-2},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220811-46776},
  pages     = {1 -- 20},
  abstract  = {In machine learning, if the training data is independently and identically distributed as the test data then a trained model can make an accurate predictions for new samples of data. Conventional machine learning has a strong dependence on massive amounts of training data which are domain specific to understand their latent patterns. In contrast, Domain adaptation and Transfer learning methods are sub-fields within machine learning that are concerned with solving the inescapable problem of insufficient training data by relaxing the domain dependence hypothesis. In this contribution, this issue has been addressed and by making a novel combination of both the methods we develop a computationally efficient and practical algorithm to solve boundary value problems based on nonlinear partial differential equations. We adopt a meshfree analysis framework to integrate the prevailing geometric modelling techniques based on NURBS and present an enhanced deep collocation approach that also plays an important role in the accuracy of solutions. We start with a brief introduction on how these methods expand upon this framework. We observe an excellent agreement between these methods and have shown that how fine-tuning a pre-trained network to a specialized domain may lead to an outstanding performance compare to the existing ones. As proof of concept, we illustrate the performance of our proposed model on several benchmark problems.},
  subject      = {Maschinelles Lernen},
  language  = {en}
}
@article{ZhaoJiangJiaetal.,
  author    = {Zhao, Jun-Hua and Jiang, Jin-Wu and Jia, Yue and Guo, Wanlin and Rabczuk, Timon},
  title     = {A theoretical analysis of cohesive energy between carbon nanotubes, graphene and substrates},
  series = {Carbon},
  journal   = {Carbon},
  doi       = {10.1016/j.carbon.2013.01.041},
  pages     = {108 -- 119},
  abstract  = {Explicit solutions for the cohesive energy between carbon nanotubes, graphene and substrates are obtained through continuum modeling of the van der Waals interaction between them. The dependence of the cohesive energy on their size, spacing and crossing angles is analyzed. Checking against full atom molecular dynamics calculations and available experimental results shows that the continuum solution has high accuracy. The equilibrium distances between the nanotubes, graphene and substrates with minimum cohesive energy are also provided explicitly. The obtained analytical solution should be of great help for understanding the interaction between the nanostructures and substrates, and designing composites and nanoelectromechanical systems.},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{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{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{AreiasRabczukCesardeSaetal.,
  author    = {Areias, Pedro and Rabczuk, Timon and Cesar de Sa, J.M. and Garcao, J.E.},
  title     = {Finite strain quadrilateral shell using least-squares _t of relative Lagrangian in-plane strains},
  series = {Finite Elements in Analysis and Design},
  journal   = {Finite Elements in Analysis and Design},
  pages     = {26 -- 40},
  abstract  = {Finite strain quadrilateral shell using least-squares _t of relative Lagrangian in-plane strains},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{GhasemiKerfridenBordasetal.,
  author    = {Ghasemi, Hamid and Kerfriden, Pierre and Bordas, St{\´e}phane Pierre Alain and Muthu, Jacob and Zi, Goangseup and Rabczuk, Timon},
  title     = {Interfacial shear stress optimization in sandwich beams with polymeric core using nonuniform distribution of reinforcing ingredients},
  series = {Composite Structures},
  journal   = {Composite Structures},
  pages     = {221 -- 230},
  abstract  = {Interfacial shear stress optimization in sandwich beams with polymeric core using nonuniform distribution of reinforcing ingredients},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{ZhaoKouJiangetal.,
  author    = {Zhao, Jun-Hua and Kou, Liangzhi and Jiang, Jin-Wu and Rabczuk, Timon},
  title     = {Tension-induced phase transition of single-layer molybdenum disulphide (MoS2) at low temperatures},
  series = {Nanotechnology},
  journal   = {Nanotechnology},
  doi       = {10.1088/0957-4484/25/29/295701},
  abstract  = {Tension-induced phase transition of single-layer molybdenum disulphide (MoS2) at low temperatures},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{JiaZhangRabczuk,
  author    = {Jia, Yue and Zhang, Yongjie and Rabczuk, Timon},
  title     = {A Novel Dynamic Multilevel Technique for Image Registration},
  series = {Computers and Mathematics with Applications},
  journal   = {Computers and Mathematics with Applications},
  abstract  = {A Novel Dynamic Multilevel Technique for Image Registration},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{AreiasRabczukQueirosdeMeloetal.,
  author    = {Areias, Pedro and Rabczuk, Timon and Queiros de Melo, F. J. M. and Cesar de Sa, J.M.},
  title     = {Coulomb frictional contact by explicit projection in the cone for _nite displacement quasi-static problems},
  series = {Computational Mechanics},
  journal   = {Computational Mechanics},
  pages     = {57 -- 72},
  abstract  = {Coulomb frictional contact by explicit projection in the cone for _nite displacement quasi-static problems},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{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{GhasemiRafieeZhuangetal.,
  author    = {Ghasemi, Hamid and Rafiee, Roham and Zhuang, Xiaoying and Muthu, Jacob and Rabczuk, Timon},
  title     = {Uncertainties propagation in metamodel-based probabilistic optimization of CNT/polymer composite structure using stochastic multi-scale modeling},
  series = {Computational Materials Science},
  journal   = {Computational Materials Science},
  pages     = {295 -- 305},
  abstract  = {Uncertainties propagation in metamodel-based probabilistic optimization of CNT/polymer composite structure using stochastic multi-scale modeling},
  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{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{JiangWangRabczuk,
  author    = {Jiang, Jin-Wu and Wang, Bing-Shen and Rabczuk, Timon},
  title     = {Phonon modes in single-walled molybdenum disulphide nanotubes: lattice dynamics calculation and molecular dynamics simulation},
  series = {Nanotechnology},
  journal   = {Nanotechnology},
  abstract  = {Phonon modes in single-walled molybdenum disulphide nanotubes: lattice dynamics calculation and molecular dynamics simulation},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{ZhaoLuRabczuk,
  author    = {Zhao, Jun-Hua and Lu, Lixin and Rabczuk, Timon},
  title     = {Binding energy and mechanical stability of single- and multi-walled carbon nanotube serpentines},
  series = {The Journal of Chemical Physics},
  journal   = {The Journal of Chemical Physics},
  doi       = {10.1063/1.4878115},
  abstract  = {Binding energy and mechanical stability of single- and multi-walled carbon nanotube serpentines},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{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{ShiraziMohebbiAzadiKakavandetal.,
  author    = {Shirazi, A. H. N. and Mohebbi, Farzad and Azadi Kakavand, M. R. and He, B. and Rabczuk, Timon},
  title     = {Paraffin Nanocomposites for Heat Management of Lithium-Ion Batteries: A Computational Investigation},
  series = {JOURNAL OF NANOMATERIALS},
  journal   = {JOURNAL OF NANOMATERIALS},
  doi       = {10.1155/2016/2131946},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170411-31141},
  abstract  = {Lithium-ion (Li-ion) batteries are currently considered as vital components for advances in mobile technologies such as those in communications and transport. Nonetheless, Li-ion batteries suffer from temperature rises which sometimes lead to operational damages or may even cause fire. An appropriate solution to control the temperature changes during the operation of Li-ion batteries is to embed batteries inside a paraffin matrix to absorb and dissipate heat. In the present work, we aimed to investigate the possibility of making paraffin nanocomposites for better heat management of a Li-ion battery pack. To fulfill this aim, heat generation during a battery charging/discharging cycles was simulated using Newman's well established electrochemical pseudo-2D model. We couple this model to a 3D heat transfer model to predict the temperature evolution during the battery operation. In the later model, we considered different paraffin nanocomposites structures made by the addition of graphene, carbon nanotubes, and fullerene by assuming the same thermal conductivity for all fillers. This way, our results mainly correlate with the geometry of the fillers. Our results assess the degree of enhancement in heat dissipation of Li-ion batteries through the use of paraffin nanocomposites. Our results may be used as a guide for experimental set-ups to improve the heat management of Li-ion batteries.},
  subject      = {Batterie},
  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{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{IlyaniAkmarKramerRabczuk,
  author    = {Ilyani Akmar, A.B. and Kramer, O. and Rabczuk, Timon},
  title     = {Multi-objective evolutionary optimization of sandwich structures: An evaluation by elitist non-dominated sorting evolution strategy},
  series = {American Journal of Engineering and Applied Sciences},
  journal   = {American Journal of Engineering and Applied Sciences},
  doi       = {10.3844/ajeassp.2015.185.201},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170418-31402},
  pages     = {185 -- 201},
  abstract  = {In this study, an application of evolutionary multi-objective optimization algorithms on the optimization of sandwich structures is presented. The solution strategy is known as Elitist Non-Dominated Sorting Evolution Strategy (ENSES) wherein Evolution Strategies (ES) as Evolutionary Algorithm (EA) in the elitist Non-dominated Sorting Genetic algorithm (NSGA-II) procedure. Evolutionary algorithm seems a compatible approach to resolve multi-objective optimization problems because it is inspired by natural evolution, which closely linked to Artificial Intelligence (AI) techniques and elitism has shown an important factor for improving evolutionary multi-objective search. In order to evaluate the notion of performance by ENSES, the well-known study case of sandwich structures are reconsidered. For Case 1, the goals of the multi-objective optimization are minimization of the deflection and the weight of the sandwich structures. The length, the core and skin thicknesses are the design variables of Case 1. For Case 2, the objective functions are the fabrication cost, the beam weight and the end deflection of the sandwich structures. There are four design variables i.e., the weld height, the weld length, the beam depth and the beam width in Case 2. Numerical results are presented in terms of Paretooptimal solutions for both evaluated cases.},
  subject      = {Optimierung},
  language  = {en}
}
@article{MortazaviPereiraJiangetal.,
  author    = {Mortazavi, Bohayra and Pereira, Luiz Felipe C. and Jiang, Jin-Wu and Rabczuk, Timon},
  title     = {Modelling heat conduction in polycrystalline hexagonal boron-nitride films},
  series = {Scientific Reports},
  journal   = {Scientific Reports},
  doi       = {10.1038/srep13228},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170425-31534},
  abstract  = {We conducted extensive molecular dynamics simulations to investigate the thermal conductivity of polycrystalline hexagonal boron-nitride (h-BN) films. To this aim, we constructed large atomistic models of polycrystalline h-BN sheets with random and uniform grain configuration. By performing equilibrium molecular dynamics (EMD) simulations, we investigated the influence of the average grain size on the thermal conductivity of polycrystalline h-BN films at various temperatures. Using the EMD results, we constructed finite element models of polycrystalline h-BN sheets to probe the thermal conductivity of samples with larger grain sizes. Our multiscale investigations not only provide a general viewpoint regarding the heat conduction in h-BN films but also propose that polycrystalline h-BN sheets present high thermal conductivity comparable to monocrystalline sheets.},
  subject      = {W{\"a}rmeleitf{\"a}higkeit},
  language  = {en}
}
@article{GuoZhuangChenetal.,
  author    = {Guo, Hongwei and Zhuang, Xiaoying and Chen, Pengwan and Alajlan, Naif and Rabczuk, Timon},
  title     = {Analysis of three-dimensional potential problems in non-homogeneous media with physics-informed deep collocation method using material transfer learning and sensitivity analysis},
  series = {Engineering with Computers},
  volume    = {2022},
  journal   = {Engineering with Computers},
  doi       = {10.1007/s00366-022-01633-6},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220811-46764},
  pages     = {1 -- 22},
  abstract  = {In this work, we present a deep collocation method (DCM) for three-dimensional potential problems in non-homogeneous media. This approach utilizes a physics-informed neural network with material transfer learning reducing the solution of the non-homogeneous partial differential equations to an optimization problem. We tested different configurations of the physics-informed neural network including smooth activation functions, sampling methods for collocation points generation and combined optimizers. A material transfer learning technique is utilized for non-homogeneous media with different material gradations and parameters, which enhance the generality and robustness of the proposed method. In order to identify the most influential parameters of the network configuration, we carried out a global sensitivity analysis. Finally, we provide a convergence proof of our DCM. The approach is validated through several benchmark problems, also testing different material variations.},
  subject      = {Deep learning},
  language  = {en}
}
@article{ZhuangHuangLiangetal.,
  author    = {Zhuang, Xiaoying and Huang, Runqiu and Liang, Chao and Rabczuk, Timon},
  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},
  doi       = {10.1155/2014/179169},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170428-31726},
  abstract  = {Renewable energy resources such as wind and solar are intermittent, which causes instability when being connected to utility grid of electricity. Compressed air energy storage (CAES) provides an economic and technical viable solution to this problem by utilizing subsurface rock cavern to store the electricity generated by renewable energy in the form of compressed air. Though CAES has been used for over three decades, it is only restricted to salt rock or aquifers for air tightness reason. In this paper, the technical feasibility of utilizing hard rock for CAES is investigated by using a coupled thermo-hydro-mechanical (THM) modelling of nonisothermal gas flow. Governing equations are derived from the rules of energy balance, mass balance, and static equilibrium. Cyclic volumetric mass source and heat source models are applied to simulate the gas injection and production. Evaluation is carried out for intact rock and rock with discrete crack, respectively. In both cases, the heat and pressure losses using air mass control and supplementary air injection are compared.},
  subject      = {Energiespeicherung},
  language  = {en}
}
@article{AmaniSaboorBagherzadehRabczuk,
  author    = {Amani, Jafar and Saboor Bagherzadeh, Amir and Rabczuk, Timon},
  title     = {Error estimate and adaptive refinement in mixed discrete least squares meshless method},
  series = {Mathematical Problems in Engineering},
  journal   = {Mathematical Problems in Engineering},
  doi       = {10.1155/2014/721240},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170413-31181},
  abstract  = {The node moving and multistage node enrichment adaptive refinement procedures are extended in mixed discrete least squares meshless (MDLSM) method for efficient analysis of elasticity problems. In the formulation of MDLSM method, mixed formulation is accepted to avoid second-order differentiation of shape functions and to obtain displacements and stresses simultaneously. In the refinement procedures, a robust error estimator based on the value of the least square residuals functional of the governing differential equations and its boundaries at nodal points is used which is inherently available from the MDLSM formulation and can efficiently identify the zones with higher numerical errors. The results are compared with the refinement procedures in the irreducible formulation of discrete least squares meshless (DLSM) method and show the accuracy and efficiency of the proposed procedures. Also, the comparison of the error norms and convergence rate show the fidelity of the proposed adaptive refinement procedures in the MDLSM method.},
  subject      = {Elastizit{\"a}t},
  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{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{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{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{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{BudarapuNarayanaRammohanetal.,
  author    = {Budarapu, Pattabhi Ramaiah and Narayana, T.S.S. and Rammohan, B. and Rabczuk, Timon},
  title     = {Directionality of sound radiation from rectangular panels},
  series = {Applied Acoustics},
  journal   = {Applied Acoustics},
  pages     = {128 -- 140},
  abstract  = {Directionality of sound radiation from rectangular panels},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{ZhangZhaoWeietal.,
  author    = {Zhang, Yancheng and Zhao, Jiyun and Wei, Ning and Jiang, Jin-Wu and Rabczuk, Timon},
  title     = {Effects of the dispersion of polymer wrapped two neighbouring single walled carbon nanotubes (SWNTs) on nanoengineering load transfer},
  series = {Composites Part B: Engineering},
  journal   = {Composites Part B: Engineering},
  pages     = {1714 -- 1721},
  abstract  = {Effects of the dispersion of polymer wrapped two neighbouring single walled carbon nanotubes (SWNTs) on nanoengineering load transfer},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{BudarapuGracieYangetal.,
  author    = {Budarapu, Pattabhi Ramaiah and Gracie, Robert and Yang, Shih-Wei and Zhuang, Xiaoying and Rabczuk, Timon},
  title     = {Efficient Coarse Graining in Multiscale Modeling of Fracture},
  series = {Theoretical and Applied Fracture Mechanics},
  journal   = {Theoretical and Applied Fracture Mechanics},
  pages     = {126 -- 143},
  abstract  = {Efficient Coarse Graining in Multiscale Modeling of Fracture},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{ArashRabczukJiang,
  author    = {Arash, Behrouz and Rabczuk, Timon and Jiang, Jin-Wu},
  title     = {Nanoresonators and their applications: a state of the art review},
  series = {Applied Physics Reviews},
  journal   = {Applied Physics Reviews},
  abstract  = {Nanoresonators and their applications: a state of the art review},
  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{ChenRabczukLiuetal.,
  author    = {Chen, Lei and Rabczuk, Timon and Liu, G.R. and Zeng, K.Y. and Kerfriden, Pierre and Bordas, St{\´e}phane Pierre Alain},
  title     = {Extended finite element method with edge-based strain smoothing (ESm-XFEM) for linear elastic crack growth},
  series = {Computer Methods in Applied Mechanics and Engineering},
  journal   = {Computer Methods in Applied Mechanics and Engineering},
  doi       = {10.1016/j.cma.2011.08.013},
  abstract  = {This paper presents a strain smoothing procedure for the extended finite element method (XFEM). The resulting "edge-based" smoothed extended finite element method (ESm-XFEM) is tailored to linear elastic fracture mechanics and, in this context, to outperform the standard XFEM. In the XFEM, the displacement-based approximation is enriched by the Heaviside and asymptotic crack tip functions using the framework of partition of unity. This eliminates the need for the mesh alignment with the crack and re-meshing, as the crack evolves. Edge-based smoothing (ES) relies on a generalized smoothing operation over smoothing domains associated with edges of simplex meshes, and produces a softening effect leading to a close-to-exact stiffness, "super-convergence" and "ultra-accurate" solutions. The present method takes advantage of both the ES-FEM and the XFEM. Thanks to the use of strain smoothing, the subdivision of elements intersected by discontinuities and of integrating the (singular) derivatives of the approximation functions is suppressed via transforming interior integration into boundary integration. Numerical examples show that the proposed method improves significantly the accuracy of stress intensity factors and achieves a near optimal convergence rate in the energy norm even without geometrical enrichment or blending correction.},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{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{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{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{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{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{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{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{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{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{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{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{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{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}
}