Anti-plane strain under post-critical deformation in the problem on equilibrium semi-infinite crack. Part I

Abstract

The paper analyzes formulations of mathematical problems on anti-plane strains in materials under post-critical deformation. Depending on a decline modulus, the system of equilibrium equations and strain compatibility conditions has one or two characteristics. Given the two characteristics, finding stress-strain state of a medium needs Cauchy stress vector and displacement vector to be set at one and the same boundary. The author shows that the post-critical deformation, if included in the problem on an equilibrium semi-infinite crack, results in the infinite growth of stresses at the crack tip under unalterable deformation. Based on this, it is necessary to account for the by now disintegrated and fractured material area that is more rigid and higher modulus under the further deformation as compared with the initial state material.