On the origin of balance equations in simple and complex continua: unified view

Here I discuss the way we can derive balance equations for continua with active microstructure, furnishing a unified view on available models and a tool for constructing new ones. I indicate how the requirement of invariance under isometrybased changes in observers of the power of the external actions alone over a generic part of the body is a tool to derive standard and non-standard action-reaction principles, the representation of contact actions in terms of stresses, the possibility of nonzero microstructural self-actions, the balance equations, demanding a very limited number of assumptions. In presence of material mutations, which suggest to take into account multiple reference shapes for a body, we need to extend the procedure by introducing the notion of relative power. Its invariance under isometry-based changes in observers furnishes once again the results listed above and in addition the balances of configurational actions. Finally, I indicate how we can consider the covariance of the second law of thermodynamics and summarize what we can derive from this concept, and how.