Stochastic model for matrix-valued random fields with constrained eigenvalues: application to stochastic elasticity and permeability tensors

Johann Guilleminot (1) , Christian Soize (1)

1 Mechanics

In this research, we address the construction of a class of prior stochastic models for non-Gaussian positive-definite matrix-valued random fields, having recourse to the MaxEnt principle and following the methodology introduced in [5]. The latter is first recalled and the mathematical derivations are presented. The proposed class is parameterized, in particular, by two deterministic fields specifying the variances of selected random eigenvalues. A few fundamental properties of the class are also summarized and discussed. The approach is finally exemplified by considering two applications. The first one is devoted to the modeling of mesoscopic apparent elasticity tensors. The second application deals with the modeling of fluid flows through random porous media and more precisely, is devoted to the modeling of random permeability tensors in the context of composite manufacturing.

Mots clés: uncertaintu quantification; non-Gaussian matrix-valued random fields; material symmetries; constrained eigenvalues; stochastic elasticity; permeability tensors

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

Johann Guilleminot, Christian Soize. Stochastic model for matrix-valued random fields with constrained eigenvalues: application to stochastic elasticity and permeability tensors. Eleventh U. S. National Congress on Computational Mechanics (USNCCM XI 2011), Jul 2011, Minneapolis, Minnesota, United States. pp.1. ⟨hal-00701591⟩