We consider thin plates whose energy density is a quadratic function of the difference between the second fundamental form of the deformed configuration and a natural curvature tensor. This tensor either denotes the second fundamental form of the stress-free configuration, if it exists, or a target curvature tensor. In the latter case, residual stress arises from the geometrical frustration involved in the attempt to achieve the target curvature: as a result, the plate is naturally twisted, even in the absence of external forces or prescribed boundary conditions. Here, starting from this kind of plate energy, we derive a new variational one-dimensional model for naturally twisted ribbons by means of γ-convergence. Our result generalizes, and corrects, the classical Sadowsky energy to geometrically frustrated anisotropic ribbons with a narrow, possibly curved, reference configuration.

A variational model for anisotropic and naturally twisted ribbons

FREDDI, Lorenzo;
2016-01-01

Abstract

We consider thin plates whose energy density is a quadratic function of the difference between the second fundamental form of the deformed configuration and a natural curvature tensor. This tensor either denotes the second fundamental form of the stress-free configuration, if it exists, or a target curvature tensor. In the latter case, residual stress arises from the geometrical frustration involved in the attempt to achieve the target curvature: as a result, the plate is naturally twisted, even in the absence of external forces or prescribed boundary conditions. Here, starting from this kind of plate energy, we derive a new variational one-dimensional model for naturally twisted ribbons by means of γ-convergence. Our result generalizes, and corrects, the classical Sadowsky energy to geometrically frustrated anisotropic ribbons with a narrow, possibly curved, reference configuration.
File in questo prodotto:
File Dimensione Formato  
Freddi-Hornung-Mora-Paroni_SIAM_2016.pdf

accesso aperto

Tipologia: Versione Editoriale (PDF)
Licenza: Non pubblico
Dimensione 480.32 kB
Formato Adobe PDF
480.32 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11390/1103163
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 21
  • ???jsp.display-item.citation.isi??? 21
social impact