Elastic Orthotropic

PythonOpenSees

Model.nDMaterial('ElasticOrthotropic', tag, Ex, Ey, Ez, vxy, vyz, vzx, Gxy, Gyz, Gzx, rho=0.0)

Parameters:

• tag (int) – unique tag identifying material

• Ex (float) – elastic modulus in x direction

• Ey (float) – elastic modulus in y direction

• Ez (float) – elastic modulus in z direction

• vxy (float) – Poisson’s ratio in xy plane

• vyz (float) – Poisson’s ratio in yz plane

• vzx (float) – Poisson’s ratio in zx plane

• Gxy (float) – shear modulus in xy plane

• Gyz (float) – shear modulus in yz plane

• Gzx (float) – shear modulus in zx plane

• rho (float) – mass density. optional default = 0.0

The material formulations for the ElasticOrthotropic object are “ThreeDimensional”, “PlaneStrain”, “Plane Stress”, “AxiSymmetric”, “BeamFiber”, and “PlateFiber”.

\[\begin{split}\mathbf{C}^{-1} = \left[\begin{array}{cccccc} \frac{1}{E_1} & -\frac{\nu_{21}}{E_2} & -\frac{\nu_{31}}{E_3} & 0 & 0 & 0 \\ -\frac{\nu_{12}}{E_1} & \frac{1}{E_2} & -\frac{\nu_{32}}{E_3} & 0 & 0 & 0 \\ -\frac{\nu_{13}}{E_1} & -\frac{\nu_{23}}{E_2} & \frac{1}{E_3} & 0 & 0 & 0 \\ 0 & 0 & 0 & \frac{1}{G_{23}} & 0 & 0 \\ 0 & 0 & 0 & 0 & \frac{1}{G_{31}} & 0 \\ 0 & 0 & 0 & 0 & 0 & \frac{1}{G_{12}} \end{array}\right]\end{split}\]

with

\[E_1>0, E_2>0, E_3>0, G_{12}>0, G_{23}>0, G_{13}>0\]

Code Developed by: Michael H. Scott