Non-Gaussian positive-definite matrix-valued random fields with constrained eigenvalues: Application to random elasticity tensors with uncertain material symmetries

摘要

This paper is devoted to the construction of a class of prior stochastic models for non-Gaussian positive-definite matrix-valued random fields. The proposed class allows the variances of selected random eigenvalues to be specified and exhibits a larger number of parameters than the other classes previously derived within a nonparametric framework. Having recourse to a particular characterization of material symmetry classes, we then propose a mechanical interpretation of the constraints and subsequently show that the probabilistic model may allow prescribing higher statistical fluctuations in given directions. Such stochastic fields turn out to be especially suitable for experimental identification under material symmetry uncertainties, as well as for the development of computational multi-scale approaches where the randomness induced by fine-scale features may be taken into account. We further present a possible strategy for inverse identification, relying on the sequential solving of least-square optimization problems. An application is finally provided.