Understanding elastic tensor matrix intuitively

[chiraganand]

Hi, I know the generalized hookes law between stress and strain is given by the elastic tensor. This matrix has 81 constants which are reduced to 9 in the isotropic case. Can someone please help me to understand intuitively how this reduction in the elastic tensor takes place and why some of the components are zero? also can someone please help me to understand the einstein summation used in the naming of the elastic tensor?

Thankyou for your help

 

[Charles Link]

I recommend you take a look at the book Physical Properties of Crystals: Their Representation by Tensors and Matrices by J.F. Nye. This is one of the better books out there to give a complete understanding of the subject.

 

[chiraganand]

I recommend you take a look at the book Physical Properties of Crystals: Their Representation by Tensors and Matrices by J.F. Nye. This is one of the better books out there to give a complete understanding of the subject.

Thanks for your reply.. Do you have suggestions for any other books?

 

[Charles Link]

Thanks for your reply.. Do you have suggestions for any other books?

The book by Nye is one of the better ones that is somewhat well-known, but not as well as it should be, in my opinion. For your topic of interest, it really does a good job. Most other physics texts for the various topics are fairly well-known.

 

[Mapes]

I concur; Nye says it all. There's a detailed description of how crystal symmetry forces many of the indices to be zero or identical.

Also, I think you mean 2 independent parameters for the isotropic case. There are 9 independent parameters for the orthotropic case.