@article{RenZhuangOterkusetal.,
  author    = {Ren, Huilong and Zhuang, Xiaoying and Oterkus, Erkan and Zhu, Hehua and Rabczuk, Timon},
  title     = {Nonlocal strong forms of thin plate, gradient elasticity, magneto-electro-elasticity and phase-field fracture by nonlocal operator method},
  series = {Engineering with Computers},
  volume    = {2021},
  journal   = {Engineering with Computers},
  doi       = {10.1007/s00366-021-01502-8},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20211207-45388},
  pages     = {1 -- 22},
  abstract  = {The derivation of nonlocal strong forms for many physical problems remains cumbersome in traditional methods. In this paper, we apply the variational principle/weighted residual method based on nonlocal operator method for the derivation of nonlocal forms for elasticity, thin plate, gradient elasticity, electro-magneto-elasticity and phase-field fracture method. The nonlocal governing equations are expressed as an integral form on support and dual-support. The first example shows that the nonlocal elasticity has the same form as dual-horizon non-ordinary state-based peridynamics. The derivation is simple and general and it can convert efficiently many local physical models into their corresponding nonlocal forms. In addition, a criterion based on the instability of the nonlocal gradient is proposed for the fracture modelling in linear elasticity. Several numerical examples are presented to validate nonlocal elasticity and the nonlocal thin plate.},
  subject      = {Bruchmechanik},
  language  = {en}
}
@article{VuBacNguyenXuanChenetal.,
  author    = {Vu-Bac, N. and Nguyen-Xuan, Hung and Chen, Lei and Lee, C.K. and Zi, Goangseup and Zhuang, Xiaoying and Liu, G.R. and Rabczuk, Timon},
  title     = {A phantom-node method with edge-based strain smoothing for linear elastic fracture mechanics},
  series = {Journal of Applied Mathematics},
  journal   = {Journal of Applied Mathematics},
  doi       = {10.1155/2013/978026},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170426-31676},
  abstract  = {This paper presents a novel numerical procedure based on the combination of an edge-based smoothed finite element (ES-FEM) with a phantom-node method for 2D linear elastic fracture mechanics. In the standard phantom-node method, the cracks are formulated by adding phantom nodes, and the cracked element is replaced by two new superimposed elements. This approach is quite simple to implement into existing explicit finite element programs. The shape functions associated with discontinuous elements are similar to those of the standard finite elements, which leads to certain simplification with implementing in the existing codes. The phantom-node method allows modeling discontinuities at an arbitrary location in the mesh. The ES-FEM model owns a close-to-exact stiffness that is much softer than lower-order finite element methods (FEM). Taking advantage of both the ES-FEM and the phantom-node method, we introduce an edge-based strain smoothing technique for the phantom-node method. Numerical results show that the proposed method achieves high accuracy compared with the extended finite element method (XFEM) and other reference solutions.},
  subject      = {Finite-Elemente-Methode},
  language  = {en}
}