Introduction to Elasticity/Constitutive example 6

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Example 6[edit | edit source]

Given:

For an isotropic material

Verify:

where .

Solution[edit | edit source]

From the second equation that has been given

or,

Therefore,

or,

or,

To find out whether the plus or the minus sign should be placed before in the above equation, we put everything in terms of and . Thus,

Plugging these into the equation for , multiplying both sides by and dividing by , we get

The limiting value of is 0.5. Plugging this value into the above equation, we get,

The above can be true only if the sign is positive. Therefore, the correct relation is

Plugging this relation into the first of the given equations, we have,