Large deformations of a soft porous material
In a porous material, deformation of the solid skeleton is mechanically coupled to flow of the interstitial fluid. For soft porous materials such as soils, gels, and biological tissues, these deformations can be very large. Large deformations are mathematically challenging because the size, shape, and properties of the material can change drastically as the material is deformed.
For elastic porous materials, the poromechanical coupling between flow and deformation is captured by the well-known theory of poroelasticity. Here, we provide an overview of the physics and mathematics of poroelasticity. We first develop the general theory for large deformations, and we then show how this simplies to classical linear poroelasticity when the deformations are small.
We also compare the large-deformation theory with the linear theory in the context of two uniaxial model problems: Fluid outflow driven by an applied mechanical load (the consolidation problem) and compression driven by a steady fluid throughflow. We show that large deformations can lead to strong steady and transient deviations from linear behavior, and that these deviations are amplified by nonlinear constitutive behavior such as deformation-dependent permeability.
We also provide a suite of
MATLAB scripts that implement the steady-state and dynamic solutions developed in the paper.
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