Page 145 - Introduction to Continuum Mechanics

130 Right Cauchy-Green Deformation Tensor

Example 3.23.1
Given

(a) Obtain C
(b) Obtain the principal values of C and the corresponding principal directions

(c) Obtain the matrix of U and U~ with respect to the principal directions

(d) Obtain the matrix of U and U~ with respect to the e/ basis
(e) Obtain the matrix of R with respect to the e, basis
Solution, (a) From Eq. (i), we obtain,

Thus,

The eigenvalues of C and their corresponding eigenvectors are easily found to be
/ . \

(b) The matrix of C with respect to the principal axis of C is