Define Orthotropic Material Properties

Defines the material properties for orthotropic behavior in terms of engineering constants.

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Orthotropic materials have three mutually perpendicular planes of symmetry in their material properties. The stress-strain relation for orthotropic linear elastic materials can be written as follows.(1)
$ε ¯ ¯ = S ¯ ¯ ¯ ¯ ¯ ¯ σ ¯ ¯$ $\underline{\underline{ε}} = \underline{\underline{S}} \underline{\underline{σ}}$
Where the compliance matrix $S ¯ ¯ ¯ ¯ ¯ ¯$ $\underline{\underline{S}}$ is given by,

Figure 3.
The compliance matrix is symmetric and must be positive definite (real numbers for every non-zero value). This implies, from Sylvester’s criterion, that all the principal minors of the matrix are positive.

Figure 4.
Then,

Figure 5.
The above set of conditions implies that,

Figure 6.

If the above conditions are not satisfied, an error occurs.

Figure 7.
The thermal expansion coefficient (along X, Y, Z) and thermal properties are given if required for thermal simulations.