A finite element implementation of finite deformation surface and bulk poroelasticity

We present a theoretical and computational model for the behavior of a porous solid undergoing two interdependent processes, the finite deformation of a solid and species migration through the solid, which are distinct in bulk and on surface. Nonlinear theories allow us to systematically study porous solids in a wide range of applications, such as drug delivery, biomaterial design, fundamental study of biomechanics and mechanobiology, and the design of sensors and actuators. As we aim to understand the physical phenomena at a smaller length scale, towards comprehending fundamental biological processes and miniaturization of devices, surface effect becomes more pertinent. Although existing methodologies provide the necessary tools to study coupled bulk effects for deformation and diffusion; however, very little is known about fully coupled bulk and surface poroelasticity at finite strain. Here we develop a thermodynamically consistent formulation for surface and bulk poroelasticity, specialized for soft hydrated solids, along with a corresponding finite element implementation that includes a three-field weak form. Our approach captures the interplay between competing multiphysical processes of finite deformation and species diffusion, accounting for surface kinematics and surface transport, and provides invaluable insight when surface effects are important.