# tensors

## Derivatives of 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 ).

∂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.

## Inverse of the 4th rank tensor

Hi all,

I am looking for an algorithm to get the inverse of a 4th 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.

Best regards,

Mubeen.

## Seeking a logarithmic operator for a 4th order tensor

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I don't know whether this question has an answer, but I'd like to see what you all think:

Does anyone know whether or not the following operation is meaningful, whether it is described and defined algorithmically somewhere, and / or how to do it?

ln(Aij) = Bkm ln(Cijkm)

A and B are second order tensors

C is a 4th order tensor

The left hand side involves the natural logarithm of the 2nd order tensor A, which is no problem. 