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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 ).

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.

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.

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

Best regards,

Mubeen.

Derivative of an expression

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Hello iMechanica!

While reading a paper, I've tried to repeat a derivation of a simple tensorial expression given in the paper and my result differs from the result in the paper. Could you please look in to the PDF-File (just 1 page long!) that I have attached to my post and see if I derived everything right? That would be great!

 Thanks a lot in advance!

Anton 

 

wvmars's picture

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. 

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