Effect of reinforcement shape on physical properties and representative volume element of particles-reinforced composites: Statistical and numerical approaches

• Equivalence between ellipsoidal and spherical particles.
• Effect of the reinforcement shape on the effective properties.
• Statistical and numerical approaches.
• Numerical homogenization technique.

We are considering the effect of the particle shape on the effective elastic properties and representative volume element of two-phase composites. In this work, microstructures with ellipsoidal and spherical particles are considered. Three dimensional particles are randomly generated for different volume fractions without any contact between neighbouring spheres according to Poisson process. The used analysis is based on numerical homogenization approaches by finite element method and morphological characterization of microstructures by random fields. The effects of various parameters such as particles volume fraction, contrast in phase properties and particles shape were identified. The statistical methods are introduced and then coupled with numerical simulations. The notion of statistically representative volume, named the deterministic representative volume element (RVE), is used. The variation of this RVE as a function of particles volume fraction for heterogeneous materials is presented. These variations suggest us to identify the morphological distribution of particles which is more anisotropic and which needs a large RVE size.