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Linking material symmetry and domain of elastic behavior: new numerical insights
[Lien entre symétrie matérielle et domaine de comportement élastique : nouvelles perspectives numériques]
Christelle J. Combescure1, 2 orcid  ; Nicolas Auffray3 orcid ; Marc L.M. François4 orcid ; Nassim Kesmia5
1CREC Saint-Cyr, Académie Militaire de Saint-Cyr Coetquidan, F-56380 Guer, France
2Univ. Bretagne Sud, UMR CNRS 6027, IRDL, F-56100, Lorient, France
3Sorbonne Université, CNRS, Institut Jean Le Rond d’Alembert, F-75005 Paris, France
4Nantes Université, École Centrale Nantes, CNRS, GeM, UMR 6183, F-44000 Nantes, France
5DMAS, ONERA, Université Paris Saclay, F-92322 Châtillon, France
Comptes Rendus. Mécanique, Volume 354 (2026), pp. 543-560

Cet article fait partie du numéro thématique Differential geometry and mechanics coordonné par : Géry De Saxce et al..

In the context of the growing industrial use of architected materials, it is crucial to predict the critical loads at which their mechanical response transitions from linear to nonlinear. The sources of nonlinearity can be multiple, including material nonlinearity and/or multiscale buckling. The set of critical loadings defines a surface in stress or strain space that delineates the region within which the behavior remains elastic, also referred to as the linearity domain. This article presents a numerical investigation of the connections between the symmetries of a periodic architected material and the corresponding symmetries of its linearity domain. This investigation yields novel insights: (i) the rotational symmetry order of the linearity domain is directly related to that of the underlying architected material; (ii) the material’s chirality manifests itself in the geometry of its linearity domain, which in this case appears tilted; and (iii) the angle of this tilt is correlated with the angle of the parent mesostructure.

Dans le contexte du développement croissant des matériaux architecturés en milieu industriel, il est essentiel de prédire les charges critiques à partir desquelles leur réponse mécanique passe d’un régime linéaire à non linéaire. Les sources de non-linéarité peuvent être multiples, incluant la non-linéarité du matériau et/ou des phénomènes d’instabilité multi-échelles. L’ensemble des chargements critiques définit une surface dans l’espace des contraintes ou des déformations, délimitant la région au sein de laquelle le comportement reste élastique, également appelée domaine de linéarité. Cet article présente une étude numérique des liens entre les symétries d’un matériau architecturé périodique et les symétries correspondantes de son domaine de linéarité. Cette investigation révèle plusieurs résultats inédits : (i) l’ordre de symétrie rotationnelle du domaine de linéarité est directement lié à celui du matériau architecturé sous-jacent ; (ii) la chiralité du matériau se manifeste dans la géométrie de son domaine de linéarité, qui apparaît alors incliné ; (iii) l’angle de cette inclinaison est corrélé à l’angle de la mésostructure parente.

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DOI : 10.5802/crmeca.364
Keywords: Symmetry, architected materials, buckling, limit surface
Mots-clés : Symétrie, matériaux architecturés, flambement, surface limite
Note : Article soumis sur invitation

Christelle J. Combescure  1 , 2   ; Nicolas Auffray  3   ; Marc L.M. François  4   ; Nassim Kesmia  5

1 CREC Saint-Cyr, Académie Militaire de Saint-Cyr Coetquidan, F-56380 Guer, France
2 Univ. Bretagne Sud, UMR CNRS 6027, IRDL, F-56100, Lorient, France
3 Sorbonne Université, CNRS, Institut Jean Le Rond d’Alembert, F-75005 Paris, France
4 Nantes Université, École Centrale Nantes, CNRS, GeM, UMR 6183, F-44000 Nantes, France
5 DMAS, ONERA, Université Paris Saclay, F-92322 Châtillon, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
Christelle J. Combescure; Nicolas Auffray; Marc L.M. François; Nassim Kesmia. Linking material symmetry and domain of elastic behavior: new numerical insights. Comptes Rendus. Mécanique, Volume 354 (2026), pp. 543-560. doi: 10.5802/crmeca.364
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     journal = {Comptes Rendus. M\'ecanique},
     pages = {543--560},
     year = {2026},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {354},
     doi = {10.5802/crmeca.364},
     language = {en},
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