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
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
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