Comptes Rendus
Principle of Virtual Work as Foundational Framework for Metamaterial Discovery and Rational Design
Comptes Rendus. Mécanique, Online first (2023), pp. 1-25.

Novel theories are needed for the discovery of innovative and exotic metamaterial and for their rational design. The current practice of mechanical analyses based upon moribund classical theories and experimental trial-error campaigns is caught in an inescapable vortex and illusion of inductive reasoning. The needed novel research paradigm is one in which the formulation of theoretical concepts precede their experimental validation. In the absence of theoretical understanding, the design experiments and collection of experimental evidence will remain unavoidably circumscribed. History of science can provide us guidance in the search for the needed powerful tools required for discovery. The principle of virtual work provides the necessary framework for development of theories that can lead to novel metamaterials, as it was the unifying principle which allowed the French-Italian School, headed by D’Alembert, Lagrange and Gabrio Piola, to found modern continuum mechanics. Based upon this framework we have conceived a metamaterial synthesis schema that exploits micro-macro identification traceable to the early days of the formulation of continuum theories for deformable solids. The schema is illustrated with application to metamaterials with pantographic and granular motifs based upon higher-gradient and higher-order theories.

La « Méchanique » Analytique a été une théorie controversée depuis sa formulation par Lagrange en 1788 et la controverse se poursuit jusqu’à nos jours : Truesdell déclare que la Mécanique doit être fondée sur le concept de « force » . Au contraire selon D’Alembert le seul principe unificateur est le Principe des Travaux Virtuels (PTV) : la force étant un concept dérivé, utile dans les applications. Ce débat épistémologique est-il inutile ? La mécanique est-elle aujourd’hui aussi fertile de problèmes théoriques et potentialités dans les applications technologiques ? En effet, la mécanique si basée sur le PTV s’avère être un outil puissant pour favoriser l’invention scientifique et l’avancement technologique : il rends possible, par exemple, la théorie moderne des méta-matériaux ou matériaux architecturés, c’est-à-dire, la théorie qui nous aide à « inventer » des matériaux qui « n’existent pas dans la nature et qui ont des propriétés à l’apparence magique »  : donc l’approche épistémologique qui avait inspiré D’Alembert semble n’avoir encore épuisé sa capacité novatrice. En effet, le PTV permet d’homogénéiser le comportement des systèmes complexes et de formuler des théories macroscopiques prédictives du comportement « global » des microstructures qui forment les métamatériaux « exotiques » . La compréhension des résultats du débat épistémologique fondé sur la dichotomie force/travail nous offre un outil puissant pour concevoir et produire des matériaux « réels » . Parmi les infinies possibilités on signale les matériaux i) avec effet Poisson négatif ; ii) qui restent dans le régime élastique même en grandes déformations ; iii) qui se comportent, dans les petites déformations, comme des fluides et, en grandes déformations, comme des solides (pentamode materials) ; iv) avec une structure granulaire, qui ont un comportement chiral au niveaux macroscopique.

Online First:
DOI: 10.5802/crmeca.151
Keywords: metamaterials, energy methods, rational design, principle of virtual work, generalized continua, microstructure
Mot clés : métamatériaux, méthodes énergétiques, conception rationnelle, principe des travaux virtuels, Milieux continus généralisés, Microstructure

Francesco dell’Isola 1; Anil Misra 2

1 Department of Civil, Construction-Architectural and Environmental Engineering (DICEEA) and International Research Center on Mathematics and Mechanics of Complex Systems (M&MoCS). Università degli Studi dell’Aquila. Via Giovanni Gronchi 18 - Zona industriale di Pile 67100, L’Aquila, Italy.
2 The University of Kansas. Civil, Environmental and Architectural Engineering Department. 1530 W. 15th Street, Lawrence, KS 66045-7609, USA.
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Francesco dell’Isola; Anil Misra. Principle of Virtual Work as Foundational Framework for Metamaterial Discovery and Rational Design. Comptes Rendus. Mécanique, Online first (2023), pp. 1-25. doi : 10.5802/crmeca.151.

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