Principle of material frame-indifference

Summary

The principle of material frame-indifference, or objectivity, requires that the response of a material does not depend on the observer. Two observers who differ by a time-dependent rigid motion must find the same constitutive equation. It restricts the form of constitutive equations strongly. For an elastic material, the stress is then fixed by its values on pure stretches. The rotation part of the deformation gradient only turns that stress.