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 General Case

created on 20 Dec 2001
modified on 16 Dec 2002


Published Paper

Inserted: 20 dec 2001
Last Updated: 16 dec 2002

Journal: Asymptotic Analysis
Volume: 29
Pages: 221-272
Year: 2002


The homogenization process for some energies of integral type arising in the modelling of rubber-like elastomers is carried out. The main feature of the variational problems taken into account is that pointwise oscillating constraints on the admissible deformations, determined by general, not necessarily bounded, constraint sets are involved. The classical homogenization result is established also in this framework, both 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 computeded homogeneous density. Some explicit computations for the homogenized integrands relative to energy densities coming from models in literature are also discussed.

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