EQUATION OF STATE AND HUGONIOT LOCUS FOR POROUS MATERIALS: P-ALPHA MODEL REVISITED

Foams, porous solids and granular materials have a characteristic Hugoniot locus that for weak shocks is concave in the (particle velocity, shock velocity)-plane. An equation of state (EOS) that has this property can be constructed implicitly from a Helmholtz free energy of the form {Psi}{sub s}(V,T,{phi}) = {Psi}{sub s}(V,T)+B({phi}) where the equilibrium volume fraction {phi}{sub eq} is determined by minimizing {Psi}, i.e., the condition {partial_derivative}{sub {psi}} {Psi} = 0. For many cases, a Hayes EOS for the pure solid {Psi}{sub s}(V,T) is adequate. This provides a thermodynamically consistent framework for the P-{alpha} model. For this form of EOS the volume fraction has a similar effect to an endothermic reaction in that the partial Hugoniot loci with fixed {psi} are shifted to the left in the (V,P)-plane with increasing f. The equilibrium volume fraction can then be chosen to match the concavity of the principal Hugoniot locus. An example is presented for the polymer estane. A small porosity of only 1.4 percent is required to match the experimental concavity in the Hugoniot data. This type of EOS can also be used to obtain the so-called ''universal'' Hugoniot for liquids