A class of motions with constant stretch history

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Abstract
The purpose of this paper is to examine the kinematics and dynamics of a class of motions with constant stretch history. A kinematical result is announced to indicate the velocity field such a motion may have and two examples, viz. helical-torsional flow and the helical flow combined with the axial motion of fanned planes, are discussed in detail. The helical-torsional flow is found to be experimentally realizable, albeit approximately, and it is shown how an apparatus may be built to measure the material functions occurring in such flows. Two nonlinear differential equations are derived to determine the velocity profile when the motion under study is treated as a nearly viscometric flow. In addition, restrictions on the proper numbers of the first Rivlin-Ericksen tensor are arrived at so that the motion with constant stretch history is completely determined by the first two or first three Rivlin-Ericksen tensors. This permits a reduction in the number of terms occurring in the full expansion of the constitutive equation.

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