Large fluid-driven deformations of porous annuli: solutions via Chebyshev spectral collocation

The radially outward flow of fluid into a porous medium occurs in many practical problems, from transport across vascular walls to the pressurisation of boreholes. As the driving pressure becomes non-negligible relative to the stiffness of the solid structure, the poromechanical coupling between the fluid and the solid has an increasingly strong impact on the flow. For very large pressures or very soft materials, as is the case for hydraulic fracturing and arterial flows, this coupling can lead to large elastic deformations or plastic flow and hence to strong deviations from a classical, linear poroelastic response. In this thesis, we investigate large deformation poroelasticity and poroelasto-plasticity via the use of a simple axisymmetric model problem. We use the relative simplicity of this model problem to conduct the first systematic analysis of the effects of driving method, geometry and numerous facets of nonlinearity on the resulting flow and deformation. We consider two different permeability laws (constant vs. Kozeny-Carman), two stress-strain relationships (Hencky vs. linear), and two constitutive solid behaviours (elasticity vs. elasto-plasticity). We solve these models analytically when possible and using Chebyshev spectral collocation in general. Large deformations are inherently nonlinear, and these nonlinear effects manifest themselves within the kinematics, permeability, and elastic or plastic stress-strain relations. By isolating each of these effects, we assess the impact of different model simplifications for a wide range of parameter values. In addition to the physical insight they provide, our results and numerical codes could prove useful for benchmarking general numerical- simulation tools.