Question

PLease help

Answer 1

@ganeshie8

Answer 2

@Michele_Laino

Answer 3

I think you have to compute the eigenvalues and the corresponding eigenvectors of the tensor you provided

Answer 4

@Michele_Laino this problem came from the course "Mathematical theory of elasticity".. I dont have any book and cannot understand anything what the tutor is teaching. So if you provide me good references regarding the thoery or problems, it will be helpful

Answer 5

here is my reference:
\[\huge \begin{gathered}
{\text{N}}{\text{.W}}{\text{.Ashcroft / N}}{\text{.D}}{\text{. Mermin}} \hfill \\
{\mathbf{Solid State Physics}} \hfill \\
{\text{Saunders College Publishing}} \hfill \\
{\text{Harcourt Brace College Publishers}} \hfill \\
\end{gathered} \]

Answer 6

the strain tensor is defined on page \(444\)

Answer 7

So we need to find the eigen values right?

Answer 8

@Michele_Laino the eigen values are really scary..

Answer 9

yes! you are right! I think that we have to construct some vector or tensor quantity, using the strain tensor.

Answer 10

please don't compute the eigenvalues. It is necessary that you study my reference above or one reference on elasticity theory

Answer 11

the book has got more than 800pages, right?

Answer 12

yes! It has 826 pages

Answer 13

but i am not getting anything about the strain tensor at page 444

Answer 14

I have the college edition, and at page \(444\) it is defined the strain tensor.
Another possible reference, is:
https://archive.org/details/TheoryOfElasticity

Answer 15

@Michele_Laino there's no way but to calculate the eigen values... I saw a similar type problem