Poroelasticity theory can be used to analyse the coupled interaction between fluid flow and porous media (matrix) deformation. The classical theory of linear poroelasticity captures this coupling by combining Terzaghi’s effective stress with a linear continuity equation. Linear poroelasticity is a good model for very small deformations; however, it becomes less accurate for moderate to large deformations. On the other hand, the theory of large-deformation poroelasticity combines Terzaghi’s effective stress with a nonlinear continuity equation. In this paper, we present a finite element solver for linear and nonlinear poroelasticity problems on triangular meshes based on the displacement-pressure two-field model. We then compare the predictions of linear poroelasticity with those of large-deformation poroelasticity in the context of a two-dimensional model problem where flow through elastic, saturated porous media, under applied mechanical oscillations, is considered. In addition, the impact of introducing a deformation-dependent permeability according to the Kozeny-Carman equation is explored. We computationally show that the errors in the displacement and pressure fields that are obtained using the linear poroelasticity are primarily due to the lack of the kinematic nonlinearity. Furthermore, the error in the pressure field is amplified by incorporating a constant permeability rather than a deformation-dependent permeability.
- Biot’s theory of linear poroelasticity
- Finite element method
- Large-deformation poroelasticity
- Nonlinear poroelastic media