Elastic, perfectly plastic hollow sphere problem: a finite strain solution and energetic analysis

The growth of a void in a sphere of an elastic perfectly plastic material subjected to an external hydrostatic loading is modeled in the framework of irrotational finite strains. It is shown that, for small initial void volume fractions, the infinitesimal plastic strain hypothesis leads to a gross overestimation of the void growth kinetics. This assumption is relaxed in the present work, and the analytical results compare exactly with numerical simulations carried out with the commercial finite element code ABAQUS. A thermodynamic analysis is then performed, and will be considered as a basis for investigating thermal softening and micro-inertia effects on the damage process.