Before proceeding as described above, it will be valuable at this time to prove the following statements for an isotropic material:*

1. Normal stresses can only generate normal strains. 2. A shear stress, say Txy , can only generate the corresponding engineering shear

strain 'YxY'

Consider statement 1 first. For this purpose we have shown an element in Fig. 5.1(a) under the normal stress Tzz • We will assume that a shear strain 'Yxy has resulted from the stress Tzz as shown in the diagram. Now rotate the element 1800 about the x axis to reach the configuration in Fig. 5.1(b). We now have the same normal stress, producing a shear strain that is different in sign. But for an isotropic material the relation between stress and the resulting strain should be independent of the orientation of an element relative to the axes. The only way to avoid the dilemma we find ourselves in now is to preclude the possibility of shear strain arising relative to a reference from normal stresses for that reference.