diffusionelasticity

Diffusionelasticity is a term used to describe the coupling between diffusion processes and elastic deformation in solids. It covers phenomena where concentration gradients induce stress and strain, and where deformation alters diffusion behavior. The framework is central to chemo-mechanics and swelling materials, including polymer gels, battery electrodes, and porous media.

In a typical model, the solid is described by a displacement field u and a concentration field c. Mechanical equilibrium is given by the balance of linear momentum, div sigma = 0, where the stress sigma arises from elastic deformation. A swelling or interaction-induced eigenstrain epsilon_sw(c) accounts for concentration-dependent expansion, so the total strain is epsilon = epsilon_elastic + epsilon_sw(c), and stress is sigma = C : (epsilon - epsilon_sw(c)). The diffusion equation for c is ∂c/∂t = div(D grad c) + S, where D may depend on strain or concentration, and S represents sources or sinks. Coupling can also be introduced via a chemical potential mu that links diffusion flux to gradients in mu, with mu including contributions from concentration and mechanical fields.

Coupled diffusion-elastic models are used to study diffusion-induced stresses, swelling dynamics, and fracture in swelling clays and gels, as well as intercalation-induced stresses in lithium-ion battery electrodes and other energy-storage materials. They are commonly solved with finite element methods and energy-based variational formulations, which handle nonlinearities from large deformations and concentration-dependent material properties.

See also poroelasticity, chemo-mechanics, swelling, intercalation. References in practice point to the literature on diffusion-assisted mechanics and swelling theory.