A Stokes theorem for second-order tensor fields and its implications in continuum mechanics

Abstract

We give a constructive proof of a particular Stokes theorem (1.4) for tensor fields in R 3 ⊗ 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.