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Homogenization of unbounded functionals and nonlinear elastomers. The case of the fixed constraints set

Published online by Cambridge University Press:  15 February 2004

Luciano Carbone ,
Doina Cioranescu ,
Riccardo De Arcangelis  and
Antonio Gaudiello
Luciano Carbone
Affiliation:
Università di Napoli “Federico II”, Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, via Cintia, Complesso Monte S. Angelo, 80126 Napoli, Italy; carbone@biol.dgbm.unina.it., dearcang@unina.it.
Doina Cioranescu
Affiliation:
Université Pierre et Marie Curie (Paris VI), Laboratoire Jacques-Louis Lions, 4 Place Jussieu, 75252 Paris Cedex 05, France; cioran@ann.jussieu.fr.
Riccardo De Arcangelis
Affiliation:
Università di Napoli “Federico II”, Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, via Cintia, Complesso Monte S. Angelo, 80126 Napoli, Italy; carbone@biol.dgbm.unina.it., dearcang@unina.it.
Antonio Gaudiello
Affiliation:
Università di Cassino, Dipartimento di Automazione, Elettromagnetismo, Ingegneria dell'Informazione e Matematica Industriale, via G. Di Biasio 43, 03043 Cassino (FR), Italy; gaudiell@unina.it.
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Abstract

The paper is a continuation of a previous work of the same authorsdealing with homogenization processes for some energiesof integral type arising in the modeling of rubber-like elastomers.The previous paper took into account the general case of thehomogenization of energies in presence of pointwise oscillatingconstraints on the admissible deformations.In the present paper homogenization processes are treated in theparticular case of fixed constraints set, in which minimalcoerciveness hypotheses can be assumed, and in which the results canbe obtained in the general framework of BV spaces.The classical homogenization result is established for Dirichlet withaffine boundary data, Neumann, and mixedproblems, by proving that the limit energy is again of integral type,gradient constrained, and with an explicitly computedhomogeneous density.

Keywords

Homogenizationgradient constrained variational problemsnonlinear elastomers
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 10 , Issue 1 , January 2004 , pp. 53 - 83
Copyright
© EDP Sciences, SMAI, 2004

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