  The radially outward flow of fluid through a porous medium occurs in many
practical problems, from transport across vascular walls to the pressurisation
of boreholes in the subsurface. When the driving pressure is non-negligible
relative to the stiffness of the solid structure, the poromechanical coupling
between the fluid and the solid can control both the steady-state and the
transient mechanics of the system. Very large pressures or very soft materials
lead to large deformations of the solid skeleton, which introduce kinematic and
constitutive nonlinearity that can have a nontrivial impact on these mechanics.
Here, we study the transient response of a poroelastic cylinder to sudden fluid
injection. We consider the impacts of kinematic and constitutive nonlinearity,
both separately and in combination, and we highlight the central role of
driving method in the evolution of the response. We show that the various
facets of nonlinearity may either accelerate or decelerate the transient
response relative to linear poroelasticity, depending on the boundary
conditions and the initial geometry, and that an imposed fluid pressure leads
to a much faster response than an imposed fluid flux.
