A variational formulation of thermomechanical constitutive update for hyperbolic conservation laws

In this paper, a variational framework is proposed for the constitutive update of thermomechanical models in special case where their input results from quantities directly updated by hyperbolic conservation laws. Both continuum and consistent first order accurate discrete settings are derived. The originality work lies that driven rates some strain measure internal energy density setting, leading to rate-type description local problem, values at time these setting. These solution system laws including principle thermodynamics, ensuring right shock speeds will be computed. This point crucial importance when simulating impact on structures instance. approach illustrated thermo-hyperelastic-viscoplastic solid media, especially using parameterization flow rule direction based pseudo-stresses Mosler & co-workers. solver then coupled with second flux difference splitting finite volume method, which permits solve set Comparisons performed test cases numerical solutions obtained elements an explicit time-stepping temperature-driven update. They allow show good behavior approach.