@Mariusz Iwaniuk Thank you Mariusz! It will certainly help I will check this out :)

@Torre Basically, it is the fact that a fourth order tensor cant be visually represented like a second order one that pushes the need of changing its notation and bringing it to a 6x6 matrix form.

I have aij and need to build aijkl from it. I can choose a linear approximation such as aijkl=A1*aij+A2*(akl*kroneckerij....etc etc)

But maple doesnt recognize the tensor im plugging nor can print it out, hence my need to go between them both and be able to visualize the aijkl.

Does it answer your question?

@tomleslie I think I already stated in my problem that Maple does quite fine what I asked of it, but this relies heavily on me and I am not the only one working with that code.

I needed a bullet proof way to write the code, but the math is there. I thought you needed more explanation to understand the purpose of going through all the steps, but apparently, it wasn't the case, my bad.

I figured out a pretty basic way of checking the code though: if a vector has certain coordinates in a primary axis, and I happen to know the coordinates it is supposed to have in the final primed axis, then the transformed vector (mathematically speaking, multiplied by my transformation matrixes) should end up having the same coordinates.

@ThU 

I felt it was the problem as it would compute a value if I ask for one but not the graph,! Thank you :)

@tomleslie 

Voila. Thank you Tom. I cannot imagine how much time and patience it must take to go through someone's sheet. I gave up on mine eventually!

I am following you. I will try to give you a background of what I am doing and hopefully, it will be clearer:

Basically, I have unidirectional laminae, which are plies of composites. Composites can be different mix of heterogeneous materials. Unidirectional laminae are sheets of matrix (resin) where there are carbon fibers aligned along the same direction.

The main feature to focus on when it comes to unidirectional laminae is the fact that their stiffness is described through a tensor.

More particular is that the stiffness tensor at first is defined according to a "local axis".

The local axis is quite typical: x1' follows the fiber direction, x2' is normal to the fibers' length and x3' is normal to x1' and x2' and is always the axis poking out of the lamina.

So when I have my lamina properties (modulus according to direction 1, 2 3 and shear modulus according to 1, 2 3 and poisson according to the three directions), I can come up with the expression of the tensor in the local coordinates.

The thing is when I orient my lamina according to the global axis (at 45degress or 90 or 30), the tensor has to be transformed according to the rotation.

Stiffness of composites and heterogeneous materials needs to be recalculated in the global axis once we settle on their location ( hence the Stiffness_At_Wall= Rotation*Stiffness_LocalCoord*Transpose(Rotation)

Which is fine as long as it doesn't become too confusing.

But I happen to have a stack of laminae, let's say six. And I have to create a beam out of them in 45degrees.

This means basically means a first rotation of 45degrees.

Then rotation according to the global axis so that I can get the stiffness of every "wall".

The walls are basically a rectangle sitting in a global axis referential.

And I am basically taking every laminae, rotating it 45degrees, gluing to a wall and pondering how to match the local coords with the global coords so that I can get my stiffness at the wall.

Which can be fine if I am the only observer and spent some time making sure Im taking all my rotations in the right sense.

But when my colleagues try to use the tool, they have their own sense of rotation in their head and things get very confusing and results as well.

So, I was basically hoping that, knowing the initial configuration, and the end configuration, I could come up with something that would spare us the lengthy discussion over Ampere man and orientation of rotation and signs issue.

I hope it is clearer now. I attached a doodle I made on paint of an example of the operation. Thank you Tom, thank you.

@John Fredsted Brilliant!!!! So Maple can understand that Im writing TENSORS?

John that is very helpful thank you so much :D

@John Fredsted Thank you John :) it is more fluid indeed. I didn't know about this package! Thanks!

@tomleslie Thank you! I think I got it. I will try it out straight away,

Again many thanks Tomleslie 

@Kitonum You are a life savior my friend :) thank you ^^