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2 - Computational Homogenization in the Micromechanics of Heterogeneous 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

This chapter discusses the role of a representative volume element (RVE) in the computational homogenization of heterogeneous materials. The use of the finite element method in modeling an RVE is discussed. The role of using the Hill-Mandel boundary conditions, and the use of periodic displacement and aperiodic traction boundary conditions on an RVE are discussed. The advantages of using the present Computational Grains method in modeling an RVE, not only to determine the macro properties of a heterogeneous material but also to determine the detailed interfacial stress states which are damage precursors at the micro level are discussed.

Keywords

computational homogenizationrepresentative volume elementfinite element methodHill-Mandel boundary conditionsComputational Grains method
Type
Chapter
Information
Computational Grains
Micromechanical Genome for Heterogeneous Materials
 , pp. 17 - 26
Publisher: Cambridge University Press
Print publication year: 2023

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References

Hill, R., “Elastic Properties of Reinforced Solids: Some Theoretical Principles,” Journal of the Mechanics and Physics of Solids, vol. 11, no. 5, pp. 357–372, 1963, https://doi.org/10.1016/0022-5096(63)90036-X.Google Scholar
Mandel, J., “Contribution théorique à l’étude de l’écrouissage et des lois de l’écoulement plastique,” in Applied Mechanics, Görtler, H., Ed., 1966: Springer Berlin Heidelberg, pp. 502–509.Google Scholar
Nemat-Nasser, S., Hori, M., and Datta, S. K., “Micromechanics: Overall Properties of Heterogeneous Materials,” Journal of Applied Mechanics, vol. 63, no. 2, p. 561, 1996, https://doi.org/10.1115/1.2788912.CrossRefGoogle Scholar

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