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Random-field model for the elasticity tensor of anisotropic random media

Christian Soize 1, *
* Corresponding author
Abstract : This Note deals with the construction of a non-Gaussian positive definite matrix-valued random field whose mathematical properties allow the fourth-order elasticity tensor of random non homogeneous anisotropic three dimensional elastic media to be modelled. If the usual parametric probabilistic approach was used, then 21 mutually dependent random fields should be modelled and identified by using experimental data. Such an approach would be very difficult because the systems of the marginal probability distributions of these random fields have to be identified due to the fact that, for a boundary value problem, the displacement field of the random medium is a non-linear mapping of the random elasticity tensor. The theory presented in this paper allows such a probabilistic model of the fourth-order elasticity tensor field to be constructed and depends only of four scalar parameters: three spatial correlation lengths and one parameter allowing the level of the random fluctuations to be controlled.
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Christian Soize. Random-field model for the elasticity tensor of anisotropic random media. Comptes Rendus Mécanique, Elsevier Masson, 2004, 332 (12), pp.1007-1012. ⟨10.1016/j.crme.2004.09.008⟩. ⟨hal-00686196⟩

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