Non-Gaussian Random Fields in Multiscale Mechanics of Heterogeneous Materials

Synonyms

Elasticity; Micromechanics; Probabilistic modeling; Random media; Uncertainty quantification; Variability

Definitions

A random field defined on a probability space (Θ, $\mathscr {T}$, P), indexed by a set $\mathbb {T}$ (with $\mathbb {T}\subseteq \mathbb {R}^{3}$, for instance), with values in a set $\mathbb {M}$, is a mapping from $\mathbb {T}$ into the space of random variables defined on (Θ, $\mathscr {T}$, P) and with values in $\mathbb {M}$. In mechanics of heterogeneous materials, random fields can be used in order to represent the $\mathbb {M}$-valued coefficients in a system of stochastic partial differential equations defining a stochastic boundary value problem at some scale of interest.

Introduction

The multiscale analysis of heterogeneous materials relies on the proper modeling of physical properties at some scale(s) of interest. Below the so-called macroscopic scale, which is defined by a characteristic length L _macroand corresponds to the scale...