Acta Mechanica

, 202:213 | Cite as

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

  • Michael FrewerEmail author


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.


Manifold Constitutive Equation Inertial Frame Active Transformation Classical Continuum Mechanic 
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© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Chair of Fluid DynamicsTechnische Universität DarmstadtDarmstadtGermany

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