An energy‐entropy‐consistent time stepping scheme for finite thermo‐viscoelasticity

This paper presents a time integrator, which is based on a time discrete spatially weak finite element formulation, but fulfills the same balance laws as the underlying (five) differential equations. Namely, in addition to the balances of linear and angular momentum as well as entropy, also the balances of total energy and LYAPUNOV function are fulfilled. The spatially weak formulation is obtained by integration by parts. Where the resulting virtual stress power term is well‐known, the virtual entropy production by conduction of heat is less known. The time discretisation is based on the midpoint rule and non‐standard time discrete differential operators. This time integrator is a further development of the TC integrator of I. ROMERO. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)