Page 119 - Introduction to Continuum Mechanics

104 Kinematics of a Continuum

V2
Since the diagonal AB was originally in the direction n = ~r-(e 1+e 2), its unit elongation is
given by

Since AB = V2,

(b) Geometrically,

or,

To take advantage of the smallness of k, we expand the first term in the right hand side of
Eq. (v) as

Therefore, in agreement with Part (a), Eq. (iv),
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Fig.3.6