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

Fosdick, Roger; Royer-Carfagni, Gianni

Int. J. Non-Linear Mech. 40, No. 2-3, 381-386 (2005).

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

Keywords:

Stokes theorem; compatibility; Cesàro representation; Beltrami representation