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Formulation of thermoelastic dissipative material behavior using GENERIC

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Abstract

We show that the coupled balance equations for a large class of dissipative materials can be cast in the form of GENERIC (General Equations for Non-Equilibrium Reversible Irreversible Coupling). In dissipative solids (generalized standard materials), the state of a material point is described by dissipative internal variables in addition to the elastic deformation and the temperature. The framework GENERIC allows for an efficient derivation of thermodynamically consistent coupled field equations, while revealing additional underlying physical structures, like the role of the free energy as the driving potential for reversible effects and the role of the free entropy (Massieu potential) as the driving potential for dissipative effects. Applications to large and small-strain thermoplasticity are given. Moreover, for the quasistatic case, where the deformation can be statically eliminated, we derive a generalized gradient structure for the internal variable and the temperature with a reduced entropy as driving functional.

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  1. WIAS, Berlin, Germany

    Alexander Mielke

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  1. Alexander Mielke
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Correspondence to Alexander Mielke.

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Communicated by L. Truskinovsky.

Research partially supported by Deutsche Forschungsgemeinschaft within Matheon via the subproject C18 Analysis and numerics of multidimensional models for elastic phase transformations in shape-memory alloys.

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Mielke, A. Formulation of thermoelastic dissipative material behavior using GENERIC. Continuum Mech. Thermodyn. 23, 233–256 (2011). https://doi.org/10.1007/s00161-010-0179-0

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