A temperature‐based GENERIC approach for the thermodynamically consistent integration of thermoelastic solids

A temperature‐based GENERIC approach for the thermodynamically consistent integration of... This work deals with the thermodynamically consistent (TC) time integration of thermoelastic systems with polyconvex density functions using the notion of the tensor‐cross‐product. While energy‐momentum preserving integrators are well‐known for conservative (isothermal) mechanical systems, Romero introduced in [7, 8] the new class of TC integrators. While [8] dealt with the sample application of thermo‐elastodynamics, the scope of application was extended in [2] to coupled thermo‐viscoelastodynamics in temperature form. A first step towards the systematic design of a TC integrator is to cast the evolution equations into the GENERIC (General Equation for Non‐Equilibrium Reversible‐Irreversible Coupling) framework [6] which reveals additional underlying physical structures of the system. Relying on a polyconvex density function and using the notion of the tensor‐cross‐product [1] we arrive at a polyconvex version of the GENERIC framework. Further applying the notion of a discrete gradient leads to a TC integrator. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Proceedings in Applied Mathematics & Mechanics Wiley

A temperature‐based GENERIC approach for the thermodynamically consistent integration of thermoelastic solids

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Publisher
Wiley
Copyright
Copyright © 2017 Wiley Subscription Services
ISSN
1617-7061
eISSN
1617-7061
D.O.I.
10.1002/pamm.201710246
Publisher site
See Article on Publisher Site

Abstract

This work deals with the thermodynamically consistent (TC) time integration of thermoelastic systems with polyconvex density functions using the notion of the tensor‐cross‐product. While energy‐momentum preserving integrators are well‐known for conservative (isothermal) mechanical systems, Romero introduced in [7, 8] the new class of TC integrators. While [8] dealt with the sample application of thermo‐elastodynamics, the scope of application was extended in [2] to coupled thermo‐viscoelastodynamics in temperature form. A first step towards the systematic design of a TC integrator is to cast the evolution equations into the GENERIC (General Equation for Non‐Equilibrium Reversible‐Irreversible Coupling) framework [6] which reveals additional underlying physical structures of the system. Relying on a polyconvex density function and using the notion of the tensor‐cross‐product [1] we arrive at a polyconvex version of the GENERIC framework. Further applying the notion of a discrete gradient leads to a TC integrator.

Journal

Proceedings in Applied Mathematics & MechanicsWiley

Published: Jan 1, 2017

References

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