Statistical approach to the Representative Volume Element Size of Random Composites
Résumé
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
- polycrystals
- apparent viscoelastic moduli
- porous media
- fibrous media
- hard-core model
- Cox Boolean model
- Boolean model
- Voronoi mosaic
- granular media
- nanomaterials
- digital materials
- numerical homogenization
- apparent elastic moduli
- integral range
- apparent permittivity
- optical properties
- Hill-Mandel lemma
- boundary conditions
- Fast Fourier Transform
- Finite Elements
- RVE
- covariance
- random set
- hyperelasticity
- elastoviscoplasticity
- elastoplasticity
- viscoplasticity
- Darcy permeability
- acoustic properties
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