Large deformations in soft porous materials

Dr Chris MacMinn (University of Oxford)

Frank Adams 1,

Flow through a porous material will drive mechanical deformation when
the fluid pressure becomes comparable to the stiffness or strength of
the solid skeleton. This has applications ranging from the recovery of
natural gas from shales via hydraulic fracturing, where fluid is
injected into the rock at high pressure, to the mechanics of
biological cells and tissues, where pressures are low but the solid
skeleton is very soft. The classical theory of linear poroelasticity
captures this coupling by combining Darcy's law with linear elasticity
and then further linearizing in the strain. This is a good model for
very small deformations, but it can become inappropriate in the
context of phenomena such as swelling, damage, and extreme softness,
which often enable much larger deformations. Here, we first motivate
the idea of large deformations in porous media with high-resolution
experiments in a model system. We then review the rigorous framework
of large-deformation poromechanics and compare this with linear
poroelasticity in the context of a model problem. We show that large
deformations can lead to surprising behaviour in even relatively
simple systems. 

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