Macroscopic and Microscopic Behavior of Narrow Elastic Ribbons

  • Roberto ParoniEmail author
  • Giuseppe Tomassetti


A one-dimensional model for a narrow ribbon is derived from the plate theory of Kirchhoff by means of a power expansion in the width variable. The energy found coincides with the corrected Sadowsky’s energy. Furthermore, we derive the Euler-Lagrange equations and use them to study an equilibrium configuration of a twisted ribbon. Within this example we also describe how to construct the fine scale oscillations that develop in the deformed configuration.


Ribbons Elasticity Relaxed energy 

Mathematics Subject Classification

74K10 74K20 74B20 49S05 



R. Paroni acknowledges support from the Università di Pisa through the project PRA_2018_61 “Modellazione multi-scala in ingegneria strutturale”.


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.DICIUniversità di PisaPisaItaly
  2. 2.Dipartimento di IngegneriaUniversità Roma TreRomaItaly

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