Orthotropic Elasticity

In this case, the stress-strain relations are of the form

{\begin{matrix} σ_{11} \\ σ_{22} \\ σ_{33} \\ σ_{12} \\ σ_{13} \\ σ_{23} \end{matrix}} = [\begin{matrix} D_{1111} & D_{1122} & D_{1133} & 0 & 0 & 0 \\ □ & D_{2222} & D_{2233} & 0 & 0 & 0 \\ □ & □ & D_{3333} & 0 & 0 & 0 \\ □ & □ & □ & D_{1212} & 0 & 0 \\ □ & s y m & □ & □ & D_{1313} & 0 \\ □ & □ & □ & □ & □ & D_{2323} \end{matrix}] {\begin{matrix} ε_{11} \\ ε_{22} \\ ε_{33} \\ γ_{12} \\ γ_{13} \\ γ_{23} \end{matrix}} = D^{e l} {\begin{matrix} ε_{11} \\ ε_{22} \\ ε_{33} \\ γ_{12} \\ γ_{13} \\ γ_{23} \end{matrix}} .

The restrictions on the elastic constants due to material stability are

D_{1111}, D_{2222}, D_{3333}, D_{1212}, D_{1313}, D_{2323} > 0

| D_{1122} | < {(D_{1111} D_{2222})}^{1 / 2}

| D_{1133} | < {(D_{1111} D_{3333})}^{1 / 2}

| D_{2233} | < {(D_{2222} D_{3333})}^{1 / 2}

\det (D^{e l}) = D_{1111} D_{2222} D_{3333} + 2 D_{1122} D_{1133} D_{2233} - D_{2222} D_{1133}^{2} - D_{1111} D_{2233}^{2} - D_{3333} D_{1122}^{2} > 0.

These restrictions in terms of the elastic stiffness parameters are equivalent to the restrictions in terms of the "engineering constants."

Parameters


Input Data	Description
Dnnnn	Nine independent elastic stiffness parameters $D_{i j k l}$ .
Use temperature-dependent data	Specifies material parameters that depend on temperature. A Temperature field appears in the data table. For more information, see Specifying Material Data as a Function of Temperature and Independent Field Variables.
Number of field variables	Specifies material parameters that depend on field variables. Field columns appear in the data table for each field variable you add. For more information, see Specifying Material Data as a Function of Temperature and Independent Field Variables.