Estimation of local modeling error and goal-oriented adaptive modeling of heterogeneous materials Part II: A computational environment for adaptive modeling of heterogeneous elastic solids

This paper addresses a classical and largely unsolved problem: given a stru ctural component constructed of a heterogeneous elastic material that is in equilibrium under the action of applied loads, determine local micromechan ical features of its response (e.g., local stresses and displacements in or around phase boundaries or in inclusions) to an arbitrary preset level of accuracy, it being understood that the microstructure is a priori unknown, may be randomly distributed, may exist at multiple spatial scales, and may contain millions, even billions, of microscale components. The approach des cribed in this work begins with a mathematical abstraction of this problem in which the material body is modeled as an elastic solid with highly varia ble, possibly randomly distributed, elastic properties. Information on the actual character of the microstructure of given material bodies is determin ed by computerized tomography (CT) imaging. A procedure is given for determ ining the effective material properties from imaging data, using either det erministic or stochastic methods. An algorithm is then described for determ ining local quantities of interest, such as average stresses on inclusion b oundaries, to arbitrary accuracy relative to the fine-scale model. A new co mputational environment for implementing such analyses is presented which e mploys parallel, adaptive, hp finite element methods, CT interfaces, automa tic meshing procedures, and, effectively, adaptive modeling schemes. Within the basic premises on which the approach is based, results of any specifie d accuracy can be obtained, independently of the number of microscale compo nents and constituents. The results of several numerical experiments are pr esented. (C) 2001 Elsevier Science B.V. All rights reserved.