Multiphysics modeling of surface diffusion coupled with large deformation in 3D solids

Abstract

This study presents a comprehensive theoretical and computational model that explores the behavior of a thin hydrated film bonded to a non-hydrated/impermeable soft substrate in the context of surface and bulk elasticity coupled with surface diffusion kinetics. This type of coupling manifests as an integral aspect in diverse engineering processes encountered in optical interference coatings, tissue engineering, soft electronics, and can prove important in the design process for the next generation of sensors and actuators, especially as the focus is shifted to systems in smaller length scales. The intricate interplay between solvent diffusion and deformation of the film is governed by surface poroelasticity, and the viscoelastic deformation of the substrate. While existing methodologies offer tools for studying coupled poroelasticity involving solvent diffusion and network deformation, there exists a gap in understanding how coupled poroelastic processes occurring in a film attached to the boundary of a highly deformable solid can influence its response. In this study, we introduce a non-equilibrium thermodynamics formulation encompassing the multiphysical processes of surface poroelasticity and bulk viscoelasticity, complemented by a corresponding finite element implementation. This study makes significant contributions to solid mechanics and computational modeling by (i) modeling surface diffusion coupled with a viscoelastic substrate, enabling the study of time-dependent responses critical for practical applications, (ii) providing a robust theoretical framework for coupling two materials (film and substrate) with distinct reference (stress-free) states, including a detailed analytical derivation of the initial state, and (iii) efficiently modeling the thin film using a 2D mesh to avoid the need for a fine 3D solid mesh, thus reducing computational costs while maintaining accuracy. This work contributes valuable insights, particularly in scenarios where the coupling of surface diffusion kinetics and substrate elasticity is an important design factor.