Elastic Disk with Isoperimetric Cosserat Coating

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.