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We present a theoretical and computational model for the behavior of a poroussolid undergoing two interdependent processes, the finite deformation of asolid and species migration through the solid, which are distinct in bulk andon surface. Nonlinear theories allow us to systematically study porous solidsin a wide range of applications, such as drug delivery, biomaterial design,fundamental study of biomechanics and mechanobiology, and the design of sensorsand actuators. As we aim to understand the physical phenomena at a smallerlength scale towards comprehending the fundamental biological processes and theminiaturization of devices, the surface effect becomes more pertinent. Althoughexisting methodologies provide the necessary tools to study coupled bulkeffects for deformation and diffusion; however, very little is known aboutfully coupled bulk and surface poroelasticity at finite strain. Here we developa thermodynamically consistent formulation for multiphysics processes ofsurface and bulk poroelasticity, specialized for soft hydrated solids, alongwith a corresponding finite element implementation. Our multiphysical approachcaptures the interplay between competing processes of finite deformation andspecies diffusion through the bulk and surface, and provides invaluable insightwhen surface effects are important.

A finite element implementation of finite deformation surface and bulk poroelasticity