Speaker
Description
We propose a unifying approach combining a mixed polyconvexity-inspired framework with the thermodynamically consistent GENERIC (General Equation for Non-Equilibrium Reversible Irreversible Coupling) formulation to simulate coupled nonlinear thermo-elastodynamic problems while preserving specific structural properties, depending on the chosen thermodynamic variable.GENERIC provides a thermodynamically consistent framework that splits the underlying Evolution equations additively into reversible and irreversible parts (see [5]). By selecting suitable thermodynamic variables, GENERIC ensures structural properties such as the conservation of total energy or a non-decreasing total entropy when discretized in time and space (see e.g. [4]). Building on this, we extend the framework to incorporate a mixed Hu-Washizu type formulation, inspired by the polyconvex stored energy functions considered in [1]. This formulation employs the properties of the tensor cross product [2] to enforce the right Cauchy-Green strain tensor, along with its cofactor and determinant, as independent variables through a set of kinematic constraints. We apply the special operator form of GENERIC (see [3]) to this mixed formulation to obtain a new mixed GENERIC formalism and subsequently the strong form of a mixed nonlinear fully coupled thermo-elastodynamical framework, where the systems temperature, internal energy or entropy can be chosen as thermodynamic variable - each offering distinct advantages. Eventually, the numerical performance of the newly designed method is investigated in representative numerical examples.
[1] Betsch, P., Janz, A., and Hesch, C. A mixed variational framework for the design of energy-momentum schemes inspired by the structure of polyconvex stored energy functions. In: Comput. Methods Appl. Mech. Engrg., 335: 660–696, 2018.
[2] Bonet, J., Gil, A. J., and Ortigosa, R. On a tensor cross product based formulation of large strain solid mechanics. In: Int. J. Solids Structures, 84: 49–63, 2016.
[3] Mielke, A. Formulation of thermoelastic dissipative material behavior using GENERIC. In: Continuum Mech. Thermodyn., 23: 233–256, 2011.
[4] Schiebl, M. and Betsch, P. Structure-preserving space-time discretization of large-strain thermo-viscoelasticity in the framework of GENERIC. In: Int. J. Numer. Methods. Eng., 122(14),
[5] Öttinger, H. Beyond equilibrium thermodynamics. John Wiley \& Sons, 2005.
