New notions of uniformity and homogeneity of Cosserat media Articles uri icon

authors

  • JIMENEZ, VICTOR MANUEL
  • LEON RODRIGUEZ, MANUEL DE

publication date

  • September 2023

start page

  • 1

end page

  • 24

issue

  • 9

volume

  • 64

International Standard Serial Number (ISSN)

  • 0022-2488

Electronic International Standard Serial Number (EISSN)

  • 1089-7658

abstract

  • In this paper, we study internal properties of Cosserat media. In fact, by using groupoids and smooth distributions, we obtain three canonical equations. The non-holonomic material equation for Cosserat media characterizes the uniformity of the material. The holonomic material equation for Cosserat media permits us to study when a Cosserat material is a second-grade material. It is remarkable that these two equations also provide us a unique and maximal division of the Cosserat medium into uniform and second-grade parts, respectively. Finally, we present a proper definition of homogeneity of the Cosserat medium, which does not need to assume uniformity. Thus, the homogeneity equation for Cosserat media characterizes this notion of homogeneity.

subjects

  • Mathematics
  • Physics

keywords

  • continuum mechanics; granular materials; lie algebras; differential geometry; differential topology; algebraic structures; general topology; group theory