Coefficients of Mutual Influence:

It is well understood by now that for an off-axis lamina there is normal-shear coupling. The terms  and  denote the normal-shear coupling. In other words, these terms express that when there is a normal stress there will be associated shear strain and in a similar way when there is a shear stress there will be associated normal strain or vice-a-versa.

The normal and shear coupling has been quantified by Lekhnitskii by coefficients of mutual influence. Two kinds of coefficients of mutual influence have been defined. The first one is defined for applied shear stress and the second one is defined for applied normal stress. These are defined as the ratio of an associated strain to the applied strain for the given state of stress. Thus, the coefficients of mutual influence of the first kind are defined as

(4.81)

where  denotes the axial normal strains, that is  or , and  denotes the in-plane engineering shear strain. For this case, the state of stress would be  and . Similarly, the coefficients of mutual influence of the second kind are defined as

(4.82)

The state of stress for this case could be either  and  or   and .
Now, let us obtain expressions for the coefficients of mutual influence of the first kind.  We have

(4.83)

(4.84

Now, we will obtain expressions for the coefficients of mutual influence of the second kind. For the loading shown in Figure 4.2, we will get

(4.85)

which will be simplified and expressed in terms of engineering constants in principle material directions and fibre orientation as

(4.86)

Similarly, for the loading shown in Figure 4.4, we get the remaining coefficient of mutual influence as

(4.87)

The variation of the coefficients of mutual influence of the first kind and second kind for AS4/3501-6 Epoxy material with fibre orientation between  to  is shown in Figure 4.9.