Random versus periodic microstructures for elasticity of fibers reinforced composites

•Random versus periodic microstructures for elasticity of composites.•We studied with the help of finite elements the influence of microstructure on effective elastic properties of composites.•We focus on homogenization using hexagonal periodic cell confronted to random materials.

Homogenization of effective elastic properties of fiber reinforced composites frequently supposed periodic arrangement of fibers because such microstructures allow analytical or low computational cost integrations. Hexagonal frame was often preferred than square one which is strongly anisotropic. In practical situations those periodical microstructures are not realistic. Real microstructures are often random or if they are periodic their boundaries don't fit with the periodic scheme. We studied with the help of finite elements samples that exhibit hexagonal arrangement of fibers embedded in a random distribution. Characteristic length scales of hexagonal area were extracted from observation of stress maps. Principal results are a short scale in which bulk and shear stresses become structured. On the other hand we nether reached a size large enough to observe local stress maps similar to those produced by a periodic model.