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arXiv · 2305.14261

New notions of uniformity and homogeneity of Cosserat media

V. M. Jiménez·M. De León
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Abstract

In this paper, we study internal properties of a Cosserat media. In fact, by using groupoids and smooth distributions, we obtain a three canonical equations. The \textit{non-holonomic material equation for Cosserat media} characterizes the uniformity of the material. The \textit{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, without assuming uniformity. Thus, the \textit{homogeneity equation for Cosserat media} characterizes this notion of homogeneity.

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BibTeXRIS

V. M. Jiménez, M. De León. 2023-05-23. New notions of uniformity and homogeneity of Cosserat media. https://arxiv.org/abs/2305.14261

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