Abstract
This chapter presents the generalization of the stress object of continuum mechanics to the settings of general manifolds. Only smooth distributions of stresses are considered here. The existence of the stress object as a tool for the determination of surface forces on the boundary of subbodies—the traction stress field—is proved in analogy with the proof of the existence of flux fields in Chap. 8. In distinction to the classical theory, the traction stress object does not determine the power expended. Another object—the variational stress field—is needed for that. The variational stress determines the traction stress but not vice-versa.
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References
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Segev, R. (2023). Stresses. In: Foundations of Geometric Continuum Mechanics. Advances in Mechanics and Mathematics(), vol 49. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-35655-1_10
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DOI: https://doi.org/10.1007/978-3-031-35655-1_10
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