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This paper investigates the validity of two different analytical homogenization methods: the Mori–Tanaka mean-field theory and Milton’s correlation function-dependent bounds. We focus on biphase linearly elastic transversely isotropic composites. The composites consist of a matrix reinforced with long fibers of either circular or irregular cross section shapes formed by overlapping circles, with different degrees of radius polydispersity. The Mori–Tanaka effective stiffness depends on the phase moduli, volume fractions, and on a few geometric descriptors of the fibers that can be readily evaluated. In contrast, the computation of Milton’s bounds requires finer knowledge of the microstructure, in terms of two and three-point spatial correlation functions, which are not always analytically tractable. We thus consider very specific random microstructure geometries with known correlation functions. The effective moduli estimates of the two methods are validated against the results of numerical homogenization using the finite element method. It is shown that the Mori– Tanaka predictions of the effective transverse bulk modulus are significantly more accurate than those of the transverse and axial shear moduli. In addition, the predictions of the scheme generally deteriorate with an increasing fiber volume fraction. By contrast, the average of Milton’s upper and lower bounds provides a highly accurate estimate for all three independent effective moduli, without any limitation on the fiber concentration. This study highlights the indisputable effect of the spatial correlation functions on the effective properties of composites, and aspires to pave the way towards the development of more predictive, correlation function-dependent homogenization methods.
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This content will become publicly available on July 14, 2026
Microstructure features that most influence the Mori-Tanaka scheme break-down in 2D solids with crack-like flat cavities
This study aims to detect in which microstructure conditions the Mori–Tanaka scheme is inappropriate to calculate the effective stiffness of a two-phase matrix-inclusion system.We analyze the discrepancy between numerical and Mori–Tanaka stiffness estimates in two-dimensional (2D) solids with crack-like flat cavities. The maximum transfer entropy that occurs between a microstructure feature and a stiffness component discrepancy cannot only detect the phase change between a Mori–Tanaka-like cracked solid to a non-Mori–Tanaka-like cracked solid, but also reveal at which load step that phase change first occurs and which microstructure features most affect that phase change. Further analysis with a binary classifier based on a support vector machine (SVM) algorithm shows that the systematic calculation of nine microstructure features based on six statistical crack network descriptors at each step of a loading path can inform the detection of a microstructure transition. The microstructure features identified here could thus be used to trigger the transition from one homogenization scheme to another during incremental stiffness updates, for example, during the simulation of a load path.
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- PAR ID:
- 10657143
- Publisher / Repository:
- ASCE
- Date Published:
- Journal Name:
- Journal of engineering mechanics
- ISSN:
- 1943-7889
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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