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On material objectivity and reduced constitutive equations

Bertram A., Svendsen B.

Archives of Mechanics

2001

Vol. 53, nr 6

653-675

The principle of material frame indifference, as it is usually stated, actually consists of two distinct assumptions. Firstly, that the stresses transform like objective tensors under change of the observer, and secondly, that the constitutive equations do not depend on the observer (form-invariance). As a consequence, superimposed rigid body motions also do not effect the material response. In the present work these three statements are formulated independently. The mutual relations between them can be clearly and generally worked out by group-theoretical concepts. If only two of these principles hold for a certain class of materials, then reduced forms exist, i.e. forms of constitutive equations that identically fulfil these principles. A general definition of reduced forms is given, its existence is proven, and a method for their construction is formulated and applied to the case of simple elastic materials.