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ESAIM: Control, Optimisation and Calculus of Variations (1)

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Homogenization of unbounded functionals and nonlinear elastomers. The case of the fixed constraints set
Luciano Carbone, Doina Cioranescu, Riccardo De Arcangelis, Antonio Gaudiello
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 10 / Issue 1 / January 2004

Published online by Cambridge University Press:

15 February 2004, pp. 53-83

Print publication:

January 2004
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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.