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I'm doing some early work in my PhD and I'm coding a micromechanical scheme in which I have many 4th order localization tensors. The problem I'm facing is taking an expression for a 4th order tensor, and then finding the inverse of it. I am assuming the isotropic case and I fully understand that a tensor is easily invertible if it is in the form [tex]\mathbf{A}=\alpha*\mathbf{J}+\beta*\mathbf{K}[/tex]. However, how does one invert a 4th order tensor if it is not in this convenient form?

For example: how do I find the inverse of [tex]\mathbf{A}[/tex] when

[tex]\mathbf{A} = \mathbf{C}-\mathbf{B}[/tex]

and when [tex]\mathbf{B}[/tex] and [tex]\mathbf{C}[/tex] are already defined somewhere else and don't particularly have any convenient symmetry?

Thank you for your help!

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# Inverse of a 4th order tensor

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