The use of the teleparallelism connection in continuum mechanics

TL;DR

This paper explores how teleparallelism geometry can be applied to continuum mechanics, particularly in modeling couple-stresses in beams and wires, by extending the geometric framework to higher dimensions within the Cosserat theory.

Contribution

It introduces a higher-dimensional teleparallelism framework for continuum mechanics, linking geometric methods to the Cosserat approach for deformable bodies.

Findings

Teleparallelism geometry relates to couple-stresses in beams.

Higher-dimensional analogues extend the geometric modeling.

Methods connect teleparallelism with Cosserat theory.

Abstract

The geometry of parallelizable manifolds (i.e., teleparallelism) is summarized in the language of local frame fields. Some problems in continuum mechanics that relate to the couple-stresses that are produced in the bending and twisting of prismatic beams and wires are then discussed. It is then shown that by going to a higher-dimensional analogue of the geometry that one used for one-dimensional deformable objects, one is basically using the methods of teleparallelism in the context of the Cosserat approach to deformable bodies.