Micromechanics of composites/Average velocity gradient in a RVE

Average velocity gradient in a RVE

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The time rate of the deformation gradient is given by

 

The average time rate of the deformation gradient is defined as

 

Following the same procedure as in the previous section, we can show that

 

The velocity gradient ( ) is given by

 

where   is the velocity.

The average velocity gradient in a RVE is defined as

 

Note that   only if  .