The Deformation Gradient and Finger Tensors

The tensor E contains information not only on the stretching of the fluid element in each of its three dimensions, but also on the rotation of the fluid element The inverse of this. 

That is, the determinant of E is unity. For a uniaxial extensional deformation, incompress-ibility therefore implies that A2 = A3 = A,j, where Ai is the stretch ratio in the direction of elongation. 

Using the chain rule of calculus, the tensor E can be related to the velocity gradient tensor Vv, as follows  

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