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The radially outward flow of fluid through a porous medium occurs in manypractical problems, from transport across vascular walls to the pressurisationof boreholes in the subsurface. When the driving pressure is non-negligiblerelative to the stiffness of the solid structure, the poromechanical couplingbetween the fluid and the solid can control both the steady-state and thetransient mechanics of the system. Very large pressures or very soft materialslead to large deformations of the solid skeleton, which introduce kinematic andconstitutive nonlinearity that can have a nontrivial impact on these mechanics.Here, we study the transient response of a poroelastic cylinder to sudden fluidinjection. We consider the impacts of kinematic and constitutive nonlinearity,both separately and in combination, and we highlight the central role ofdriving method in the evolution of the response. We show that the variousfacets of nonlinearity may either accelerate or decelerate the transientresponse relative to linear poroelasticity, depending on the boundaryconditions and the initial geometry, and that an imposed fluid pressure leadsto a much faster response than an imposed fluid flux.

From arteries to boreholes: Transient response of a poroelastic cylinder to fluid injection