General coupling of porous flows and hyperelastic formulations—From thermodynamics principles to energy balance and compatible time schemes

We formulate a general poromechanics model– within the framework of a two-phase mixture theory– compatible with large strains and without any simplification in the momentum expressions, in particular concerning the fluid flows. The only specific assumptions made are fluid incompressibility and isothermal conditions. Our formulation is based on fundamental physical principles– namely, essential conservation and thermodynamics laws– and we thus obtain a Clausius–Duhem inequality which is crucial for devising compatible constitutive laws. We then propose to model the solid behavior based on a generalized hyperelastic free energy potential– with additional viscous effects– which allows to represent a wide range of mechanical behaviors. The resulting formulation takes the form of a coupled system similar to a fluid–structure interaction problem written in an Arbitrary Lagrangian–Eulerian formalism, with additional volume-distributed interaction forces. We achieve another important objective by identifying the essential energy balance prevailing in the model, and this paves the way for further works on mathematical analyses, and time and space discretizations of the formulation.