SO(3) invariance and covariance in mixtures of simple bodies

TL;DR

This paper develops a framework for analyzing mixtures of simple bodies using SO(3) invariance and covariance principles to derive balance equations and understand constituent stresses.

Contribution

It introduces a novel application of SO(3) invariance to mixtures, deriving classical axioms and clarifying the covariance of constituent balance equations.

Findings

Derived classical axioms on momentum growths

Established covariance properties of constituent balance equations

Analyzed the nature of constituent stresses

Abstract

We adapt to mixtures the procedure of invariance of external power under the action of SO(3) to deduce balance equations. The two classical axioms about the growths of momentum and moment of momentum are derived with the help of a rule on the structure of the total power. We discuss also the covariance of the balance equations of each constituent and the nature of the constituent stress.