Calculus of Variations and Geometric Measure Theory

L. Carbone - D. Cioranescu - R. De Arcangelis - A. Gaudiello

An Approach to the Homogenization of Nonlinear Elastomers via the Theory of Unbounded Functionals

created on 20 Dec 2001
modified on 26 Dec 2001


Published Paper

Inserted: 20 dec 2001
Last Updated: 26 dec 2001

Journal: C. R. Acad. Sci. Paris Sér. I Math.
Volume: 332
Pages: 283-288
Year: 2001


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 the presence of pointwise oscillating constraints on the gradients of the admissible deformations. 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. An explicit computation for the homogenized integrand relative to energy density in a particular relevant case is derived.