A convenient formulation of Sadowsky model for elastic ribbons

Sébastien Neukirch (1) , Basile Audoly (2, 3)

1 DALEMBERT - Institut Jean Le Rond d'Alembert
2 LMS - Laboratoire de mécanique des solides
3 IP Paris - Institut Polytechnique de Paris

Elastic ribbons are elastic structures whose length-to-width and width-to-thickness aspectratios are both large. Sadowsky proposed a one-dimensional model for ribbons featuring a nonlinear constitutive relation for bending and twisting: it brings in both rich behaviors and numerical difficulties. By discarding non-physical solutions to this constitutive relation, we show that it can be inverted; this simplifies the system of differential equations governing the equilibrium of ribbons. Based on the inverted form, we propose a natural regularization of the constitutive law that eases the treatment of singularities often encountered in ribbons. We illustrate the approach with the classical problem of the equilibrium of a Möbius ribbon, and compare our findings to the predictions of the Wunderlich model. Overall, our approach provides a simple method for simulating the statics and the dynamics of elastic ribbons.

Mots clés: boundary value problems; elastic plates; twisted rods

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des structures [physics.class-ph]

Sébastien Neukirch, Basile Audoly. A convenient formulation of Sadowsky model for elastic ribbons. 2021. ⟨hal-03278697v1⟩