Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-10T17:04:57.827Z Has data issue: false hasContentIssue false

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Muskhelishvili, N. I., Some Basic Problems of the Mathematical Theory of Elasticity. Berlin: Springer Dordrecht, 1953.Google Scholar
Liu, C.-S., “A Modified Trefftz Method for Two-Dimensional Laplace Equation Considering the Domain’s Characteristic Length,” Computer Modeling in Engineering \& Sciences, vol. 21, no. 1, 2007, https://doi.org/10.3970/cmes.2007.021.053.Google Scholar
Liu, C.-S., “An Effectively Modified Direct Trefftz Method for 2D Potential Problems Considering the Domain’s Characteristic Length,” Engineering Analysis with Boundary Elements, vol. 31, no. 12, pp. 983–993, 2007, https://doi.org/10.1016/j.enganabound.2007.04.006.CrossRefGoogle Scholar
Lurie, A. I. and Belyaev, A., “Three-Dimensional Problems in the Theory of Elasticity,” in Theory of Elasticity, Lurie, A. I. and Belyaev, A., Eds. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005, pp. 243–407.CrossRefGoogle Scholar
Wachspress, E. L. and Rohde, S. M., “A Rational Finite Element Basis,” Journal of Lubrication Technology, vol. 98, no. 4, pp. 635–635, 1976, https://doi.org/10.1115/1.3452953.CrossRefGoogle Scholar
Eshelby, J. D. and Peierls, R. E., “The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Related Problems,” Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, vol. 241, no. 1226, pp. 376–396, 1957, https://doi.org/10.1098/rspa.1957.0133.Google Scholar
Nemat-Nasser, S., and Hori, M., Micromechanics: Overall Properties of Heterogeneous Materials, 2nd ed. Amsterdam: Elsevier, 1999.Google Scholar
Chawla, N., Ganesh, V. V., and Wunsch, B., “Three-Dimensional (3D) Microstructure Visualization and Finite Element Modeling of the Mechanical Behavior of SiC Particle Reinforced Aluminum Composites,” Scripta Materialia, vol. 51, no. 2, pp. 161–165, 2004, https://doi.org/10.1016/j.scriptamat.2004.03.043.CrossRefGoogle Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×