A numerical comparison between the additive and multiplicative decomposition applied to large strain thermo-elastic models

Resumo

In this work, we develop a numerical framework, using the finite element method, to perform two-
dimensional analysis of solids with thermo-elastic constitutive model, subject to large displacements and large

strains. Both the thermo-elastic model and the heat conduction equation are derived from the first and second
laws of thermodynamics, where the latter is expressed by the Clausius-Duhem inequality. The formulation uses
the concept of Helmholtz free energy, from which the stress and the entropy are derived. The elastic and thermal
parts of deformations are distinguished by two main strategies: the additive decomposition of the Green-Lagrange
strain tensor, and the multiplicative decomposition of the deformation gradient. For each, both the linear and
exponential thermal expansion laws are considered, and a neo-Hookean model is applied for the elastic part.
Numerical examples are proposed to show the differences and limitations of the applied models on moderate and
large strain levels.