Initiation and Propagation of Shear Bands in Antiplane Shear Deformation

摘要

A large block of material is subjected to a constant average strain rate resulting in deformation in the antiplane shear mode. The material is assumed to be isotropic, incompressible and hyperelastic. To simulate the situation in which strain hardening of the material is overwhelmed by thermal softening, the shear stress as a function of shear strain has a local maximum. The block contains a material imperfection in the form of a small region in which the material is less stiff than the otherwise homogeneous block, and in which the maximum possible stress is less than in the surrounding material. The transient deformation is analyzed numerically by means of the finite element method. It is found that a shear band initiates in the region of the material defect, and then propagates in a crack-like fashion into the rest of the body. A prediction of the speed of propagation of the edge of the band is made on the basis of a linearization of the governing field equations around a state corresponding to the strain level at which the local maximum in stress occurs. (Author)