Page 113 - Introduction to Continuum Mechanics
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98 Kinematics of a Continuum
where
From Eq. (3.7.4b) and (3.7.6), it is clear that the tensor E characterizes the changes of lengths
in the continuum undergoing small deformations. This tensor E is known as the infinitesimal
strain tensor.
1
Consider two material elements (DP- * and dx®. Due to motion, they become
(1)
(1)
(2
(1)
Jx and d^ at time t with </x = F^X and d^ = ¥dX \ Taking the dot product of
die ' and chr \ we obtain
Thus, using Eq. (3.7.6), we have the important equation
This equation will be used in the next section to establish the meanings of the components of
the infinitesimal strain tensor E.
The components of the infinitesimal strain tensor E can be obtained easily from the
components of the gradient of u given in Chapter 2. We have
(a) In rectangular coordinates:
or,
(B) In cylindrical coordinates:
