A class of tensor-valued random fields for random anisotropic elastic microstructure modeling and stochastic homogenization

Christian Soize (1)

1 LaM - Laboratoire de Mécanique

A generic micro-scale stochastic model is presented for a large class of random anisotropic elastic microstructures allowing a parametric analysis of the Representative Volume Element (RVE) size to be performed. This new approach can be useful for a direct experimental identification of random anisotropic elastic microstructures when the standard method cannot easily be applied. Such a RVE is used to construct the macroscopic properties in the context of stochastic homogenization. The probability analysis is not performed as usual for a given particular random microstructure defined in terms of its constituents, but is performed for a large class of random anisotropic elastic microstructures. For this class, the probability istribution of the random effective stiffness tensor is explicitly constructed and allows a full probability analysis of the RVE size to be carried out with respect to the spatial correlation length of the random microstructure.

Mots clés: random fields; non-Gaussian; tensor; random microstructure; anisotropic; elastic microstructure; stochastic homogenization; micro-scale stochastic model; Representative Volume Element (RVE); random effective stiffness tensor

Domaines: Probabilités [math.PR]; Mécanique des matériaux [physics.class-ph]; Mécanique des matériaux [physics.class-ph]

Christian Soize. A class of tensor-valued random fields for random anisotropic elastic microstructure modeling and stochastic homogenization. 5th Computational Stochastic Mechanics Conference (CSM), 2006, Jun 2006, Rhodes, Greece. pp.613-622. ⟨hal-00689699⟩