Shock Thickness in Viscoplastic Solids

Abstract

In this paper a system of constitutive relations for plane-strain finite deformation in strain-rate sensitive elastic-plastic materials is developed. A method is presented for computing the main features of steady-state one-dimensional plastic-strain waves by elementary numerical techniques in materials of this type. This method is applicable to a wide variety of material constitutive relations and provides an alternative to computing complete wave profiles for investigators interested primarily in the effects of certain numerical parameters on the principal features of waves. The method is illustrated by use of particular constitutive relations but is applicable to a much wider class of relations. Maximum normal stress, pressure, and shear stress are computed, using this method, as a function of wave speed. For two different plastic strain-rate relations the maximum plastic strain rate and total strain are computed as a function of wave speed. Making use of these results, estimates are provided for the wave-front thickness in terms of wave speed and the parameters of the particular viscoplastic constitutive equations used. These results suggest ways in which plastic wave experiments can be used to motivate the construction of constitutive equations for finite deformation in strain-rate sensitive plastic solids.