On prescribing the number of singular points in a Cosserat-elastic solid

TL;DR

This paper develops a method to prescribe an arbitrary number of singular points in Cosserat-elastic solids by controlling the energy through inserting dipole pairs of singularities, leveraging harmonic map techniques.

Contribution

It introduces a novel approach to control singularities in Cosserat-elastic models using harmonic map connections and boundary data manipulation.

Findings

Successfully prescribes singular points in Cosserat solids.

Connects harmonic maps with Cosserat elasticity theory.

Provides a method to control energy for singularity insertion.

Abstract

In a geometrically non-linear Cosserat model for micro-polar elastic solids, we insert dipole pairs of singularities into smooth maps and control the amount of Cosserat energy needed to do so. We use this method to force an arbitrary number of singular points into Cosserat-elastic solids by prescribing smooth boundary data. Throughout this paper, we exploit connections between harmonic maps and Cosserat-elastic solids, so that we are able to adapt and incorporate ideas of R. Hardt and F.-H. Lin, as well as F. B\'ethuel.