On mesoscopic probabilistic modeling of random anisotropic media under material symmetry constraints

Johann Guilleminot (1) , Christian Soize (1)

1 MSME - Laboratoire de Modélisation et Simulation Multi Echelle

In this study, we consider the probabilistic modeling of random media at mesoscale. More specifically, we address both the construction of a probabilistic model and the definition of a methodology allowing the numerical simulation (and consequently, the inverse experimental identification) of random elasticity tensors whose mean distance to a given class of material symmetry is specified. Following the eigensystem characterization of the material symmetries, the proposed approach relies on a probabilistic model allowing the variance of selected eigenvalues of the elasticity tensor to be partially prescribed. In this context, a new methodology is defined and applied to a transversely isotropic material. It is shown that the methodology allows the mean of the distance to this symmetry class to be reduced as the overall level of statistical fluctuations increases, no matter the initial distance of the mean model used in the simulations. A comparison between this approach and the non-parametric probabilistic model is finally provided.

Mots clés: uncertainty quantification; heterogeneous random microstructure; mesoscopic probabilistic modeling; random anisotropic media; material symmetry; nonparametric probabilistic method

Domaines: Mécanique [physics.med-ph]; Matériaux; Probabilités [math.PR]; Statistiques [math.ST]

Johann Guilleminot, Christian Soize. On mesoscopic probabilistic modeling of random anisotropic media under material symmetry constraints. 16th US National Congress of Theoretical and Applied Mechanics, USNCTAM 2010, State College, University Park, Jun 2010, University Park, PA, United States. pp.USNCTAM2010-476-1. ⟨hal-00692834⟩