Application of the Gram–Schmidt factorization of the deformation gradient to a cone and plate rheometer

Abstract

In this paper, we study the cone and plate rheometer using the Gram–Schmidt factorization of the deformation gradient. This new solution has several advantages over the traditional approach. It is shown that with the use of these kinematics, one can avoid the need for using a convected, curvilinear, coordinate system, which often leads to cumbersome calculations. Here, the use of a convected coordinate system has been replaced with a certain orthonormal coordinate system that arises from the Gram–Schmidt factorization of the deformation gradient. Moreover, by using this solution procedure, it is possible to obtain the normal stress differences and shear stress explicitly. Therefore, this solution procedure opens up a possibility for characterizing material properties by using only a cone and plate rheometer.