A multiphase compressible flow model including elasto-viscoplastic solids with irreversible compaction

  • Favrie, Nicolas (IUSTI, Aix Marseille University)
  • Schmidmayer, Kevin (INRIA Pau,)

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We present a diffuse-interface, multiphase Eulerian framework for the numerical simulation of porous solids interacting with compressible fluids under dynamic loading. The model is formulated at the mixture level and is designed to handle large deformations, elastic–plastic behavior, irreversible compaction, and finite-rate pressure relaxation between phases. A macroscopic configuration variable is introduced to represent the deformation of the porous solid and is multiplicatively decomposed into elastic and plastic parts. The constitutive equations and relaxation mechanisms are formulated within a generalized standard material framework, ensuring thermodynamic consistency. In particular, total mixture energy is conserved while entropy production is guaranteed by construction through convex dissipation potentials and non-negative relaxation multipliers. Irreversible source terms account for porosity evolution and bubble growth, leading to a progressive loss of load-carrying capacity at the macroscopic scale. The proposed framework provides a robust and thermodynamically consistent basis for the simulation of coupled fluid–porous solid dynamics and offers a natural foundation for future extensions toward more advanced degradation or damage models.