Interstitial energy flux and stress-power for second-gradient elasticity

Theories of second-gradient elastic materials have been constructed either through the notion of an interstitial energy flux, an additional term to be included in the balance of energy, or through an appropriate extension of the power of internal stresses via a hyperstress applied to the second-order gradient of velocity. This article provides a critical comparison of such apparently alternative points of view and shows how, in some cases, they can be reconciled with each other through an appropriate choice for the expression of the working of the internal stresses. This is accomplished by allowing the hyperstress to be non-symmetric.