Page 185 - Introduction to Continuum Mechanics

170 Problems

volume, (h) the deformed area (magnitude and its normal) for the area whose normal was in
the direction of 62 and whose magnitude was unity in the undeformed state.
3.62. Do Prob. 3.61 for the following deformation

3.63. Do Prob. 3.61 for the following deformation

3.64. Do Prob. 3.61 for the following deformation

3.65. Given

Obtain
(a)F,C.
(b) the eigenvalues and eigenvectors of C.

(c) the matrix of U and U using the eigenvectors of C as basis.
1
(d) the matrix of U and U" with respect to the e/ basis,
(d) the rotation tensor R with respect to the e/ basis.
You may check your results with the formulas given in the next problem.
3.66. Verify that with respect to rectangular Cartesian base vectors, the right stretch tensor
U and the rotation tensor R for the simple shear deformation

are given by