Anisotropic Elasticity

For fully anisotropic elasticity 21 independent elastic stiffness parameters are needed. The stress-strain relations are as follows:

{\begin{matrix} σ_{11} \\ σ_{22} \\ σ_{33} \\ σ_{12} \\ σ_{13} \\ σ_{23} \end{matrix}} = [\begin{matrix} D_{1111} & D_{1122} & D_{1133} & D_{1112} & D_{1113} & D_{1123} \\ □ & D_{2222} & D_{2233} & D_{2212} & D_{2213} & D_{2223} \\ □ & □ & D_{3333} & D_{3312} & D_{3313} & D_{3323} \\ □ & □ & □ & D_{1212} & D_{1213} & D_{1223} \\ □ & s y m & □ & □ & D_{1313} & D_{1323} \\ □ & □ & □ & □ & □ & 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}} .

When the material stiffness parameters (the $D_{i j k l}$ ) are given directly, the constraint $σ_{33} = 0$ is imposed for the plane stress case to reduce the material's stiffness matrix as required.

The restrictions imposed upon the elastic constants by stability requirements are too complex to express in terms of simple equations. However, the requirement that $D^{e l}$ is positive definite requires that all its eigenvalues be positive.

Parameters


Input Data	Description
Dnnnn	Independent elastic stiffness parameter $D_{i j k l}$ .
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.