Page 148 - Introduction to Continuum Mechanics
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Kinematics of a Continuum 133
thus, for this material element
(d) For dX = dS^ and dX = dS 2e 2
Example 3.23.3
Show that (a) the eigenvectors of U and C are the same and (b) an element which was
in the principal direction n of C becomes, in the deformed state, an element in the direction
ofRn.
7 *7
Solution, (a) Since Un = An, therefore U n = AUn = A n
i.e.,
"7
Thus, n is also an eigenvector of C with A as its eigenvalue.
(b) If dX = dSn where n is a principal direction of U and C , then UdX = dSUn = dS&n so
that
That is, the deformed vector is in the direction of Rn.
