Second-neighbor interactions in classical field theories: invariance of the relative power and covariance

We propose a model-building framework unifying those continuum models of condensed matter accounting for second-neighbor interactions. A notion of material isomorphism justifies restrictions that we impose to changes in observers on the material manifold. In the presence of dissipation due to evolution of inhomogeneities, we extend the notion of relative power including hyperstresses and derive pertinent balance equations by exploiting an invariance axiom. The scheme presented here permits an extension of the multi-field model-building framework for complex materials to account at a gross scale for second-neighbor microstructural interactions.