tensors

Hi all,

I am looking for a general definition of the derivative of a tenorial product (e.g. when the expression for Stress contains nonlinear terms in deformation gradient, F ).

I start with a very simple example:

∂F_pq/∂F_mn = δ_pm  δ_qn , i.e. Kronecker delta with first index of F_pq and first index of  F_mn, and second Kronecker delta for second pair of indices q & n.

However the problem arises when we have a product of two or more tensors. Is the following (using chain rule) a valid derivative?

Hello all,

Hi all,

I am looking for an algorithm to get the inverse of a 4^th rank tensor (e.g. the compliance tensor S_(ijkl) from elastic stiffness tensor C_{_(ijkl)}) S_(ijkl)=C_{_(ijkl)}^{^(-1)}

I am programming in FORTRAN, and for this purpose I wasn't able to find neither any algorithm nor any existing subroutine.

If anyone at this forum has any idea about this inversion, kindly guide me.

Best regards,

Mubeen.