A continuous loading solution for spherical elastic-plastic waves of small amplitude

A solution is constructed for the wave motion induced by the application of a continuously increasing uniform pressure on the surface of a spherical cavity in an infinite elastic-plastic medium. The small amplitude linearization in conjunction with parabolic work-hardening leads to constant wave speeds in both elastically and plastically deforming regions, so that linear wave function representations can be used. The induced wave pattern is an elastic (continuous) front propagating into the medium followed by an expanding region of continuous elastic loading, in turn followed by a region of continuous plastic loading which persists to the cavity boundary. The motion of the continuous elastic-plastic interface is part of the solution to be determined, in contrast to discontinuous interfaces which move with a pre-determined wave speed. Validity of this wave pattern requires appropriate pressure increase on the boundary. Several examples are presented to illustrate different forms of interface motion.