EQUATION OF STATE AND HUGONIOT LOCUS FOR POROUS MATERIALS: P–a 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 Ψ(V;T;φ) = Ψs(V;T )+B(φ) where the equilibrium volume fraction φeq is determined by minimizing Ψ, i.e., the condition ∂φΨ = 0. For many cases, a Hayes EOS for the pure solid Ψs(V;T ) is adequate. This provides a thermodynamically consistent framework for the P–α 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 φ are shifted to the left in the (V;P)-plane with increasing φ. 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