Page 116 - Introduction to Continuum Mechanics

Geometrical Meaning of the Components of the infinitesimal Strain Tensor 101

Therefore

Fig. 3.4 (repeated)

(b) At the point C, Xi= 1, therefore

For the element dX^ = dX^, the unit elongation is EH, which is zero. For the element
dXs ' ~ dX2*2> the unit elongation is £22 which is also zero. The decrease in angle between
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these elements is given by 2£^2, which is equal to 2k, i.e., 2x 10~ radians,
(c) In Example 3.7.1, we found that

4
and siny = 2fc=2xlO so that y«2xlO 4
We see that the results of this example is accurate up to the order of k.