Numerical simulations of strain localization in inelastic solids using mesh-free methods

Shaofan Li*, Wing K Liu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

81 Scopus citations


In this paper, a comprehensive account on using mesh-free methods to simulate strain localization in inelastic solids is presented. Using an explicit displacement-based formulation in mesh-free computations, high-resolution shear-band formations are obtained in both two-dimensional (2-D) and three-dimensional (3-D) simulations without recourse to any mixed formulation, discontinuous/incompatible element or special mesh design. The numerical solutions obtained here are insensitive to the orientation of the particle distributions if the local particle distribution is quasi-uniform, which, to a large extent, relieves the mesh alignment sensitivity that finite element methods suffer. Moreover, a simple h-adaptivity procedure is implemented in the explicit calculation, and by utilizing a mesh-free hierarchical partition of unity a spectral (wavelet) adaptivity procedure is developed to seek high-resolution shear-band formations. Moreover, the phenomenon of multiple shear band and mode switching are observed in numerical computations with a relatively coarse particle distribution in contrast to the costly fine-scale finite element simulations.

Original languageEnglish (US)
Pages (from-to)1285-1309
Number of pages25
JournalInternational Journal for Numerical Methods in Engineering
Issue number9
StatePublished - Jan 1 2000


  • Hierarchical reproducing kernel partition of unity
  • Mesh-free methods
  • Spectral adaptivity
  • Strain localization
  • Wavelet kernel
  • h-adaptivity

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics


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