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

An integral equatmn method for the analysas of elasUc-plastac wave propagaUon as presented. The elastic-plastic solution is thereby found as the superposttaon of the corresponding elastic result with waves produced by dynamically induced plastic stratus. The solutions are represented m the form of integrals with elastodynanuc Greenʹs functions as lntegrataon kernels The spherically symmetric problem of a dynamically loaded spherical cavity is considered and the corresponding Greenʹs functions for this geometry are derived in closed form Tame convolution as carried out analytically over a prescribed time step and the spatial integration is performed by Gausslan quadrature. If the wave travels within each time step just the distance of one spatml element the evaluation of the integrals leads to a tridiagonal system of algebraic equahons. Numerical results are compared to some knowt~ analytical solutions, prowng the accuracy of the method. Computations a re carried out for rate sensitwe power law hardening-thermal softening matermls