Abstract
This paper deals with finite strain isotropic thermo-elasticity without any specific Ansatz regarding the Helmholtz free energy. On the theoretical side, an Eulerian setting of isotropic thermo-elasticity is developed, based on the objective left Cauchy–Green tensor along with the Cauchy stress. The construction of the elastic model relies on a particular invariants choice of the strain measure. These invariants are built so that a succession of elementary experiments, in which the invariants evolve independently, ensures the complete identification of the Helmholtz free energy and thus of the thermo-elastic constitutive law. Expressions idealizing these experimental tests are proposed. A wide range of hyperelastic models are found to be a special case of the model proposed herein.
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