The Finite Anti-Plane Shear Field near the Tip of a Crack for a Class of Incompressible Elastic Solids.

摘要

The present paper is concerned with an infinite slab containing a crack and deformed at infinity to a state of finite simple shear. The material of the slab is taken to be homogeneous,isotropic,elastic,and incompressible,and is further assumed to belong to a class of materials which admit nontrivial states of anti-plane shear. The analysis is carried out for the fully nonlinear equilibrium theory of finite elasticity. The stress field near the crack-tips is studied in detail;one of the special materials considered in such that the shear stresses near a crack tip remain bounded,despite the presence of unbounded displacement gradients. An analogy between the crack problem in finite anti-plane shear and the problem of transonic flow of a gas past a flat plate is pointed out and discussed. (Author)