  Compressing a porous material will decrease the volume of the pore space,
driving fluid out. Similarly, injecting fluid into a porous material can expand
the pore space, distorting the solid skeleton. This poromechanical coupling has
applications ranging from tissue mechanics to hydrogeology. 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. Linear poroelasticity 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. The well-known theory
of large-deformation poroelasticity combines Darcy's law with Terzaghi's
effective stress and nonlinear elasticity in a rigorous kinematic framework.
This theory has been used extensively in biomechanics to model large elastic
deformations in soft tissues, and in geomechanics to model large elastoplastic
deformations in soils. Here, we first provide an overview and discussion of
this theory with an emphasis on the physics of poromechanical coupling. We
present the large-deformation theory in an Eulerian framework to minimize the
mathematical complexity, and we show how this nonlinear theory simplifies to
linear poroelasticity under the assumption of small strain. We then compare the
predictions of linear poroelasticity with those of large-deformation
poroelasticity 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 use these problems to
explore the steady and dynamical errors associated with the linear model in
both situations, as well as the impact of introducing a deformation-dependent
permeability.
