Kinematics and Mechanics of Large Elastic Deformations - Continuum Mechanics of Anisotropic Materials - page 300

Fig. 11.10 The deformation
of a unit square by the F of
Example 11.3.1

Fig. 11.11 The deformation
of a unit square by the R of
Example 11.3.1

2 or II

1 or I

15°

order of the deformation and the rotation. The deformation or right stretch U is first
applied to the unit square and it deforms the square into the shape illustrated in
Fig. 11.12 . The clockwise rotation of 15 is then applied and it rotates the deformed
shape illustrated in Fig. 11.9 into its final position illustrated in Fig. 11.8

Problems
11.3.1. Prove that a·F T

a .
11.3.2. Using the polar decomposition theorem, F

¼ F

¼ R U ¼ V R , find the U and R

2 3

1 10

110
00 1

p 2

4 5 .

associated with the F given by F ¼

2 p

11.3.3. Find the square root of the matrix

2 3

1
160

41

4 5 :

V 2

¼

102