Equilibrium of a prestressed elastic body weakened by a plane elliptical crack
type: Item
instance of: scholarly article
title: Equilibrium of a prestressed elastic body weakened by a plane elliptical crack
zbMATH Open document ID: 0605.73103
DOI: 10.1016/0021-8928(85)90117-0
author: V. M. Aleksandrov
author: B. V. Sobol'
published in: Journal of Applied Mathematics and Mechanics
publication date: 1985-01-01T00:00:00Z
review text: The problem of normal pressure loading of the edges of a plane elliptical crack is considered. The crack subjected to the load is in the open state. The medium in which it is located is first subjected to homogeneous biaxial tension or compression along the plane of the crack. A model of incompressible neo-Hooke material is considered. The problem is reduced to solving a singular integral equation of the first kind. In the case when the intensity of the initial loading is identical in both directions, the problem has an exact solution. If the coefficients of preliminary tension differ slightly, construction of the solution of the problem is possible by an asymptotic method. It is shown that as in the case of equal coefficients, the initial stress does not alter the order of the singularity of the stress field near the crack edge and only affects the normal stress intensity factor.
Mathematics Subject Classification ID: 74R05
zbMATH DE Number: 3978575
zbMATH Keywords: normal pressure loading
zbMATH Keywords: edges
zbMATH Keywords: plane elliptical crack
zbMATH Keywords: open state
zbMATH Keywords: homogeneous biaxial tension
zbMATH Keywords: compression
zbMATH Keywords: incompressible neo-Hooke material
zbMATH Keywords: singular integral equation of the first kind
zbMATH Keywords: exact solution
zbMATH Keywords: asymptotic method
zbMATH Keywords: equal coefficients
zbMATH Keywords: initial stress
zbMATH Keywords: normal stress intensity factor
MaRDI profile type: Publication
full work available at URL: 0021-8928(85)90117-0
OpenAlex ID: W1979968407
cites work: Q4743816
cites work: Theory of cracks in elastic bodies with initial stresses (three-dimensional static problems)
cites work: Axisymmetric contact and crack problems for an initially stressed neo- Hookean elastic layer
cites work: Penny-shaped cracks in a finitely deformed elastic solid
cites work: Three-dimensional contact problem for a prestressed elastic body
cites work: Q3915482
cites work: Q4743891
description: scientific article; zbMATH DE number 3978575