Steady shock waves in porous plastic solids

The affect of material porosity on propagation of shock waves in solids is examined in the context of finite strain, associated plasticity, with porosity incorporated via the Gurson model and accounting for material hardening. Setting is analogous to the fluid dynamics piston shock model so that deformation of the semi-infinite medium is permitted only in the longitudinal direction. The steady response, which develops by imposing constant piston velocity in either tension or compression, is examined by sectors mapping of the characteristic velocity as determined by the constitutive model. It is shown that even the slightest levels of initial porosity can have an appreciable effect on field response, inducing destructive unsteady behavior accompanied by increased shock dissipation. Numerical illustration of limit velocities at appearance of a plastic shock and at onset of that unsteady behavior are presented, showing that material porosity delays initiation of plastic shock waves and promotes higher energy consumption which may, in turn, enhance protective capabilities.