The dot represents material time derivative. A and B are second order tensors, eg Stress.
I myself am not clear what \nabla J means here. However, I guess it represents divergence.
This was as a homework question for a Continuum Mechanics course. I have not got any luck trying to understand...
Some one please help me how to prove the following:
\dot{A}:B + A:\dot{B}=A^{\nabla J}:B+A:B^{\nabla J}
A and B are II order tensors and : represents the inner product.