Non-local boundary integral formulation for softening damage

Ján Sládek, Vladimir Sládek, Zdenek P Bazant

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


A strongly non-local boundary element method (BEM) for structures with strain-softening damage treated by an integral-type operator is developed. A plasticity model with yield limit degradation is implemented in a boundary element program using the initial-stress boundary element method with iterations in each load increment. Regularized integral representations and boundary integral equations are used to avoid the difficulties associated with numerical computation of singular integrals. A numerical example is solved to verify the physical correctness and efficiency of the proposed formulation. The example consists of a softening strip perforated by a circular hole, subjected to tension. The strain-softening damage is described by a plasticity model with a negative hardening parameter. The local formulation is shown to exhibit spurious sensitivity to cell mesh refinements, localization of softening damage into a band of single-cell width, and excessive dependence of energy dissipation on the cell size. By contrast, the results for the non-local theory are shown to be free of these physically incorrect features. Compared to the classical non-local finite element approach, an additional advantage is that the internal cells need to be introduced only within the small zone (or band) in which the strain-softening damage tends to localize within the structure.

Original languageEnglish (US)
Pages (from-to)103-116
Number of pages14
JournalInternational Journal for Numerical Methods in Engineering
Issue number1
StatePublished - May 7 2003


  • Boundary elements
  • Computational mechanics
  • Damage
  • Fracture
  • Non-local models
  • Softening

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics


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