The Double Generator Boundary Augmented bracket structure: a structure-preserving space-time integration framework for coupled thermo-visco-elastodynamics

The Double Generator Boundary Augmented bracket structure is a double generator bracket formulation, tailored to model continuum thermodynamics. Based on the idea of bracket generated formulations, this framework encompasses balance principles and thermodynamics laws within a unique expression. The present paper develops the methodology to derive this structure from classical equations of continuum thermodynamics for two examples. We consider first a unidimensional small strains generalized standard material, with a general quadratic dissipation potential. Then, we consider the example of large strain thermo-visco-elastodynamics, within the multisymplectic framework. We derive, for the first time, a multisymplectic Poisson bracket for thermo- (visco)-elastodynamics. Eventually, both formulations are shown to recover exactly balance principles and thermodynamics laws. This paper sets grounds necessary to develop variational integrators from the Double Generator Boundary Augmented bracket structure.