Hypertractions and hyperstresses convey the same mechanical information

Abstract

A strengthened and generalized version of the standard Virtual Work Principle is shown to imply, in addition to bulk and boundary balances, a one-to-one correspondence between surface and edge hypertractions and hyperstrestress fields in second-grade continua. When edge hypertractions are constitutively taken null, the hyperstress is shown to take the form it has for a Navier-Stokes$-\alpha$ fluid, a relevant example of second-grade fluid-like material.