On the influence of non-linearity within two-phase poro-elasticity: Numerical examples and counterexamples

Porous materials can be described either by Biot’s consolidation theory or the Theory of Porous Media (TPM). Depending on the loading regime, permeability or compressibility of the solid matrix, either small or finite deformations occur. Numerical solution procedures for the case of finite deformation are prone to instabilities and computationally costly. Simplified models assuming small deformations increase stability of the solution process. Within this work, limitations of two simplified models in comparison with the fully non-linear TPM are studied. Therefore a Mandel-like problem is considered. Differences arise especially for rapid consolidation processes and for elongations larger than 3%. It can be further shown, that the simplified models have an inherent mass error.