Thermodynamic formulation for non-linear finite element applied to multi-coupled materials

Resumen

This thesis presents a general framework that combines several theories applied to multiphysics of coupled materials, taking into account the mechanical, thermal, electric and magnetic fields. This framework is specialized for non-linear finite element formulations with non-equilibrium interactions. The resulting computer code is validated and applied to several advanced aspects of thermoelectric materials. From a theoretical point of view, the multi-coupled governing equations are obtained from the energy, momentum and entropy balances; the total energy is the sum of the thermal, mechanical and electromagnetic energies. The momentum balance takes into account the mechanical and the electromagnetic balances, for the latter the Abraham representation is considered. Finally, the entropy balance is formulated using the Extended Non-Equilibrium Thermodynamic formalism. This formalism permits to study thermodynamic systems for which the local equilibrium hypothesis is not valid, introducing in the entropy balance dissipative fluxes closely related with empirical parameters. These empirical parameters represent thermal and electric viscosities and are denominated relaxation times. Numerically, the governing equations are developed into a variational formulation. The resulting multi-coupled problem is implemented in the research computer code FEAP. Standard isoparametric eight-node elements with six degrees of freedom per node (three displacements, temperature, voltage and magnetic scalar potential) are used. Non-linearities are addressed with the Newton-Rhapson algorithm. For the dynamic problem with relaxation times, HHT and Newmark-B (regularized by relating time steps and element sizes) methods are compared to obtain accurate results. Finally, the finite element implementation is validated and the time integration algorithm is tested using applications of practical interest, investigating: * Propagation of temperatures, voltages and heat fluxes due to thermal relaxation time * Elasto-thermo-electric responses for materials subjected to electric pulses * Hysteretic behavior of photovoltaic materials due to coupling between relaxation times * Galvanomagnetic and thermomagnetic interactions to improve efficiency of Peltier cells taking into account the induced thermal stresses