Elastic disk with isoperimetric Cosserat coating

TL;DR

This paper models a coated elastic disk with an isoperimetric constraint, analyzing stress fields and validating results with experiments, relevant for micro and nano-scale fiber design.

Contribution

It introduces a novel mechanical model for an elastic disk coated with an elastic beam under isoperimetric constraints, with analytical solutions and experimental validation.

Findings

Stress fields match photoelastic experiments

Model effectively describes coated fiber indentation

Provides insights for micro/nano-scale fiber design

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 inexstensibility 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 modelling 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.