Asymptotic solution of the elasticity equations in the vicinity of an elliptical crack front

Yaron Schapira, Zohar Yosibash

Research output: Contribution to journalArticlepeer-review

Abstract

The asymptotic solution of the elasticity equations in the vicinity of an elliptical singular edge is derived and presented explicitly for an elliptical crack with traction free BCs. It is composed of edge stress intensity functions (ESIFs), which are functions along the singular edge, eigenfunctions and their shadows. The recursive equations to derive the eigenfunctions and their shadows are provided. The explicit presentation of the series is required to identify the different quantities of interest as the ESIFs and the T-stresses and allows the extension of the quasi dual function method for the extraction of the ESIFs along elliptical singular edge. We also present the dual eigenfunctions needed to extract KI in the case of an elliptical crack with traction free BCs.

Original languageEnglish
Pages (from-to)463-477
Number of pages15
JournalEngineering Fracture Mechanics
Volume211
DOIs
StatePublished - 15 Apr 2019

Keywords

  • 3-D singularities
  • Elliptical crack
  • Stress intensity functions

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