[Optimisation de l’anisotropie des nouveaux matériaux basée sur la micromécanique granulaire]
We propose an evolutionary algorithm that seeks to determine the optimal anisotropy of a deforming body in response to a given applied mechanical load, under the constraint of assigned mass. The algorithm is based for the first time upon a granular micromechanics approach to determine the effective material behavior, making use of an orientation-dependent distribution of normal and tangential elastic grain-grain interactions, whose associated stiffnesses are assumed to depend on an orientation-dependent angular mass density. This novel idea is intrinsically simple and takes advantage of both those penalization techniques, that are generally used in topological optimization, and on those basic concepts of continuum granular micromechanics that are particularly prone to be used in this field. The algorithm is initialized with an isotropic distribution of mass such that the total mass exceeds the desired one. Grain-grain interaction stiffnesses along orientations that are only lightly stressed by the applied load are penalized and the angular mass density is accordingly reduced along these orientations. This yields a non-uniform orientation-dependent mass density and, in turn, an anisotropic constitutive law. The proposed algorithm is numerically evaluated for two load cases implying homogeneous deformations and the response to loading produced by the optimal effective fourth-rank elasticity tensor is compared with that obtained by isotropic angular mass density reduction. The proposed algorithm can be employed for engineering microstructures and as a building block for topology optimization algorithms.
Nous proposons un algorithme évolutionnaire visant à déterminer l’anisotropie optimale d’un corps déformable sous l’effet d’une charge mécanique appliquée, sous la contrainte d’une masse imposée. Cet algorithme repose, pour la première fois, sur une approche de micromécanique granulaire pour déterminer le comportement effectif du matériau. Il exploite une distribution, dépendante de l’orientation, des interactions élastiques normales et tangentielles entre les grains, dont les rigidités associées sont supposées dépendre d’une densité de masse angulaire également dépendante de l’orientation. Cette idée novatrice est intrinsèquement simple et tire parti à la fois des techniques de pénalisation généralement utilisées en optimisation topologique et des concepts fondamentaux de la micromécanique granulaire continue, particulièrement pertinents dans ce domaine. L’algorithme est initialisé avec une distribution isotrope de la masse telle que la masse totale excède celle souhaitée. Les rigidités des interactions entre les grains selon les orientations faiblement sollicitées par la charge appliquée sont pénalisées, et la densité de masse angulaire est réduite en conséquence le long de ces orientations. Il en résulte une densité de masse non uniforme dépendant de l’orientation et, par conséquent, une loi constitutive anisotrope. L’algorithme proposé est évalué numériquement pour deux cas de charge impliquant des déformations homogènes, et la réponse à la charge obtenue avec le tenseur d’élasticité effectif optimal de rang quatre est comparée à celle obtenue par réduction isotrope de la densité de masse angulaire. Cet algorithme peut être utilisé pour l’ingénierie des microstructures et comme élément de base pour les algorithmes d’optimisation topologique.
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Mots-clés : Micromécanique granulaire, optimisation de l’anisotropie, rigidité dépendante de l’orientation, métamatériaux, conception de matériaux multi-échelles
Luca Placidi 1 , 2 ; Anil Misra 2 , 3 ; Emilio Barchiesi 2 , 4 ; Raimondo Luciano 5 ; Francesco Fabbrocino 1
CC-BY 4.0
@article{CRMECA_2026__354_G1_165_0,
author = {Luca Placidi and Anil Misra and Emilio Barchiesi and Raimondo Luciano and Francesco Fabbrocino},
title = {Novel material anisotropy optimization based upon granular micromechanics},
journal = {Comptes Rendus. M\'ecanique},
pages = {165--182},
year = {2026},
publisher = {Acad\'emie des sciences, Paris},
volume = {354},
doi = {10.5802/crmeca.345},
language = {en},
}
TY - JOUR AU - Luca Placidi AU - Anil Misra AU - Emilio Barchiesi AU - Raimondo Luciano AU - Francesco Fabbrocino TI - Novel material anisotropy optimization based upon granular micromechanics JO - Comptes Rendus. Mécanique PY - 2026 SP - 165 EP - 182 VL - 354 PB - Académie des sciences, Paris DO - 10.5802/crmeca.345 LA - en ID - CRMECA_2026__354_G1_165_0 ER -
%0 Journal Article %A Luca Placidi %A Anil Misra %A Emilio Barchiesi %A Raimondo Luciano %A Francesco Fabbrocino %T Novel material anisotropy optimization based upon granular micromechanics %J Comptes Rendus. Mécanique %D 2026 %P 165-182 %V 354 %I Académie des sciences, Paris %R 10.5802/crmeca.345 %G en %F CRMECA_2026__354_G1_165_0
Luca Placidi; Anil Misra; Emilio Barchiesi; Raimondo Luciano; Francesco Fabbrocino. Novel material anisotropy optimization based upon granular micromechanics. Comptes Rendus. Mécanique, Volume 354 (2026), pp. 165-182. doi: 10.5802/crmeca.345
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