Hypertractions and hyperstresses convey the same mechanical information

TL;DR

This paper extends the Virtual Work Principle to establish a direct correspondence between hypertractions and hyperstresses in second-grade continua, revealing their equivalence in conveying mechanical information.

Contribution

It introduces a generalized Virtual Work Principle linking hypertractions and hyperstresses, and demonstrates the hyperstress form for a Navier-Stokes-α fluid.

Findings

Hypertractions and hyperstresses are equivalent in conveying mechanical information.

The generalized principle applies to second-grade continua with null edge hypertractions.

Hyperstress form matches that of a Navier-Stokes-α fluid.

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.