Micromechanics of composites/Proof 5

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,