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On the notion of the stress tensor associated with Rn-invariant constitutive laws admitting integral representations

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  • 510 Mathematik


By an Rn-invariant constitutive law F we mean a smooth Rn-invariant one form on the Fréchet manifold E(M,Rn) of all Euclidean smooth embeddings of a compact manifold M. Associated with it are a natural integrable Rn-valued one form and a natural two tensor, both embedding dependent, provided F is induced by a one form ~F on E(M,Rn)/Rn and ~F admits an integral representation. This two tensor plays the role of the stress tensor in elasticity theory.

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