Multi-scale methods

Wing K Liu*, Su Hao, Ted Belytschko, Shaofan Li, Chin Tang Chang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

45 Scopus citations


In this paper four multiple scale methods are proposed. The meshless hierarchical partition of unity is used as a multiple scale basis. The multiple scale analysis with the introduction of a dilation parameter to perform multiresolution analysis is discussed. The multiple field based on a 1-D gradient plasticity theory with material length scale is also proposed to remove the mesh dependency difficulty in softening/localization problems. A non-local (smoothing) particle integration procedure with its multiple scale analysis are then developed. These techniques are described in the context of the reproducing kernel particle method. Results are presented for elastic-plastic one-dimensional problems and 2-D large deformation strain localization problems to illustrate the effectiveness of these methods.

Original languageEnglish (US)
Pages (from-to)1343-1361
Number of pages19
JournalInternational Journal for Numerical Methods in Engineering
Issue number7
StatePublished - Mar 10 2000


  • Large deformation
  • Localization
  • Mesh dependency
  • Meshfree methods
  • Multi-scale
  • Plasticity

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics


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