An equation of state consistent with the Hugoniot abnormality

Development of Equations of State (EOSs) for the description of highly porous materials exhibiting Hugoniot abnormality is of interest to physicists because of the need to understand shock compression of these materials within a high temperature range. The Mie-Gruneisen EOS is usually a basis of such new EOSs. The present work also follows the Mie-Gruneisen approximation, which is complemented with a two-phase consideration for the porous material analysed, while employing simple EOSs for each of the two phases. The Hugoniot abnormality has previously been analysed with a two-phase material model implemented in the CTH hydrocode. The analysis has shown that the inter-phase pressure and temperature equilibrium that is achieved under moderate shock waves, is the necessary condition for manifestation of the abnormality in highly porous materials, whereas under stronger waves the equilibrium achieved only by pressure connects metastable states in the high-pressure section of a Hugoniot manifesting normal behaviour. The present Hugoniot in analytical form consists of the two sections distinguished by equilibrium conditions and correlates well with the experimental data available in the literature.