HAL : hal-00724048, version 1

DOI : 10.1007/s10659-012-9396-z

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Journal of Elasticity 111, 2 (2013) Pages: 109-130

On the statistical dependence for the components of random elasticity tensors exhibiting material symmetry properties

J. Guilleminot 1, C. Soize 1

(2013)

This work is concerned with the characterization of the statistical dependence between the components of random elasticity tensors that exhibit some given material symmetries. Such an issue has historically been addressed with no particular reliance on probabilistic reasoning, ending up in almost all cases with independent (or even some deterministic) variables. Therefore, we propose a contribution to the eld by having recourse to the Information Theory. Speci cally, we ci rst introduce a probabilistic methodology that allows for such a dependence to be rigorously characterized and which relies on the Maximum Entropy (MaxEnt) principle. We then discuss the induced dependence for the highest levels of elastic symmetries, ranging from isotropy to orthotropy. It is shown for instance that for the isotropic class, the bulk and shear moduli turn out to be independent Gamma-distributed random variables, whereas the associated stochastic Young modulus and Poisson ratio are statistically dependent random variables.

1 :	Laboratoire de Modélisation et Simulation Multi Echelle (MSME)
	Université Paris-Est Marne-la-Vallée (UPEMLV) – Université Paris-Est Créteil Val-de-Marne (UPEC) – CNRS : UMR8208

Équipe de recherche : Mechanics

Domaine

:

Sciences de l'ingénieur/Mécanique Sciences de l'ingénieur/Matériaux Mathématiques/Probabilités

Mots Clés : Elasticity tensor – Statistical dependence – Elastic moduli – Probabilistic model – MaxEnt approach

hal-00724048, version 1

http://hal-upec-upem.archives-ouvertes.fr/hal-00724048

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Contributeur : Christian Soize <>

Soumis le : Jeudi 16 Août 2012, 19:01:32

Dernière modification le : Jeudi 14 Mars 2013, 17:44:25