Computing edge singularities in elastic anisotropic three-dimensional domains

Zohar Yosibash*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Computation of eigen-pairs characterizing the linear elastostatic solution in three-dimensional anisotropic domains in the vicinity of edge singularities is addressed. The singularities may be caused by re-entrant corners, abrupt changes in boundary conditions or material properties. Edge singularities in three-dimensional domains are of great interest from the point of view of failure initiation: The eigen-pairs characterize the straining modes and their amplitudes quantify the amount of energy residing in particular straining modes. For this reason, failure theories directly or indirectly involve the eigen-pairs and their amplitudes. Herein we address the problem of determining the edge eigen-pairs numerically on the basis of the modified Steklov formulation in conjunction with the p-version of the finite element method. The method is very accurate, efficient and robust, and provides complex eigen-pairs if they exist. Several practical problems are studied, and examples are presented for cases including multi-material inclusion problems, cracks in dissimilar materials, and multi-material interfaces at free and clamped edges.

Original languageEnglish
Pages (from-to)221-245
Number of pages25
JournalInternational Journal of Fracture
Volume86
Issue number3
DOIs
StatePublished - 1997
Externally publishedYes

Keywords

  • Delamination
  • Finite element methods
  • Fracture-mechanics
  • Multi-material interfaces
  • Singularities
  • Steklov method
  • Three-dimensional elasticity
  • p-version

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