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Micromechanics of composites/Proof 5

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Surface-volume integral relation 2

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Let be a body and let be its surface. Let be the normal to the surface. Let be a vector field on . Show that

Proof:

Recall that

where is any second-order tensor field on . Let us assume that . Then we have

Now,

where is any second-order tensor. Therefore,

Rearranging,