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Examples of eonstraints are rigidity (every possible motion is a rigid motion) and ineompressibility (every possible motion is isoehorie). e. that all motions f} are possible. We shall investigate eonstitutive assumptions in the form of funetional relations between the stress Sand the motion f} of a proeess {f}, S}. Sueh relations will be ealled eonstitutive equations. e 11. The prineiple 01 objeetivity 01 material properties A ehange ollrame is a transformation of spaee and time speeified by a pointvalued funetion C of a real variable, a function Q of a real variable whose values are orthogonal transformations, and areal eonstant a.

L'. A deformation LI will be ealled isoehorie if there is a volume preserving loeal homeomorphism Cl in the dass LI. i. AI" is a subgroup of f. 8) Idet GI = 1. l', ealled the unimodular group. They are also ealled unimodular transformations. ). /. /+. l'. 202 WALTER NOLL: 4. B eontaining X. 1) 1p(X) = O. We define an equivalenee relation among all sueh homeomorphisms by the eondition that 1p --1P if and only if 1p (Z) = 1P (Z) for all Z in some neighborhood of X. The resulting equivalenee dasses f/J will be ealled the loeal eonfigurations of X.

These axioms insure that the customary not ions and operations are meaningful. However, in some of the considerations of this paper, continuity and differentiability conditions stronger than those implied by the axioms of [6] have to be assumed. It will be dear from the context when this is the case, and we shall not mention these conditions explicitly. 3. Deformations and linear transformations A smooth homeomorphism 15 which maps a neighborhood of the null-vector 0 of the vector space l ' onto another such neighborhood and which maps 0 into itself, (3.

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