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

We give a constructive proof of a particular Stokes theorem (1.4) for tensor fields in R3⊗R3. 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.