Homogenization of a soft elastic material reinforced by fibers

Article type: Research Article

Authors: Bouchitté, Guy^; | Bellieud, Michel

Affiliations: Département de Mathématiques, Université de Toulon et du Var, BP 132, 83957 La Garde cedex, France E‐mail: bouchitte@univ‐tln.fr | Département de Mathématiques, Université de Perpignan, 52 av. de Villeneuve, 66100 Perpignan, France E‐mail: bellieud@univ‐perp.fr

Note: [] Corresponding author.

Abstract: We study the effective properties of an elastic composite medium under the assumption of small deformations. This composite is made of a periodic possibly disconnected subset filled up with a strong material surrounded by another material whose elastic coefficients are very small. The effective macroscopic behaviour obtained by homogenization turns out to be nonlocal and depends highly on the geometry of the strong component. In particular, second order derivative of the displacement appear in the limit energy when disconnected fibers are considered. These results were announced in [8].

Keywords: homogenization, linear elasticity, fiber reinforced structures, two‐scale convergence, Γ‐convergence

Journal: Asymptotic Analysis, vol. 32, no. 2, pp. 153-183, 2002