Asymptotic Analysis of the Plane Strain State Generated by a Finite Longitudinal Shear Crack

Abstract

In the linear theory of elasticity, an arbitrary crack is represented as a combination of three: longitudinal shear cracks, transverse shear cracks, and normal tear cracks that do not interact with each other. In the nonlinear theory, for some types of strain energy potentials, a finite longitudinal shear crack necessarily generates a strain in the transverse plane. This article proposes an asymptotic description of the deformed state of a crack in the transverse plane under the action of a finite longitudinal shear in an incompressible material with a Mooney–Rivlin potential, and an assessment is made of the effect of additional deformation on the condition of the start of a crack.