The principle of material frame indifference and the covarianee principle

Abstract

A comparison between the formulations of the principle of material frame indifference in continuum mechanics, which principle refers to stress-strain relations without inertial forces, and the covariance principle in the theory of general relativity indicates that a relationship between them can be established. It is shown that the principle of material frame indifference follows from the covariance principle in the nonrelativistic limit when inertia is considered to be absent. As a result, the principle of material frame indifference has received further justification but it cannot retain its status of a fundamental principle.