A stochastic model for elasticity tensors exhibiting uncertainties on material symmetries

Johann Guilleminot (1) , Christian Soize (1)

1 MSME - Laboratoire de Modélisation et Simulation Multi Echelle

This study addresses the stochastic modeling of media whose elasticity tensor exhibits uncertainties on the material symmetry class to which it belongs. More specifically, we focus on the construction of a nonparametric probabilistic model which allows realizations of random elasticity tensors to be simulated, under the constraint that the mean distance (in a sense to be defined) to a given class of material symmetry is specified. Following the eigensystem characterization of the material symmetries, the proposed approach relies on the nonparametric probabilistic model in which a new ensemble SE++ of symmetric positivedefinite random matrices, allowing the variance of selected stochastic eigenvalues to be partially prescribed, is introduced and defined having recourse to the MaxEnt principle. A new methodology and parameterization of the model are then defined.

Mots clés: uncertainty quantification; elasticity tensors; material symmetries; nonparametric probabilistic model; model uncertainties; mesoscopic scale; heterogeneous material; random microstructure

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

Johann Guilleminot, Christian Soize. A stochastic model for elasticity tensors exhibiting uncertainties on material symmetries. Sixth International Conference on Computational Stochastic Mechanics, Jun 2010, Rhodos, Greece. pp.P032, Pages: 298-303, ⟨10.3850/978-981-08-7619-7_P032⟩. ⟨hal-00692832⟩