Many materials often show very different behaviors between volume changing deformation and volume-preserving deformation. The former is called dilatation, while the latter is called distortion.
In such a case, it is necessary to separate the dilatational and distortional parts from the deformation gradient.
For example, the deformation gradient can be decomposed into F = Fv · Fd, where Fv is the dilatational part and Fd is the distortional part. Calculate Fv and Fdusing the third invariant of the deformation tensor.