This work deals with the thermodynamically consistent (TC) time integration of thermoelastic systems with polyconvex density functions using the notion of the tensor‐cross‐product. While energy‐momentum preserving integrators are well‐known for conservative (isothermal) mechanical systems, Romero introduced in [7, 8] the new class of TC integrators. While  dealt with the sample application of thermo‐elastodynamics, the scope of application was extended in  to coupled thermo‐viscoelastodynamics in temperature form. A first step towards the systematic design of a TC integrator is to cast the evolution equations into the GENERIC (General Equation for Non‐Equilibrium Reversible‐Irreversible Coupling) framework  which reveals additional underlying physical structures of the system. Relying on a polyconvex density function and using the notion of the tensor‐cross‐product  we arrive at a polyconvex version of the GENERIC framework. Further applying the notion of a discrete gradient leads to a TC integrator.
Proceedings in Applied Mathematics & Mechanics – Wiley
Published: Jan 1, 2017
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