Homogenization of stratified thermoviscoplastic materials

Authors:
Nicolas Charalambakis and François Murat

Journal:
Quart. Appl. Math. **64** (2006), 359-399

MSC (2000):
Primary 74Q15, 74Q10, 35B27; Secondary 74C10, 74F05, 35Q72, 35M20, 35K55

DOI:
https://doi.org/10.1090/S0033-569X-06-01017-3

Published electronically:
May 22, 2006

MathSciNet review:
2243868

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Abstract | References | Similar Articles | Additional Information

Abstract: In the present paper we study the homogenization of the system of partial differential equations

This sequence of one-dimensional systems is a model for the homogenization of nonhomogeneous, stratified, thermoviscoplastic materials exhibiting thermal softening and a temperature-dependent rate of plastic work converted into heat.

Under the above hypotheses we prove that this system is stable by homogenization. More precisely one can extract a subsequence for which the velocity and the temperature converge to some homogenized velocity and some homogenized temperature which solve a system similar to the system solved by and , for coefficients , and which satisfy hypotheses similar to the hypotheses satisfied by , and . These homogenized coefficients , and are given by some explicit (even if sophisticated) formulas. In particular, the homogenized heat coefficient in general depends on the temperature even if the heterogeneous heat coefficients do not depend on it.

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Additional Information

**Nicolas Charalambakis**

Affiliation:
Department of Civil Engineering, Aristotle University, GR 54124 Thessaloniki, Greece

Email:
charalam@civil.auth.gr

**François Murat**

Affiliation:
Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Boîte courrier 187, 75252 Paris Cedex 05, France

Email:
murat@ann.jussieu.fr

DOI:
https://doi.org/10.1090/S0033-569X-06-01017-3

Keywords:
Homogenization,
thermoviscoplastic materials

Received by editor(s):
December 1, 2005

Published electronically:
May 22, 2006

Article copyright:
© Copyright 2006
Brown University

The copyright for this article reverts to public domain 28 years after publication.