@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{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{ZhaoGuoRabczuk,
  author    = {Zhao, Jun-Hua and Guo, Wanlin and Rabczuk, Timon},
  title     = {An analytical molecular mechanics model for the elastic properties of crystalline polyethylene},
  series = {Journal of Applied Physics},
  journal   = {Journal of Applied Physics},
  doi       = {10.1063/1.4745035},
  abstract  = {We present an analytical model to relate the elastic properties of crystalline polyethylene based on a molecular mechanics approach. Along the polymer chains direction, the united-atom (UA) CH2-CH2 bond stretching, angle bending potentials are replaced with equivalent Euler-Bernoulli beams. Between any two polymer chains, the explicit formulae are derived for the van der Waals interaction represented by the linear springs of different stiffness. Then, the nine independent elastic constants are evaluated systematically using the formulae. The analytical model is finally validated by present united-atom molecular dynamics (MD) simulations and against available all-atom molecular dynamics results in the literature. The established analytical model provides an efficient route for mechanical characterization of crystalline polymers and related materials.},
  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{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}
}