Page 118 - Introduction to Continuum Mechanics

Geometrical Meaning of the Components of the infinitesimal Strain Tensor 103

Fig. 3.5

and

1
Thus, as previously obtained, there is no change of angle between dXs ' and dX^ \

Example 3.8.3

A unit cube, with edges parallel to the coordinates axes, is given a displacement field

Find the increase in length of the diagonal^/? (see Fig. 3.6) (a) by using the infinitesimal strain
tensor E and (b) by geometry
Solution, (a) The strain tensor is easily obtained to be