Page 152 - Introduction to Continuum Mechanics
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Kinematics of a Continuum 137
and
We see both the finite and the infinitesimal strain tensor components lead to the same answer
whether k is large or small.
Z^AdJ
confirmed by the geometry in Fig. 3.12 for any value of k. On the other hand, the infinitesimal
strain component
k
Thus, from which we find Ay = (1 + —) AS. From Fig 3.12, we can easily
**
conclude that this result is acceptable only if A: is very small.
This example demonstrates clearly that in the case of finite deformations, the concept of
unit elongation (i.e., change of length per unit length) is inadequate.
