A certain counterpart in dissipative setting of the Noether theorem with no dissipation pseudo-potentials

We look at a mechanical dissipation inequality differing from the standard one by what we call a relative power, a notion that is appropriate in the presence of material mutations. We prove that a requirement of structural invariance for such an inequality under the action of diffeomorphism-based changes of observers (covariance) implies (i) the representation of contact actions in terms of the first Piola–Kirchhoff stress, (ii) local balances of standard and configurational actions, (iii) a priori constitutive restrictions in terms of free energy, and (iv) a representation of viscous-type stress components. This article is part of the theme issue ‘Foundational issues, analysis and geometry in continuum mechanics’.