MICROMECHANICALLY BASED STOCHASTIC FINITE-ELEMENTS - LENGTH SCALES AND ANISOTROPY

The present stochastic finite element (SFE) study amplifies a recently developed micromechanically based approach in which two estimates (up per and lower) of the finite element stiffness matrix and of the globa l response need first to be calculated. These two estimates correspond , respectively, to the principles of stationary potential and compleme ntary energy on which the SFE is based. Both estimates of the stiffnes s matrix are anisotropic and tend to converge towards one another only in the infinite scale limit; this points to the fact that an approxim ating meso-scale continuum random field is neither unique nor isotropi c. The SFE methodology based on this approach is implemented in a Mont e Carlo sense for a conductivity (equivalently, out-of-plane elasticit y) problem of a matrix-inclusion composite under mixed boundary condit ions. Two versions are developed: in one an exact calculation of all t he elements' stiffness matrices from the microstructure over the entir e finite element mesh is carried out, while in the second one a second -order statistical characterization of the mesoscale continuum random held is used to generate these matrices. Copyright (C) 1996 Elsevier S cience Ltd.