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Large deformations in soft porous materials: Squishing, swelling, and yielding

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MIMW01 - From foundations to state-of-the-art in magma/mantle dynamics

In an elastic solid, the state of stress depends on the displacement of material points from a relaxed reference state. In a poroelastic solid, the mechanics of the solid skeleton are additionally coupled to flow through the pore structure. The classical theory of linear poroelasticity captures this coupling by combining Darcy’s law with Terzaghi’s effective stress and linear elasticity in a linearized kinematic framework. This is a good model for very small deformations, but it becomes increasingly inappropriate for moderate to large deformations, which are common in the context of phenomena such as swelling and damage, and for soft materials such as gels and tissues. Here, we review the well-known theory of large-deformation poroelasticity and then consider the implications of large deformations in the context of two model problems: (1) Classical uniaxial consolidation and (2) the swelling and drying of a spherical gel.

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