Analysis of Monolithic Algorithmic Schemes for an Energy-Consistent Variational Formulation of a Coupled Thermo-Visco-Elastic Problem

A new variational formulation of coupled thermo-mechanical boundary-value problems has been recently proposed [1, 2], allowing to write mechanical and thermal balance equation under the form of an optimisation problem of a scalar energy-like functional. This functional is analysed in the framework of a thermo-visco-elastic problem, considering a strong coupling by taking into account the temperature dependency of mechanical properties. Different algorithmic schemes were tested, aiming to find the one that exhibits best computational performance. A simplified case shows that the optimum of the scalar energy-like functional is a saddle point.