Energy-Consistent Time-Integration for Dynamic Finite Deformation Thermo-Viscoelasticity

Abstract eng:
The present paper is based on the works of Romero [1] and Groß [2]. Both approaches use energy consistent time-integrators for dynamic finite thermoelasticity and thermo-viscoelasticity, respectively. In Romero [1] partitioned discrete derivatives (see Gonzalez [3]) for an energyconsistent time integration are used. The system of partial differential equations is described in the format of GENERIC (General equations for non-equilibrium reversible irreversible coupling), which was introduced by Öttinger [4]. Furthermore the Poissonian variables (linear momentum, configuration, entropy) are employed. In contrast to Romero[1], Groß [2] utilizes a continuousdiscontinuous Galerkin method for the time-integration using a stress approximation for energy consistency in the sense of Gonzalez [3]. The system of differential equations is described in Lagrangian variables (velocity, configuration, temperatures). In the work of Krüger et al. [5], both time integrators are compared for a two-dimensional thermoelastic double-pendulum. Once again the enhanced numerical stability of structure-preserving integrators in comparison to standard integrators is evidenced, but the difference of these approaches is also elaborated. The main goal of the present work is the extension of the time integrator in Romero [1] to dynamic finite thermo-viscoelasticity for a comparison with the method in Groß [2]. This yields an additional evolution equation for the time-dependent internal variable, which will be inserted in the system. The computer implementation of both approaches is for the time being done with a monolithic solution strategy. The numerical performance of the two schemes is compared in the context of representative examples.

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