Question

Good night. I need help with this problem of continuum mechanics. It is taken from George E. Mase book, "Continuum mechanics for engineers". The picture has the final answer, but I don't know the steps to obtain it. Please, explain it step by step. Thank you so much.

3.28. A certain homogeneous deformation feld results in the finite strain tensor 1 32 Lui = 1 3 1-2 |. Determine the principal strains and their directions for this -22 6 deformation Being a symmetrie second order Cartesian tensor, the principal strains are the roots of [CHAP. 3 102 DEFORMATION AND STRAIN 1-L 32 -26-L Thus LL-. L . The transformation matrix for prineipa! direetions is v212

Answer 1

3 2 Stra 2. 2 2. 一2(-什2

1-C2) 3-72 1-2) 2 2.

ni 1-2 3 2 1-2 2 2 6J'h กา ー2 Fra 彸 GO 6-占 -「

s=[3 3 -2;3 3 -2;-2 -2 8];
>> null(s)

ans =

-0.7071
0.7071
0.0000

>> u=[-1 3 -2;3 -1 -2;-2 -2 4];
>> null(u)

ans =

0.5774
0.5774
0.5774

>> v=[-7 3 -2;3 -7 -2;-2 -2 -2];
>> null(v)

ans =

0.4082
0.4082
-0.8165