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
Ks. Vemaganti et Jt. Oden, 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, COMPUT METH, 190(46-47), 2001, pp. 6089-6124
Citations number
31
Categorie Soggetti
Mechanical Engineering
Journal title
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
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.