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More clarity on the concept of material frame-indifference in classical continuum mechanics

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A Publishers Erratum to this article was published on 16 September 2008

Abstract

There was and still is a considerable amount of confusion in the community of classical continuum mechanics on the concept of material frame-indifference. An extensive review is presented which will point out and try to resolve various misconceptions that still accompany the literature of material frame-indifference. With the tools of differential geometry a precise terminology is developed ending in a consequent mathematical framework, in which not only the concept of material frame-indifference can be formulated naturally, but showing advantages that go beyond all conventional considerations on invariance used so far in classical continuum mechanics. As an exemplification the Navier-Stokes equations and the corresponding Reynolds averaged equations are written in a general covariant form within Newtonian mechanics.

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  1. Chair of Fluid Dynamics, Technische Universität Darmstadt, Hochschulstraße 1, 64289, Darmstadt, Germany

    Michael Frewer

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  1. Michael Frewer
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Correspondence to Michael Frewer.

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An erratum to this article can be found at http://dx.doi.org/10.1007/s00707-008-0087-6

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Frewer, M. More clarity on the concept of material frame-indifference in classical continuum mechanics. Acta Mech 202, 213–246 (2009). https://doi.org/10.1007/s00707-008-0028-4

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  • DOI: https://doi.org/10.1007/s00707-008-0028-4

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