Energy-consistent time integration for nonlinear viscoelasticity. (English) Zbl 1398.74368
Summary: This paper is concerned with the numerical solution of the evolution equations of thermomechanical 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. This method intrinsically satisfies the laws of thermodynamics arising from the continuum, as well as the possible additional symmetries. 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.
MSC:
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 74D10 | Nonlinear constitutive equations for materials with memory |
| 74B20 | Nonlinear elasticity |
| 74F05 | Thermal effects in solid mechanics |
| 74S20 | Finite difference methods applied to problems in solid mechanics |
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