Galerkin methods in time for semi‐discrete viscoelastodynamics

Abstract

AbstractIn semi‐discrete nonlinear elastodynamics, higher order energy and momentum conserving time stepping schemes turned out to be well suited for computing long time motions [1]. In comparison to standard ODE integrators, conserving schemes exhibit superior stability properties which are of utmost importance in a nonlinear .nite element framework. We show that conserving schemes are particularly well suited as starting point for the development of energy consistent schemes for dissipative dynamical systems. In particular, viscoelastic material behaviour is considered. A key advantage of energy consistent schemes lies in the fact that the equilibrium state of viscoelastic systems can be de.nitely reached, independent of the material parameters. In the paper, we compare two Galerkin methods for the temporal discretisation of semi‐discrete nonlinear viscoelastodynamics: the standard continuous Galerkin (cG) method and an enhanced continuous Galerkin (eG) method which ful.ls the total energy balance exactly. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)