The expansion of a shell node leads to a set of nodes lying on a straight line. Therefore, the stretch tensor is reduced to the stretch along this line. Let be a unit vector parallel to the expansion and and unit vectors such that and . Then can be written as:
leading to one stretch parameter . Since the stretch along and is immaterial, Equation (155) can also be replaced by
representing an isotropic expansion. Equation (154) can now be replaced by
Consequently, a knot resulting from a shell expansion is characterized by 3 translational degrees of freedom, 3 rotational degrees of freedom and 1 stretch degree of freedom.