Complete finite-strain isotropic thermo-elasticity: Application to shock-tail analysis

Following the shock-front associated with a multitude of complex nonlinear events, the relaxation at the shock-tail induces a large-strain elastic return. The correct interaction of the spherical stress with it's deviatoric counterpart is too rarely considered as most hyper-elastic models simply neglect this coupling by splitting the Helmholtz free energy.

This study 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. This complete model fully take into account the volumetric/deviatoric coupling which is relevant for high velocity impact.