A multiphase irreversible-compaction model for granular-porous materials

Nicolas Favrie (1) , Kevin Schmidmayer (1) , Jacques Massoni (1)

1 IUSTI - Institut universitaire des systèmes thermiques industriels

An Eulerian, hyperbolic, multiphase-flow model for dynamic and irreversible compaction of porous materials is constructed. A reversible model for elastic, compressible, porous material is derived. Classical homogenization results are obtained. The irreversible model is then derived in accordance with the following basic principles. First, the entropy inequality is satisfied by the model. Second, the stress coming from the elastic energy decreases in time (the material behaves as Maxwell-type materials). The irreversible model admits an equilibrium state corresponding to a Gurson-type limit which varies with the porosity. The sound velocity at the yield limit is smaller than that of the reversible model. Such an embedded model structure ensures a thermodynamically correct formulation of the porous-material model. The usual model used in the detonation community is recovered. The model is then validated on quasi-static loading-unloading experiments with HMX. The ability of the model to capture strong shock propagation in porous material as well as its ability to deal with interface between a fluid and a porous material is demonstrated and validated on Hugoniot curve of aluminium with various porosities for a unique set of empirical parameters.

Mots clés: Multiphase-flow model; compaction; porous media; granular media; Godunov-type scheme

Domaines: Mécanique des fluides [physics.class-ph]

Nicolas Favrie, Kevin Schmidmayer, Jacques Massoni. A multiphase irreversible-compaction model for granular-porous materials. Continuum Mechanics and Thermodynamics, 2022, 34 (1), pp.217-241. ⟨10.1007/s00161-021-01054-8⟩. ⟨hal-03257608v2⟩