  Soft porous materials, such as biological tissues and soils, are exposed to
periodic deformations in a variety of natural and industrial contexts. The
detailed flow and mechanics of these deformations have not yet been
systematically investigated. Here, we fill this gap by identifying and
exploring the complete parameter space associated with periodic deformations in
the context of a 1D model problem. We use large-deformation poroelasticity to
consider a wide range of loading periods and amplitudes. We identify two
distinct mechanical regimes, distinguished by whether the loading period is
slow or fast relative to the characteristic poroelastic timescale. We develop
analytical solutions for slow loading at any amplitude and for infinitesimal
amplitude at any period. We use these analytical solutions and a full numerical
solution to explore the localisation of the deformation near the permeable
boundary as the period decreases and the emergence of nonlinear effects as the
amplitude increases. We show that large deformations lead to asymmetry between
the loading and unloading phases of each cycle in terms of the distributions of
porosity and fluid flux.
