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Higher‐order energy consistent time integrators for nonlinear thermoviscoelastodynamics
Author(s) -
Groß Michael,
Betsch Peter
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700183
Subject(s) - integrator , dissipation , nonlinear system , galerkin method , energy (signal processing) , energy balance , stability (learning theory) , consistency (knowledge bases) , mathematics , thermal conduction , control theory (sociology) , computer science , mathematical analysis , physics , geometry , computer network , statistics , control (management) , bandwidth (computing) , quantum mechanics , machine learning , artificial intelligence , thermodynamics
An advantage of the temporal fe method is that higher‐order accurate time integrators can be constructed easily. A further important advantage is the inherent energy consistency if applied to equations of motion. The temporal fe method is therefore used to construct higher‐order energy‐momentum conserving time integrators for nonlinear elastodynamics (see Ref. [1]). Considering finite motions of a flexible solid body with internal dissipation, an energy consistent time integration is also of great advantage (see the references [2, 3]). In this paper, we show that an energy consistent time integration is also advantageous for dynamics with dissipation arising from conduction of heat as well as from a viscous material. The energy consistency is preserved by using a new enhanced hybrid Galerkin (ehG) method. The obtained numerical schemes satisfy the energy balance exactly, independent of their accuracy and the used time step size. This guarantees numerical stability. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)