Strain-softening materials and finite-element solutions

Ted Belytschko*, Zdenék P. Bažant, Hyun Yul-Woong, Chang Ta-Peng

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

95 Scopus citations


Closed form and finite-element solutions are examined for several problems with strain-softening materials. In the closed form solutions, strain-softening causes localization of the strain which is accompanied by an instantaneous vanishing of the stress. The finite-element solutions agree closely with analytic solutions in many cases and exhibit a rate of convergence only slightly below that for linear problems. The main difficulty which has been identified in strain-softening constitutive models for damage is the absence of energy dissipation in the strain-softening domain, and this can be corrected by a nonlocal formulation. Finite-element solutions for the converging spherical wave problem exhibit multiple points of localization which change dramatically with mesh refinement. With a nonlocal material formulation, this pathology is eliminated.

Original languageEnglish (US)
Pages (from-to)163-180
Number of pages18
JournalComputers and Structures
Issue number2
StatePublished - 1986

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Modeling and Simulation
  • Materials Science(all)
  • Mechanical Engineering
  • Computer Science Applications


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