Modeling Dynamic Compaction of Porous Materials

Abstract

To model dynamic compaction of a porous material we need: 1) an equation of state (EOS) for the porous material in terms of the EOS of its matrix; and 2) a compaction law. For an EOS people usually use Hermann's suggestion, as in his Pα [1] model. For a compaction law people usually use the results of a spherical shell collapse analysis (Carroll and Holt model [2]). In their original paper Carroll and Holt do both: the quasi-static shell collapse and the dynamic shell collapse. In their dynamic analysis, however, they ignore density changes of the matrix. In what follows we: 1) revisit the spherical shell collapse problem but with density changes taken into account; 2) develop a dynamic compaction law based on our overstress principle; 3) implement the different compaction laws mentioned above in a hydro-code; and 4) run a planar impact problem and compare histories and profiles obtained with the different compaction laws. We find that: 1) dynamic compaction laws give entirely different results from quasi-static compaction laws; 2) taking density changes into account do make a certain difference.