A fully coupled theory and variational principle for Thermal-electrical-chemical-mechanical processes

Thermal-electrical-chemical-mechanical coupling controls the behavior of many transport and electrochemical reactions processes in physical, chemical and biological systems. Hence, advanced understanding of the coupled behavior is crucial and attracting a large research interest. However, most of the existing coupling theories are limited to the partial coupling or particular process. In this paper, on the basis of irreversible thermodynamics, a variational principle for the thermal electrical chemical mechanical fully coupling problems is proposed. The complete fully coupling governing equations, including the heat conduction, mass diffusion, electrochemical reactions and electrostatic potential, are derived from the variational principle. Here, the piezoelectricity, conductivity, and electrochemical reactions are taken into account. Both the constitutive relations and evolving equations are fully coupled. This theory can be used to deal with coupling problems in solids, including conductors, semiconductors, piezoelectric and nonpiezoelectric dielectrics. As an application of this work, a developed boundary value problem is solved numerically in a mixed ion-electronic conductor (MIEC). Numerical results show that the coupling between electric field, diffusion, and chemical reactions influence the defect distribution, electrostatic potential and mechanical stress.