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5 - Computational Grains for Particulate Composites and Porous Materials

Published online by Cambridge University Press:  05 October 2023

Leiting Dong  and
Satya N. Atluri
Leiting Dong
Affiliation:
Beihang University, China
Satya N. Atluri
Affiliation:
University of California, Irvine
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Summary

In this chapter, 2D Computational Grains (CGs) with elastic inclusions or voids and 3D CGs with spherical/ellipsoidal inclusions/voids or without inclusions/voids are developed for micromechanical modeling of composite and porous materials. A compatible displacement field is assumed along the outer boundary of each CG. Independent displacement fields in the CG are assumed as characteristic-length-scaled T-Trefftz trial functions. Muskhelishvili’s complex functions are used for 2D CGs, and Papkovich-Neuber solutions are used for 3D CGs to construct the T-Trefftz trial displacement fields. The Papkovich-Neuber potentials are linear combinations of spherical/ellipsoidal harmonics. To develop CG stiffness matrices, multi-field boundary variational principles are used to enforce all the conditions in a variational sense. Through numerical examples, we demonstrate that the CGs developed in this chapter can estimate the overall material properties of heterogeneous materials, and compute the microscopic stress distributions quite accurately, and the time needed for computing each SERVE is far less than that for the finite element method.

Keywords

Computational GrainsinclusionsvoidsTrefftz trial functionsMuskhelishvili’s complex functionsPapkovich-Neuber solutionsspherical harmonicsellipsoidal harmonicsboundary variational principle
Type
Chapter
Information
Computational Grains
Micromechanical Genome for Heterogeneous Materials
 , pp. 72 - 109
Publisher: Cambridge University Press
Print publication year: 2023

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References

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