Objectivity and frame indifference of acceleration-sensitive materials

Constitutive equations have to be compatible with material axioms. Here, the axioms of material frame indifference and material motion dependence, that are the transformation properties of the constitutive equations by changing observer and by changing the motion of the material, are discussed. Starting out with the observer-independent material mapping, its domain – the state space – is extended by a second entry describing the motion of the material with regard to a fixed standard frame of reference. This results in observer-independent tensorial constitutive equations. Different component representations of these equations belong to different observers. Finally, two examples –anisotropic heat conduction and Maxwell's equations – are considered.