Affiliations: Laboratoire de Mécanique et de Génie Civil, UMR-CNRS 5508, Université Montpellier 2, Case courrier 048, Place Eugène Bataillon, 34095 Montpellier cedex 5, France E-mail: [email protected] | ACSIOM and EMIAN, UMR-CNRS 5149, Université Montpellier 2 and CUFR de Nîmes, Case courrier 051, Place Eugène Bataillon, 34095 Montpellier cedex 5, France E-mail: [email protected]
Note: [] Corresponding author.
Abstract: We obtain a nonlocal functional as the variational limit of an integral functional associated with the strain energy of a pseudo-plastic material reinforced by a ε-periodic distribution of pseudo plastic fibers. We begin by studying separately the variational limit behavior, when ε goes to zero, of the structure made of the soft material without fibers, and of the structure constituted by the distribution of the small fibers. We show that the complete structure is, in the sense of the Γ-convergence, equivalent to a new homogeneous structure whose functional energy is the epigraphical sum of the limit integral functionals energies modeling each two previous structures.
Keywords: homogenization, Γ-convergence, convex functional of measures, pseudo-plasticity
