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Derivation of a
one-dimensional nonlinear third gradient beam model by
$\Gamma$-convergence of a periodic elastic microstructure
Jean-Jacques Alibert, Francesco dell’Isola, Nicola Luigi Rizzi and Pierre Seppecher |
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Vol. 15 (2027), No. 1, 65–81
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Abstract |
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We prove the -convergence of the elastic energy of a slender periodic truss structure. The limit model is an inextensible one-dimensional nonlinear continuum whose energy density is proportional to the square of the derivative of the curvature, leading to a nonlinear inextensible third-gradient beam model. |
Keywords
third-gradient beam, geometrically nonlinear systems,
system of trusses, metamaterials, higher gradient continuum
models
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Mathematical Subject Classification
Primary: 49J45, 74-10, 74K10, 74Q05
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Milestones
Received: 6 June 2026
Accepted: 30 June 2026
Published: 22 September 2026
Communicated by Emilio Barchiesi
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Authors |
| Jean-Jacques Alibert | |
| Institut de Mathématiques de Toulon
(IMATH) Université de Toulon Toulon France |
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| Francesco dell’Isola | |
| DICEAA Università degli Studi dell’Aquila L’Aquila Italy |
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| Nicola Luigi Rizzi | |
| Dipartimento di Strutture Universitá Roma Tre Roma Italy |
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| Pierre Seppecher | |
| Institut de Mathématiques de Toulon
(IMATH) Université de Toulon Toulon France |
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| © 2027 MSP (Mathematical Sciences Publishers). |
