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<p>This note discusses the balance of angular momentum and the balances of director momentum in a small deformation model of a deformable Cosserat continuum. It is shown that for small deformation elastic response, the deformable Cosserat model in Rubin [<CitationRef CitationID="CR14">14</CitationRef>] and the theory of microstructure in Mindlin [<CitationRef CitationID="CR8">8</CitationRef>] both satisfy the balance of angular momentum and both predict the same response for the same given strain energy function. This result corrects a discussion in Rubin [<CitationRef CitationID="CR14">14</CitationRef>] (Appendix C) related to equations for the microstretch theory in Eringen [<CitationRef CitationID="CR3">3</CitationRef>] and the microstructure theory in Mindlin [<CitationRef CitationID="CR8">8</CitationRef>].</p>

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On the Balance of Angular Momentum and the Balances of Director Momentum in a Deformable Cosserat Continuum

  • 期刊论文

  • 发表日期：

    2026年6月23日

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  • M. B. Rubin

摘要

This note discusses the balance of angular momentum and the balances of director momentum in a small deformation model of a deformable Cosserat continuum. It is shown that for small deformation elastic response, the deformable Cosserat model in Rubin [14] and the theory of microstructure in Mindlin [8] both satisfy the balance of angular momentum and both predict the same response for the same given strain energy function. This result corrects a discussion in Rubin [14] (Appendix C) related to equations for the microstretch theory in Eringen [3] and the microstructure theory in Mindlin [8].