Elastic disk with isoperimetric Cosserat coating

Matteo Gaibotti, Davide Bigoni, Sofia G. Mogilevskaya

Research output: Contribution to journalArticlepeer-review

Abstract

A circular elastic disk is coated with an elastic beam, absorbing shear and normal forces without deformation and linearly reacting to a bending moment with a change in curvature. The inextensibility of the elastic beam introduces an isoperimetric constraint, so that the length of the initial circumference of the disk is constrained to remain fixed during the loading of the disk/coating system. The mechanical model for this system is formulated, solved for general loading, and particularized to the case of two equal and opposite traction distributions, each applied on a small boundary segment (thus modeling indentation of a coated fiber). The stress fields, obtained via complex potentials, are shown to evidence a nice correspondence with photoelastic experiments, ad hoc designed and performed. The presented results are useful for the design of coated fibers at the micro and nano scales.

Original languageEnglish (US)
Article number104568
JournalEuropean Journal of Mechanics, A/Solids
DOIs
StateAccepted/In press - 2022

Bibliographical note

Funding Information:
D.B. remembers with great pleasure and emotion the longstanding, intense, fruitful, and beautiful cooperation with Natasha and Sasha on so many topics of science. He looks forward to continue enjoying scientific collaboration with them and sincere friendship for many more years to come. D.B. and M.G. gratefully acknowledges the funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 955944-REFRACTURE2. S.G.M. gratefully acknowledges support from National Science Foundation, USA, award NSF CMMI - 2112894.

Funding Information:
D.B. and M.G. gratefully acknowledges the funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 955944-REFRACTURE2 . S.G.M. gratefully acknowledges support from National Science Foundation, USA , award NSF CMMI - 2112894 .

Publisher Copyright:
© 2022 Elsevier Masson SAS

Keywords

  • Complex potentials
  • Nonlocal elastic coating
  • Photoelasticity

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