Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Two stable-by-homogenization models in simple shearing of rate-dependent non-homogeneous materials

Authors: Nicolas Charalambakis and François Murat
Journal: Quart. Appl. Math. 68 (2010), 395-419
MSC (2000): Primary 74Q15, 74Q10, 35B27
DOI: https://doi.org/10.1090/S0033-569X-10-01199-9
Published electronically: June 8, 2010
MathSciNet review: 2676968
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Abstract | References | Similar Articles | Additional Information


In this paper we study two models, the viscoplastic model and the thermoviscous model, of rate-dependent non-homogeneous materials with non-oscillating strain-rate sensitivity submitted to simple quasistatic shearing. We prove that the two models are stable by homogenization, i.e. that the equations in both the heterogeneous problems and the homogenized one have the same form, and we give explicit formulas for the homogenized (effective) coefficients. These formulas depend on the initial conditions, but not on the boundary conditions. Our theoretical results are illustrated by a numerical example.

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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-10-01199-9
Received by editor(s): November 21, 2007
Published electronically: June 8, 2010
Article copyright: © Copyright 2010 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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