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A Stokes theorem for second-order tensor fields and its implications in continuum mechanics. (English) Zbl 1349.74048

Summary: We give a constructive proof of a particular Stokes theorem (1.4) for tensor fields in \(\mathbb{R}^{3}\otimes \mathbb{R}^{3}\). Its specialization to symmetric tensor fields, given in (1.5), bears a close relation to compatibility in linear elasticity theory and to the generalized Beltrami representation of symmetric tensor fields in continuum mechanics. These issues are discussed.

MSC:

74A99 Generalities, axiomatics, foundations of continuum mechanics of solids
74B05 Classical linear elasticity
74B99 Elastic materials
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