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Notes on Metric Independent Analysis of Classical Fields

Abstract : A metric independent geometric framework for some fundamental objects of continuum mechanics is presented. In the geometric setting of general differentiable manifolds, balance principles for extensive properties are formulated and Cauchy's theorem for fluxes is proved. Fluxes in an n-dimensional space are represented as differential (n − 1)-forms. In an analogous formulation of stress theory, a distinction is made between the traction stress, enabling the evaluation of the traction on the boundaries of the various regions, and the variational stress, which acts on the derivative of a virtual velocity field to produce the virtual power density. The relation between the two stress fields is examined as well as the resulting differential balance law. As an application, metric-invariant aspects of electromagnetic theory are presented within the framework of the foregoing flux and stress theory.
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Reuven Segev. Notes on Metric Independent Analysis of Classical Fields. Mathematical Methods in the Applied Sciences, Wiley, 2013, 36 (5), pp.497-566. ⟨hal-01068262⟩

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