Energy-Consistent Integration Scheme for Multi-body Systems with Dissipation

Abstract

This work is concerned with the numerical solution of the evolution equations of thermo-mechanical systems, in such a way that the scheme itself satisfies the laws of thermodynamics. Within this framework, we present a novel integration scheme for the dynamics of viscoelastic continuum bodies in isothermal conditions. The proposed scheme intrinsically satisfies the laws of thermodynamics arising from the continuous. This approach enables us to address the inclusion of dissipation in bodies which is typically present in multi-body applications of interest. The resulting solutions are physically accurate since they preserve the fundamental physical properties of the model. Furthermore, the method gives an excellent performance with respect to robustness and stability. Proof for these claims as well as numerical examples that illustrate the performance of the novel scheme are provided.