Stable long-term simulation of dynamically loaded elastomers

A well–known problem in long–term simulations of flexible solid bodies is the restriction to small time steps of standard time integrators in order to obtain a stable simulation. One approach is to achieve exact energy conservation while simulating a nonlinear elastic body (see Reference 1] and the references therein). Additionally, total linear and total angular momentum is conserved for a free motion. This approach leads to a qualitatively improved solution, because the approximated time evolution exactly fulfills the same physical laws as the exact time evolution. Incorporating energy dissipation, the energy conserving time integration is extended to an energy consistent time integration. It turned out that such an energy consistent time integration is also of great advantage when computing finite motions of flexible solid bodies with material dissipation (see References 2,3]). This paper points out that an energy consistent time discretisation is also advantageous for dynamic finite deformation thermoviscoelasticity under dynamic loads. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)