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Estimation of local model error and goal-oriented adaptive modeling of heterogeneous materials. II: A computational environment for adaptive modeling of heterogeneous elastic solids. (English) Zbl 1030.74051

[For part I see the authors, J. Comput. Phys. 164, No. 1, 22-47 (2000; Zbl 0992.74072).]
Summary: This paper addresses a classical and largely unsolved problem: given a structural component constructed of a heterogeneous elastic material that is in equilibrium under the action of applied loads, determine local micromechanical 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 described in this work begins with a mathematical abstraction of this problem in which the material body is modeled as an elastic solid with highly variable, possibly randomly distributed, elastic properties. Information on the actual character of the microstructure of given material bodies is determined by computerized tomography (CT) imaging. A procedure is given for determining the effective material properties from imaging data, using either deterministic or stochastic methods. An algorithm is then described for determining local quantities of interest, such as average stresses on inclusion boundaries, to arbitrary accuracy relative to the fine-scale model. A new computational environment for implementing such analyses is presented which employs parallel, adaptive, \(hp\)-finite element methods, CT interfaces, automatic meshing procedures, and, effectively, adaptive modeling schemes. Within the basic premises on which the approach is based, results of any specified accuracy can be obtained, independently of the number of microscale components and constituents. The results of several numerical experiments are presented.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74Q15 Effective constitutive equations in solid mechanics
74Q20 Bounds on effective properties in solid mechanics
74E30 Composite and mixture properties
74E05 Inhomogeneity in solid mechanics

Citations:

Zbl 0992.74072

Software:

SPOOLES; MPI/MPICH
PDFBibTeX XMLCite
Full Text: DOI

References:

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