Abstract
Locally averaged random fields can be used to represent composite material properties at an intermediate scale. These types of fields provide the basis for stochastic simulation to generate nominally identical realizations of random composite microstructures to be used in reliability analysis. One challenge in choosing an appropriate local averaging technique and mesoscale length parameter is the difficulty of quantifying the accuracy of the locally averaged model. Although mesoscale models may offer advantages over the use of a representative volume element (RVE), particularly in regions of high stress gradients, mesoscale approximations do not converge to an effective medium, so the accuracy of the mesoscale representation cannot be quantified. In this paper, a matrix norm error is developed to test locally averaged material property approximations where loading is not specified a priori. This norm-based approach illustrates the advantage of local averaging over global averaging when small-scale variation in load may be present. This metric provides a basis for comparing locally averaged material property approximations of a benchmark composite microstructure. (c) 2015 American Society of Civil Engineers.