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.

多孔弹性理论可用于分析流体流动与多孔介质（基质）变形之间的耦合相互作用。线性多孔弹性的经典理论通过将Terzaghi的有效应力与线性连续性方程相结合来捕获这种耦合。线性多孔弹性是很小变形的良好模型。但是，对于中等到较大的变形，它的准确性降低了。另一方面，大变形孔隙弹性理论将Terzaghi的有效应力与非线性连续性方程相结合。在本文中，我们基于位移压力两场模型，提出了三角形网格上线性和非线性多孔弹性问题的有限元求解器。然后，在二维模型问题的背景下，我们将线性多孔弹性的预测与大变形多孔弹性的预测进行了比较，其中考虑了在施加机械振动的情况下流经弹性，饱和多孔介质的情况。此外，还探讨了根据Kozeny-Carman方程引入依赖变形的渗透率的影响。我们通过计算表明，使用线性多孔弹性获得的位移和压力场中的误差主要是由于缺乏运动非线性。此外，通过引入恒定的磁导率而不是依赖变形的磁导率，可以扩大压力场中的误差。此外，还探讨了根据Kozeny-Carman方程引入依赖变形的渗透率的影响。我们通过计算表明，使用线性多孔弹性获得的位移和压力场中的误差主要是由于缺乏运动非线性。此外，通过引入恒定的磁导率而不是依赖变形的磁导率，可以扩大压力场中的误差。此外，还探讨了根据Kozeny-Carman方程引入依赖变形的渗透率的影响。我们通过计算表明，使用线性多孔弹性获得的位移和压力场中的误差主要是由于缺乏运动非线性。此外，通过引入恒定的磁导率而不是依赖变形的磁导率，可以扩大压力场中的误差。