Statistical approach to the Representative Volume Element Size of Random Composites

Dominique Jeulin (1) , Samuel Forest (2)

1 CMM - Centre de Morphologie Mathématique
2 CDM - Centre des Matériaux

Apparent properties of random structures may be estimated by homogenization from the numerical solution of the PDE concerning the physical fields on real images or on simulations of random media in bounded domains. For this purpose, numerical calculations are made by Finite Elements or by FFT. This numerical approach involves a statistical definition of a representative volume element RVE to provide intervals of confidence of the estimated apparent properties. For large enough domains, bias errors generated by applied boundary conditions can be neglected. The statistical approach of the RVE is summarized. It is illustrated by examples of application to linear and nonlinear micromechanics, optics, fluid flows and wave propagation, for various types of microstructures of industrial materials, as well as of models of random sets.

Mots clés: acoustic properties; Darcy permeability; viscoplasticity; elastoplasticity; elastoviscoplasticity; hyperelasticity; random set; covariance; integral range; RVE; Finite Elements; Fast Fourier Transform; boundary conditions; Hill-Mandel lemma; Voronoi mosaic; Boolean model; Cox Boolean model; hard-core model; fibrous media; porous media; polycrystals; granular media; nanomaterials; digital materials; numerical homogenization; apparent elastic moduli; apparent viscoelastic moduli; apparent permittivity; optical properties

Domaines: Probabilités [math.PR]; Mécanique des matériaux [physics.class-ph]; Sciences de l'ingénieur [physics]; Statistiques [stat]

Dominique Jeulin, Samuel Forest. Statistical approach to the Representative Volume Element Size of Random Composites. Digital materials, Continuum numerical methods at the mesoscale, In press. ⟨hal-03701237v2⟩