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An energy‐entropy‐consistent time stepping scheme for finite thermo‐viscoelasticity
Author(s) -
Krüger Melanie,
Groß Michael,
Betsch Peter
Publication year - 2014
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201410097
Subject(s) - integrator , discretization , finite element method , mathematics , lyapunov function , midpoint , entropy (arrow of time) , mathematical analysis , control theory (sociology) , physics , computer science , geometry , nonlinear system , voltage , thermodynamics , control (management) , quantum mechanics , artificial intelligence
Abstract 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)