Can we ignore C13, C23,... parameters and anything related to the third axis of the orthotropic material in the Hook's law implementing the model to the FEM using shell elements? There are some examples in the books for plane stress conditions with just C11, C12, C21, C22 and C66 in the tensor.
In plane stress conditions, you assume that the stresses are null for 3, 4 and 5. Looking at your tensor, this gives you linear relations providing the strains in directions 3, 4 and 5 as function of the strains in directions 1, 2 and 6.
You can then write you problem in a reduced way by replacing the expression of the 3, 4, and 5 strains in the equation of 1, 2 and 6.
Your coefficients C13,... are thus not ignored, but integrated in the outer diagonal values C12,... of the problem in reduced form.
You C12,... values in reduced tensors are thus not the same than the ones in your full tensor, so care must be taken regarding the constitutive law used by your FE software.
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