A simplified mesh-free method for shear bands with cohesive surfaces

Timon Rabczuk, P. M.A. Areias, Ted Belytschko

Research output: Contribution to journalArticlepeer-review

175 Citations (Scopus)

Abstract

A simple methodology to model shear bands as strong displacement discontinuities in a mesh-free particle method is presented. The shear band is represented as a set of sheared particles. A sheared particle is developed through enrichment by tangential displacement discontinuities. The representation of the shear band as set of cohesive segments provides a simple and versatile model of shear bands. The loss of material stability is used as the criterion for switching from a classical continuum description of the constitutive behaviour to a traction-separation law acting on the discontinuity surface. The method is implemented for two and three dimensions. Examples of shear band progression in rate-dependent and rate-independent materials are presented, including the Kalthoff problem, where the transition from brittle fracture to shear banding is studied.

Original languageEnglish
Pages (from-to)993-1021
Number of pages29
JournalInternational Journal for Numerical Methods in Engineering
Volume69
Issue number5
DOIs
Publication statusPublished - 2007 Jan 29

Keywords

  • Loss of hyperbolicity
  • Mesh-free methods
  • Shear bands
  • Traction-separation laws

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics

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