Mathematical/Analytical Modelling of Electrothermal - Structural physics coupling.

I am working on a project for my master thesis in which i am simulating an Electrothermal -structural multiphysics problem. I am looking for a help in modelling the whole coupling mathematically that must contain a sensible connection(in mathematical form-complexity is not a restriction) between transfer of energy from Voltage > Thermal > Mechanical Deformation of the body. The analytical results must match with the simulation result(will be provided by me) within acceptable level of tolerance. To give you an idea of mutiphysics problem, there is structure to which Voltage is applied which heat up the structure(by joule thomson effect) and then that heat energy resulted in expansion/contraction of the structure. Thank you for your time.