Given:
For an isotropic material
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Verify:
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where .
From the second equation that has been given
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or,
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Therefore,
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or,
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or,
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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,
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Plugging these into the equation for , multiplying both sides by and dividing by , we get
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The limiting value of is 0.5. Plugging this value into the above equation, we get,
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The above can be true only if the sign is positive. Therefore, the
correct relation is
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Plugging this relation into the first of the given equations, we have,
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