Derivation of Cosserat’s medium equations using different multi-dimensional frameworks
Résumé
Cosserat’smedium is of both academic and technological interest. Thismedium offers a wider range of possible applications allowing a better description of the mechanical effectswithin materials; it should thus be used preferentially. It should be noted that the advantages of this kind ofmedia are nevertheless counterbalanced by the simplicity of Cauchy’s medium.One objective of this article is to investigate the correspondence between different multi-dimensional representations of Cosserat’s medium and hence advocate the advantages of this representation. It is demonstrated that the equations representing Cosserat’s medium may be derived from different frameworks. The comparison between these different approaches shows that Cosserat’s medium can be seen as the natural medium to describe material behaviors accurately. As an illustration, constitutive models for isotropic linear elastic behaviors are then derived using different multi-dimensional mechanical theories.