Geometric charges and nonlinear elasticity of two-dimensional elastic metamaterials.
elastic charges
mechanical metamaterials
nonlinear elasticity
Journal
Proceedings of the National Academy of Sciences of the United States of America
ISSN: 1091-6490
Titre abrégé: Proc Natl Acad Sci U S A
Pays: United States
ID NLM: 7505876
Informations de publication
Date de publication:
12 05 2020
12 05 2020
Historique:
pubmed:
1
5
2020
medline:
1
5
2020
entrez:
1
5
2020
Statut:
ppublish
Résumé
Problems of flexible mechanical metamaterials, and highly deformable porous solids in general, are rich and complex due to their nonlinear mechanics and the presence of nontrivial geometrical effects. While numeric approaches are successful, analytic tools and conceptual frameworks are largely lacking. Using an analogy with electrostatics, and building on recent developments in a nonlinear geometric formulation of elasticity, we develop a formalism that maps the two-dimensional (2D) elastic problem into that of nonlinear interaction of elastic charges. This approach offers an intuitive conceptual framework, qualitatively explaining the linear response, the onset of mechanical instability, and aspects of the postinstability state. Apart from intuition, the formalism also quantitatively reproduces full numeric simulations of several prototypical 2D structures. Possible applications of the tools developed in this work for the study of ordered and disordered 2D porous elastic metamaterials are discussed.
Identifiants
pubmed: 32350137
pii: 1920237117
doi: 10.1073/pnas.1920237117
pmc: PMC7229665
doi:
Types de publication
Journal Article
Research Support, Non-U.S. Gov't
Research Support, U.S. Gov't, Non-P.H.S.
Langues
eng
Sous-ensembles de citation
IM
Pagination
10195-10202Informations de copyright
Copyright © 2020 the Author(s). Published by PNAS.
Déclaration de conflit d'intérêts
The authors declare no competing interest.
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