Localized shear discontinuities near the tip of a mode I crack
type: Item
instance of: scholarly article
title: Localized shear discontinuities near the tip of a mode I crack
zbMATH Open document ID: 0603.73097
DOI: 10.1007/BF00043018
author: Jae-Sung Yang
author: Rohan Abeyaratne
published in: Journal of Elasticity
publication date: 1987-01-01T00:00:00Z
review text: In this paper we study the deformation and stress fields near the tip of a crack under plane strain mode I conditions. A fully nonlinear theory of finite deformations is used and the material, which is assumed to be homogeneous, isotropic, incompressible and elastic, is characterized by its stress-strain behavior in simple shear. For the class of materials considered the governing system of differential equations may lose ellipticity at sufficiently severe strains. The analysis is based on a direct asymptotic calculation. The results involve two curves, issuing from each crack-tip, across which the deformation gradient, the 'effective shear' and the stresses are discontinuous.
Mathematics Subject Classification ID: 74R05
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 35C99
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 3974482
zbMATH Keywords: overlapping subdomains
zbMATH Keywords: two asymptotic solutions
zbMATH Keywords: one non-elliptic
zbMATH Keywords: other elliptic
zbMATH Keywords: linear boundary-value problem
zbMATH Keywords: two shocks
zbMATH Keywords: discontinuous stress and deformation gradient fields
zbMATH Keywords: continuous displacements and tractions
zbMATH Keywords: near-tip states
zbMATH Keywords: tip of a crack
zbMATH Keywords: plane strain mode I conditions
zbMATH Keywords: homogeneous
zbMATH Keywords: isotropic
zbMATH Keywords: incompressible
zbMATH Keywords: stress-strain behavior
zbMATH Keywords: simple shear
zbMATH Keywords: system of differential equations
zbMATH Keywords: lose ellipticity at sufficiently severe strains
zbMATH Keywords: direct asymptotic calculation
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3974482