Mechanics of Cosserat media: I. non-relativistic statics

TL;DR

This paper derives the equilibrium equations for Cosserat media using virtual work and jet manifold methods, emphasizing the importance of Euclidian fundamental forms in the formulation.

Contribution

It introduces a novel derivation of Cosserat equations based on virtual work and jet manifolds, differing from traditional action functional approaches.

Findings

Derivation of Cosserat equilibrium equations using virtual work.

Highlighting the role of Euclidian fundamental forms.

Establishing a geometric framework for Cosserat media.

Abstract

The Cosserat equations for equilibrium are derived by starting from the action of the group of smooth functions with values in the Lie group of rigid spatial motions on rigid frames in Euclidian space. The method of virtual work is employed, instead of the method of action functionals, and is defined using the methods of of jet manifolds. It is shown how the restriction to fundamental forms (which define the dynamical state of the Cosserat object) that are Euclidian is essential to obtaining the Cosserat equations.