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This paper formulates variational integrators for finite elementdiscretizations of deformable bodies with heat conduction in the form of finitespeed thermal waves. The cornerstone of the construction consists in takingadvantage of the fact that the Green-Naghdi theory of type II forthermo-elastic solids has a Hamiltonian structure. Thus, standard techniques toconstruct variational integrators can be applied to finite elementdiscretizations of the problem. The resulting discrete-in-time trajectories arethen consistent with the laws of thermodynamics for these systems: for anisolated system, they exactly conserve the total entropy, and nearly exactlyconserve the total energy over exponentially long periods of time. Moreover,linear and angular momenta are also exactly conserved whenever the exact systemdoes. For definiteness, we construct an explicit second-order accuratealgorithm for affine tetrahedral elements in two and three-dimensions, anddemonstrate its performance with numerical examples.

Variational integrators for the dynamics of thermo-elastic solids with finite speed thermal waves