@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}
}