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.
alternate method for similar problem
Though I have not found any direct way to get the inverse of 4th rank tensor, I have a different idea related to similar problem for the case.
I had to solve the equation
A:B=C
for B (where A=4th rank tensor, B,C = 2nd rank tensors), and A & C have already known values.
Instead of searching for inverse of A to get B, I expanded A:B , which resulted in 9 expressions A_ijkl * B_kl (i,j=1,2,3), and these 9 expressions were equal to the 9 entries in 2nd rank tensor C_ij (i,j=1,2,3).
With this result, I setup a system of 9 linear algebraic equations (LAEs) in which B_kl (k,l=1,2,3) were the only unknowns.
e.g.
A_11kl * B_kl = C_11
A_12kl * B_kl = C_12
...
A_33kl * B_kl=C_33 (for k,l=1,2,3)
These LAEs can be solved by one of the many existing methods e.g. Gaussian elimination.
Hence using this route, the inverse tensor wasn't required anymore.