Inhomogeneous behavior of antiplane shear crack in softening material with local unloading

Examined in this work is the anti-plane stress and strain near a crack in a material that softens beyond the elastic peak and unloads on a linear path through the initial state. The discontinuity in the constitutive relation is carried into the analysis such that one portion of the local solution is elliptic in character and the other hyperbolic. Material elements in one region may cross over to another as the loading is increased. Local unloading can thus prevail. Presented are the inhomogeneous character of the asymptotic stress and strain in the elliptic and hyperbolic region, in addition to the region in which the material elements had experienced unloading. No one single stress or strain coefficient would be adequate for describing crack instability.