On a Crack in a Material with a Nonlinear StressStrain Law
Abstract
A boundaryvalue problem in longitudinal shear in which the stressstrain law is physically nonlinear, and given by τ =τ _{0}γ /(1 + γ ^{2})^{1/2}, is considered. The method of solution involves a hodograph transformation, and a further transformation to reduce the governing equations to Laplace's equation for the displacement w in terms of appropriate strain variables. It is shown that near the tip of a crack in this type of material it is not possible to obtain the behaviour of w by a local analysis: the asymptotic behaviour may only be found from a full analysis of the problem. Having found the local crack tip behaviour for our problem, the answer is checked using a path independent integral.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 May 1993
 DOI:
 10.1098/rspa.1993.0067
 Bibcode:
 1993RSPSA.441..377C