Plasticity coupled with thermo-electric fields: Thermodynamics framework and finite element method computations

A consistent thermodynamic-based theoretical framework and three-dimensional finite element formulation is presented, capable of coupling elastic, thermal and electric fields. The complete set of governing equations is obtained from conservation principles for electric charge, energy and momentum. The second principle of thermodynamics is taken into account to introduce the irreversible phenomena, such as plastic dissipation or Joule heating. The constitutive relations are derived consistently from the Helmholtz free-energy potential for each corresponding dual variable in terms of the defined set of state variables. We consider the case of linear isotropic hardening model for plasticity, and provide the consistent form of the tangent thermo-electro-elastoplastic modulus through dual variable computations. The latter plays the crucial role in ensuring fast convergence properties of the finite element computations with the proposed coupled plasticity model. The implementation is carried out in a research version of the well-known computer code FEAP. Several numerical simulations are presented in order to illustrate the proposed model and formulation capabilities for providing an enhanced formulation of an important practical application in terms of Peltier cells.