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

Loading next page...
 
/lp/wiley/a-temperature-based-generic-approach-for-the-thermodynamically-KHYIQdbYLg
Publisher
Wiley Subscription Services, Inc., A Wiley Company
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

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve Freelancer

DeepDyve Pro

Price
FREE
$49/month

$360/year
Save searches from Google Scholar, PubMed
Create lists to organize your research
Export lists, citations
Access to DeepDyve database
Abstract access only
Unlimited access to over
18 million full-text articles
Print
20 pages/month
PDF Discount
20% off