Equation of state and Hugoniot locus for porous materials: P-α model revisited

Menikoff, Ralph; Kober, Edward
April 2000
AIP Conference Proceedings;2000, Vol. 505 Issue 1, p129
Academic Journal
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 &Psgr;(V, T, &phis;) = &Psgr;[SUBs] (V, T) + B(&phis;) where the equilibrium volume fraction &phis;[SUBeq] is determined by minimizing &Psgr;, i.e., the condition &Part;[SUB&phis;] &Psgr; = 0. For many cases, a Hayes EOS for the pure solid &Psgr;[SUBs](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 &phis; are shifted to the left in the (V, P)-plane with increasing &phis;. 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.


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