Onsager’s reciprocal relationship applied to multiphysics poromechanics

Abstract

Onsager’s theory of linear irreversible thermodynamics has been successfully applied to explain findings from experiments. However, its application to multiphysics processes in deformable porous media is a non-trivial undertaking. This contribution presents an extension of Onsager’s theorem to include the flux of the matter of weakly coupled two-phase porous systems. It also relates Onsager to Ziegler’s nonlinear approach including the classical acoustic tensor criterion for localisation phenomena in such nonlinear media. The results are illustrated by Terzaghi consolidation problem using the well established modified Cam-Clay plasticity model. We show that a generalised dissipative stress can act as an appropriate thermodynamic force quantity rendering the non-associated yield envelope into Onsager’s associated form ensuring the thermodynamic condition of no-work free plastic deformation. We present in this contribution an attempt of using the theory of thermodynamics of internal state variables to develop a generic poromechanics approach that relaxes isothermal constraints for weakly coupled problems. This approach lends itself to a promising future extension of a dynamic Onsager diffusional operator for conditions where the multiphysics processes are strongly coupled in the porous system and emergent phenomena may occur.