Steady shock waves in porous metals: Viscosity and micro-inertia effects

The structure of steady shock waves in porous solids is a complex phenomenon involving in general the interplay of micro-inertia effects with the nonlinear elastic viscoplastic matrix response. Micro-inertia effects are due to the important acceleration of material particles in the vicinity of collapsing voids. By adopting the analytical approach recently developed for porous metals by Czarnota et al. [J. Mech. Phys. Solids 107 (2017)], we analyze the effects of matrix rate sensitivity, shock stress amplitude and micro-inertia on the structure of planar shock waves. We also analyze the relationship that links the strain rate within the shock to the jump of the stress across the shock. The fourth power law experimentally revealed for dense metals, Swegle & Grady [J. Appl. Phys. 58 (1985)] does not hold for heterogeneous materials. By considering the case of porous aluminum, we show that this relationship is characterized by two distinct regimes: (i) the first regime holds for weak shock intensities and is representative of the viscoplastic response of the dense matrix material, (ii) the second regime, that holds for shock of higher amplitude, is dominated by micro-inertia effects and is strongly influenced by the pore size. Micro-inertia effects appear to be quite beneficial since they are conducive to shock mitigation by attenuating the level of strain rate and of acceleration sustained by material particles.