Calculus of Variations and Geometric Measure Theory
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L. Carbone - D. Cioranescu - R. De Arcangelis - A. Gaudiello

Homogenization of Unbounded Functionals and Nonlinear Elastomers. The Case of the Fixed Constraints Set

created on 16 Dec 2002
modified by dearcange on 09 Dec 2005

[BibTeX]

Published Paper

Inserted: 16 dec 2002
Last Updated: 9 dec 2005

Journal: ESAIM Control. Optim. Calc. Var.
Volume: 10
Number: 1
Pages: 53-83
Year: 2004

Abstract:

The paper is a continuation of a previous work of the same authors dealing with homogenization processes for some energies of integral type arising in the modelling of rubber-like elastomers. The previous paper took into account the general case of the homogenization of energies in presence of pointwise oscillating constraints on the admissible deformations. In the present paper homogenization processes are treated in the particular case of fixed constraints set, in which minimal coerciveness hypotheses can be assumed, and in which the results can be obtained in the general framework of $BV$ spaces. The classical homogenization result is established for Dirichlet with affine boundary data, Neumann, and mixed problems, by proving that the limit energy is again of integral type, gradient constrained, and with an explicitly computed homogeneous density.

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