Material function reference invariant representation

Example 13 Reference-invariant representation of the material function p(X x)... 

In general, standard representation depends upon the choice of the reference point. The question is posed Do mathematical functions exist whose standard representations do not depend on the choice of the reference point and therefore could be named reference-invariant functions In case of an affirmative answer on the one hand the reference point p0 - here T0 - could be omitted (constriction of the pi-space by one pi-number) and on the other hand the dimensionless representation of the material function would stretch over the entire recorded range. 

The regions of existence and appearance of reference-invariant functions % (u, i j) are represented in Fig. 10. Curves with maxima and minima cannot be described in a reference-invariant manner. In this case, both the dimensional-analytical representation and the model material system are confined to the region close to the standardization range . 

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