Example 1

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Convert the stress-strain relation for isotropic materials (in matrix form) into an equation in index notation. Show all the steps in the process.

Solution

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The stress-strain relation is

 

Let us expand out the terms and put all of them in a similar form. Thus,

 

We know that  . Also a quantity that is   when   and   when   can be represented by the Kronecker  . Therefore, we can write the above equations as

 

or,