De-Hydration and Remodeling of Biological Materials: Swelling Theory for Multi-Domain Bodies

Abstract

Biological materials always exhibit heterogeneous physical properties, both mechanical and chemical, which give them a rich phenomenology that poses significant challenges in the developing of effective models. The Flory–Rehner theory revolutionized our understanding of the dynamics of the liquid-polymers coupling in soft swollen gels, recognizing polymers as elastic networks stretched by the presence of liquid. Despite its foundational role, applying this theory to bodies with non uniform physical properties requires further improvements. This article proposes a unified approach to address mechano-diffusion challenges in multi-domain bodies, that is in material bodies made of regions having different chemo-mechanical properties, and focuses on the dehydration and remodeling of biological-like materials. Drawing inspiration from natural systems, we integrate principles from nonlinear mechanics and swelling theories; in particular, what is specifically new is the idea of applying the notion of the multiplicative decomposition of the strain–developed for plasticity–to model the swelling properties of a body made of two or more materials. The article gives a systematic presentation of the subject, and guides readers through key concepts and practical insights, aiming to provide a robust framework for modeling chemo-mechanical interactions. Moreover, it paves the way for the modeling of heterogenous bodies having spatially-varying properties.