Premium
Higher‐order energy‐momentum consistent time‐stepping schemes for dynamic finite thermo‐viscoelasticity
Author(s) -
Groß Michael,
Betsch Peter
Publication year - 2009
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200910157
Subject(s) - finite element method , nonlinear system , viscoelasticity , constitutive equation , classical mechanics , isotropy , physics , field (mathematics) , dissipation , displacement field , time derivative , finite strain theory , internal energy , mathematical analysis , mathematics , thermodynamics , quantum mechanics , pure mathematics
This paper is concerned with the energy consistent simulation of a finite thermo‐viscoelastic continuum body. The algorithm is based on a four‐field formulation in the Lagrangian description, in which the deformation field, the velocity field, the temperature field and a strain‐like viscous internal variable field are independent unknowns. The Lagrangian temperature field is determined by the entropy evolution equation associated with Fourier's law of isotropic heat conduction. The viscous evolution equation is derived from a nonlinear internal dissipation. The coupled nonlinear differential equations are discretised by a new space‐time finite element method, consisting of continuous as well as discontinuous finite element approximations in time. Owing to particular time approximations in the constitutive laws, the energy and momentum balances are exactly fulfilled in the fully discrete case. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)