Calculus of Variations and Geometric Measure Theory

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

An Approach to the Homogenization of Nonlinear Elastomers in the Case of the Fixed Constraints Set

created on 26 Dec 2001


Published Paper

Inserted: 26 dec 2001

Journal: Rendiconto dell'Accademia delle Scienze Fisiche e Matematiche della Società Nazionale di Scienze Lettere e Arti in Napoli (4)
Volume: 67
Pages: 235-244
Year: 2000


The homogenization process for some energies of integral type arising in the modelling of nonlinear rubber-like elastomers is presented. Such process is characterized by the presence of pointwise constraints on the gradient of the admissible deformations, and is carried out in the particular case of fixed constraints set. In such case minimal coerciveness hypotheses can be assumed, and the results can be obtained in the general framework of $BV$ spaces. The minimum problems taken into account are of Dirichlet, Neumann, and mixed type.