The left hand side of 22.4 is a constant and the r.h.s. signifies an ellipsoid. It has the property that in any direction, the length of its radius is inversely proportional to .
Such an ellipsoid is called the reciprocal strain ellipsoid:

Elements of length, which are parallel to the axes of the reciprocal strain ellipsoid in the un-deformed state becomes parallel to the strain ellipsoid in the deformed state. Such elements having lengths in the undeformed state, have lengths ,  and  respectively in the deformed state, where,,  are the principal extensions and ,  and  are the roots of the equation:
                       

(22.6)

An element of volume situated at  in the undeformed state has a volume in the deformed state, where,

(22.7)

For an incompressible material, the volume of an element in the deformed and undeformed states are equal, so that. Notice that the quantities ,  and  are invariant.The stress strain relationship for an incompressible material:
Hooke’s law,
 

,etc.	(22.8)
,etc.
,
, ,

neo-Hookean law:

,

(22.9)