Lamina Elasticity

Under plane stress conditions, such as in a shell element, only the values of $E_{1}$ , $E_{2}$ , $ν_{12}$ , $G_{12}$ , $G_{13}$ , and $G_{23}$ are required to define an orthotropic material. (In all of the plane stress elements in the $(1, 2)$ surface is the surface of plane stress, so that the plane stress condition is $σ_{33} = 0$ . The shear moduli $G_{13}$ and $G_{23}$ are included because they may be required for modeling transverse shear deformation in a shell. The Poisson's ratio $ν_{12}$ is implicitly given as $ν_{12} = (E_{2} / E_{1}) ν_{21}$ . In this case the stress-strain relations for the in-plane components of the stress and strain are of the form

{\begin{matrix} ε_{1} \\ \begin{matrix} \begin{matrix} ε_{2} \end{matrix} \\ γ_{12} \end{matrix} \end{matrix}} = [\begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} 1 / E_{1} \end{matrix} \\ \begin{matrix} \begin{matrix} - ν_{12} / E_{1} \end{matrix} \\ 0 \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} - ν_{12} / E_{1} \end{matrix} \end{matrix} \\ \begin{matrix} \begin{matrix} 1 / E_{2} \end{matrix} \\ 0 \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} 0 \end{matrix} \\ \begin{matrix} \begin{matrix} 0 \end{matrix} \\ 1 / G_{12} \end{matrix} \end{matrix} \end{matrix} \end{matrix} \end{matrix}] {\begin{matrix} σ_{11} \\ \begin{matrix} \begin{matrix} σ_{22} \end{matrix} \\ τ_{12} \end{matrix} \end{matrix}}

The restrictions on the elastic constants due to material stability are

E_{1}, E_{2}, G_{12}, G_{13}, G_{23} > 0

| ν_{12} | < {(E_{1} {/ E}_{2})}^{1 / 2} .

Parameters


Input Data	Description
E1	Young's modulus in the first in-plane local direction, $E_{1}$ .
E2	Young's modulus in the second in-plane local direction, $E_{2}$ .
Nu12	Poisson's ratio in the plane defined by the first and second local directions, $ν_{12}$ .
G12	In-plane shear modulus, $G_{12}$ .
G13	Shear modulus in the plane defined by the first and third local directions, $G_{13}$ .
G23	Shear modulus in the plane defined by the second and third local directions, $G_{23}$ .
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.