The Role of the Relative Fluid Velocity in an Objective Continuum Theory of Finite Strain Poroelasticity

We revisit the general theory of finite-strain deformations in fluid-saturated porous media via the thermodynamics of nonequilibrium processes. Our aim is the thermodynamically consistent derivation of governing equations that satisfy the principle of material frame indifference, starting with the minimal number of assumptions. In the first part, we treat the relative fluid velocity as a constitutive variable, and hence fully determined by the macroscopic thermodynamic state of the continuum. However, this hypothesis is not rich enough to account for the tortuosity effect in poroacoustics, second-gradient effects, or Brinkman’s correction to Darcy’s law, thus motivating its relaxation in the second part, where we consider the relative fluid velocity as an independent kinematic variable. This approach yields an additional balance equation reflecting, in an average sense, the micromechanics of the fluid flow, which is derived from the principle of virtual power. Finally, we show that the resulting general model is consistent with Biot’s linear theory of acousto-poro-elasticity.