Numerical method for elastic-plastic waves in cracked solids. I: Anti- plane shear problem (Q1261836)

The paper deals with a numerical method combining a characteristic-based scheme and Zwas' method in order to solve the hyperbolic PDE's of elastic-plastic anti-plane shear waves in two space dimensions. First, the need of new physically reasonable numerical methods for stress waves in solids is demonstrated by numerical applications to problems with impulsive loading, where defects of some standard methods are shown. Then, the new second-order accurate method is derived. For comparison with numerical results, a similarity solution for the semi-infinite crack undergoing an elastic-plastic shock loading is derived in the appendix.