I'm current stuck on a continuum mechanics problem, in which I need to find: $$ \nabla \cdot\frac{\partial}{\partial \nabla P}\left[G\circ\left(\nabla P \otimes \nabla P\right)\right] $$ Where $P$ is a vector in R3, i.e. $P = P_i,P_j,P_k$, and $G$ is a coefficient tensor with the same size as $\nabla P \otimes \nabla P$.
Of course, I could expand it into each component of the grad(P) tensors, but with 81 terms this would become a nightmare fairly soon.
Is there an elegant way to simplify this?