The propagation of spherical waves in rate-sensitive elastic-plastic materials

An integral equation method for the analysis of elastic-plastic wave propagation is presented. The elastic-plastic solution is thereby found as the superposition of the corresponding elastic result with waves produced by dynamically induced plastic strains. The solutions are represented in the form of integrals with elastodynamic Green's functions as integration kernels. The spherically symmetric problem of a dynamically loaded spherical cavity is considered and the corresponding Green's functions for this geometry are derived in closed form. Time convolution is carried out analytically over a prescribed time step and the spatial integration is performed by Gaussian quadrature. If the wave travels within each time step just the distance of one spatial element the evaluation of the integrals leads to a tridiagonal system of algebraic equations. Numerical results are compared to some known analytical solutions, proving the accuracy of the method. Computations are carried out for rate sensitive power law hardening-thermal softening materials.