Material groupoids and algebroids
Differential Geometry
2017-12-27 v1
Abstract
Lie groupoids and their associated algebroids arise naturally in the study of the constitutive properties of continuous media. Thus, Continuum Mechanics and Differential Geometry illuminate each other in a mutual entanglement of theory and applications. Given any material property, such as the elastic energy or an index of refraction, affected by the state of deformation of the material body, one can automatically associate to it a groupoid. Under conditions of differentiability, this material groupoid is a Lie groupoid. Its associated Lie algebroid plays an important role in the determination of the existence of material defects, such as dislocations. This paper presents a rather intuitive treatment of these ideas.
Cite
@article{arxiv.1712.08831,
title = {Material groupoids and algebroids},
author = {Marcelo Epstein and Manuel de Leon},
journal= {arXiv preprint arXiv:1712.08831},
year = {2017}
}