Page 142 - Introduction to Continuum Mechanics

Kinematics of a Continuum 127

Example 3.22.1

Given

Find (a) the deformation gradient F, (b) the right stretch tensor U, and (c) the rotation tensor
R and (d) the left stretch tensor V.
Solution, (a)

(b)

'Thus, the positive definite tensor U is given by

(c)

(d)

We can also obtain V from

fj-t
In this example, the calculation of [U ] and [R] are simple because F F happens to be
-1
diagonal. If not, one can first diagonalize it to obtain [ U ] and [ U ] as diagonal matrices