Advanced mean-field homogenization schemes to model particulate composites

Abstract: 

When one is interested in modeling the macroscopic behavior of particulate composites, typically to estimate their effective conductive or elastic properties and field statistics, classical mean-field homogenization methods such as the Mori-Tanaka (MT) estimate are often used. They typically account for particle volume fraction, shape, and orientation, but may lack accuracy for non-standard particle spatial distribution or high volume fractions.

First, focusing on spatial distribution, the Ponte-Castañeda and Willis (PCW, [1]) and Interaction Direct Derivative (IDD, [2]) methods, which embed additional distribution-dependent parameters, are leveraged. In the context of 2D linear conductivity, and given representative images of the microstructure, we propose a self-contained approach based on these methods. In particular, we implement an image analysis method using Voronoı̈ diagrams, inspired by a proposition in [2], to determine the distribution-dependant parameters.

The method is validated by comparisons between the resulting IDD and PCW estimates, the Mori-Tanaka (MT) model and benchmark full-field numerical simulations. Accounting for the inclusion distribution leads to improved estimates, both qualitatively (by capturing anisotropic behaviors due solely to the distribution) and quantitatively. These results were published in [3].

Next, I will present our recent work on the differential scheme applied to composites with high particle volume fraction. After discussing its application and relevance for predicting the effective elastic properties of increasingly complex microstructures, we demonstrate how to compute phase-averaged strains and their second-order moments. Finally, we apply these tools to model bio-based composites, characterized by high porosity and wooden particle volume fraction, and to an example of non-linear composite, whose homogenization process makes use of the aforementioned second-order moments. First results were published in [4].

[1] Ponte-Castañeda, P. & Willis, J. R. ; The effect of spatial distribution on the effective behavior of composite materials and cracked media ; JMPS, 1995
[2] Du, D. X. & Zheng, Q. S. ; A further exploration of the interaction direct derivative (IDD) estimate for the effective properties of multiphase composites taking into account inclusion distribution ; Acta Mechanica, 2002
[3] Cruz-González, O.; Cornaggia, R.; Dartois, S. & Brenner, R. ; Accounting for spatial distribution in mean-field homogenization of particulate composites ; International Journal of Solids and Structures, 2024
[4] Bourdier, É.; Dartois, S.; Cornaggia, R. & Brenner, R. ; Estimation of local field statistics in highly filled composites based on an incremental mean-field homogenization scheme ; European Journal of Mechanics - A/Solids, 2026 

‼️ Le séminaire peut être suivi en ligne via le lien : https://univ-amu-fr.zoom.us/j/81984994806?pwd=4V0kim9Bw6NTbEw92mAwDg5cl0wLBf.1

Le mardi 24 novembre 2026 à 11h00 / Amphithéâtre François Canac, LMA

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