We study fluid-saturated porous materials that undergo poro-elastic deformations in thin domains. The mechanics in such materials are described using a biphasic model based on the theory of porous media (TPM) and consisting of a system of differential equations for material’s displacement and fluid’s pressure. These equations are in general strongly coupled and nonlinear, such that exact solutions are hard to obtain and numerical solutions are computationally expensive. This paper reduces the complexity of the biphasic model in thin domains with a scale separation between domain’s width and length. Based on standard asymptotic analysis, we derive a reduced model that combines two sub-models. Firstly, a limit model consists of averaged equations that describe the fluid pore pressure and displacement in the longitudinal direction of the domain. Secondly, a corrector model re-captures the mechanics in the transverse direction. The validity of the reduced model is finally tested using a set of numerical examples. These demonstrate the computational efficiency of the reduced model, while maintaining reliable solutions in comparison with original biphasic TPM model in thin domain.

我们研究在薄域中经历孔隙弹性变形的流体饱和多孔材料。使用基于多孔介质（TPM）理论的双相模型描述这种材料的力学，该模型由用于材料位移和流体压力的微分方程组组成。这些方程通常是强耦合的并且是非线性的，从而使得难以获得精确的解并且数值解在计算上是昂贵的。本文通过在域的宽度和长度之间进行比例分隔来降低薄域中的双相模型的复杂性。基于标准渐近分析，我们得出了一个简化模型，该模型结合了两个子模型。首先，极限模型由描述流体孔隙压力和在区域纵向上的位移的平均方程组成。其次，校正器模型会在横向方向上重新捕获力学。最后使用一组数值示例来测试简化模型的有效性。这些证明了精简模型的计算效率，同时在薄域中与原始双相TPM模型相比保持了可靠的解决方案。