Geometric meaning of components of strain

Let us go back to equation 1.9, under new notations it has the form:

(1.17)

Consider a vector which is parallel to the Ox axis.

For this vector: which results in , i.e. denotes the relative increase in length of the vectors.

Consider two vectors and which are initially directed towards and , after deformation turn to vectors and , the angle between which is written as:

(1.18)

For a small ,

(1.19)

But for and we have from 1.15:

(1.20)

Introducing this formula into equation 1.19, one obtains .

The angle represents the decrease in angle between the two vectors originally in the directions Oy and Oz .