Analysis of cone-like singularities in twisted elastic ribbons - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of the Mechanics and Physics of Solids Année : 2023

Analysis of cone-like singularities in twisted elastic ribbons

Résumé

Twisting a thin elastic ribbon is known to produce a localised deformation pattern resembling a cone whose tip is located on the edge of the ribbon. Using the theory of inextensional ribbons, we present a matched asymptotic analysis of these singularities for ribbons whose width-to-length ratio w/ℓ ≪ 1 is small. An inner layer solution is derived from the finite-w Wunderlich model and captures the fast, local variations of the bending and twisting strains in the neighbourhood of the cone-like region; it is universal up to a load intensity factor. The outer solution is given by the zero-w Sadowsky model. Based on this analysis, we propose a new standalone ribbon model that combines the Sadowsky equations with jump conditions providing a coarse-grained description of cone-like singularities, and give a self-contained variational derivation of this model. Applications to the Möbius band and to an end-loaded open ribbon are presented. Overall, the new model delivers highly accurate approximations to the solutions of the Wunderlich model in the limit w ≪ ℓ while avoiding the numerical difficulties associated with cone-like singularities.
Fichier principal
Vignette du fichier
MoebiusStripAsymptotic.pdf (11.99 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04084398 , version 1 (28-04-2023)

Identifiants

Citer

Basile Audoly, G.H.M. van der Heijden. Analysis of cone-like singularities in twisted elastic ribbons. Journal of the Mechanics and Physics of Solids, 2023, 171, pp.105131. ⟨10.1016/j.jmps.2022.105131⟩. ⟨hal-04084398⟩
24 Consultations
29 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More