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 modeling 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.