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Acta Mechanica

, 202:213 | Cite as

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

  • Michael FrewerEmail author
Article

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.

Keywords

Manifold Constitutive Equation Inertial Frame Active Transformation Classical Continuum Mechanic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Chair of Fluid DynamicsTechnische Universität DarmstadtDarmstadtGermany

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