Revisiting finite deformation poromechanics: Deriving a nonlinear Biot coefficient from first principles

This paper presents a novel framework that integrates mixture theory with finite deformation poromechanics to derive a nonlinear Biot coefficient from first principles, eliminating the need for constitutive assumptions prevalent in prior formulations. By applying the extended Hamilton’s principle to a binary mixture of solid and fluid phases, we fully account for finite deformations and employ a Legendre transformation to shift the internal energy dependence from specific volume to pressure. This approach naturally yields a new nonlinear form of the Biot coefficient that is shown to reduce to the classical Biot coefficient under small deformations. Our method provides a clear physical interpretation of the Biot coefficient as a measure of the solid’s specific volume change with respect to skeleton deformation at constant pore pressure. This work bridges mixture theory and finite deformation poromechanics, offering a fundamental derivation that enhances the understanding and applicability of poromechanical models in large deformation scenarios.