Question

please solve it by hand, do not use matlab or stuff like that. thank you :)

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 field results in the finite strain tensor 1 3-2 Lul = 1 3 1-2- Determine the principal strains and their directions for this L-2-2 6 deformation. Being a aymmetrie second order Cartesisn tensor, the prineipal strains are the roots of CHAP. 102 DEPORMATION AND STRAIN 1-L 3-2 22 6-L Thus La,--2, L(2) 2, Lt3)=8. The transformation matrix for principal directions is

Answer 1

1 3 -2 2 ου λί

3-2 l-λ thutx to Li 12 3-2 3 2 -2 2. 2 6+2 0 2- 9) 3,312 -213 0

3 2 emale d 2. yo

2 3 2 巌乐
In your given solution the third row is -1/Sqrt[6], -1/Sqrt[6], 2/Sqrt[6]. This we can also get if we take l1=l2=-1/Sqrt[6] and l3= 2/Sqrt[6]. The solution, I have given is also equally valid.