@article{ChauDinhZiLeeetal.,
  author    = {Chau-Dinh, T. and Zi, Goangseup and Lee, P.S. and Song, Jeong-Hoon and Rabczuk, Timon},
  title     = {Phantom-node method for shell models with arbitrary cracks},
  series = {Computers \& Structures},
  journal   = {Computers \& Structures},
  doi       = {10.1016/j.compstruc.2011.10.021},
  abstract  = {A phantom-node method is developed for three-node shell elements to describe cracks. This method can treat arbitrary cracks independently of the mesh. The crack may cut elements completely or partially. Elements are overlapped on the position of the crack, and they are partially integrated to implement the discontinuous displacement across the crack. To consider the element containing a crack tip, a new kinematical relation between the overlapped elements is developed. There is no enrichment function for the discontinuous displacement field. Several numerical examples are presented to illustrate the proposed method.},
  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}
}