A theoretical model and finite element formulation for coupled thermo-electro-chemo-mechanical media

Many synthetic and natural media which are often described as multifunctional smart materials demonstrate thermo-electro-chemo-mechanical coupling behavior and are sensitive to external environmental stimuli. This paper presents a set of basic equations, a variational principle and a finite element procedure for investigating the coupled behavior of thermo-electro-chemo-elastic media. Emphasis here is placed on introducing chemical effects into the coupled equation system. Using the governing equations of thermal conduction, electric flow, ionic diffusion and momentum balance, a variational principle is deduced for a linearly coupled system by means of the extended Gibb's free energy function. The variational principle is then used to derive a fully coupled multi-field finite element formulation for simulating the coupled thermo-electro-chemo-elastic behavior of biological tissues. Numerical examples are considered to illustrate the coupled phenomena of the materials and to verify the proposed variational theory and numerical procedure.