Introduction to Elasticity/Constitutive example 2

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Example 1[edit | edit source]

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[edit | edit source]

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,