 |
|
Functions for the description of orthotropic elastic behavior. More...
Functions | |
| Matrix6d | complianceTensor (const double E1, const double E2, const double E3, const double nu12, const double nu23, const double nu13, const double G12, const double G23, const double G31) |
| Matrix6d | stiffnessTensor (const double E1, const double E2, const double E3, const double nu12, const double nu23, const double nu13, const double G12, const double G23, const double G31) |
Functions for the description of orthotropic elastic behavior.
| Matrix6d Marmot::ContinuumMechanics::Elasticity::Orthotropic::complianceTensor | ( | const double | E1, |
| const double | E2, | ||
| const double | E3, | ||
| const double | nu12, | ||
| const double | nu23, | ||
| const double | nu13, | ||
| const double | G12, | ||
| const double | G23, | ||
| const double | G31 | ||
| ) |
Computes the orthotropic compliance tensor defined in the principal directions of the material \( x_1 \), \( x_2 \) and \( x_3 \) :
\[ \displaystyle \mathbb{ C }^{-1} = \begin{bmatrix} \frac{1}{E_1} & \frac{-\nu_{12}}{E_2} & \frac{-\nu_{13}}{E_3} & 0 & 0 & 0 \\ \frac{-\nu_{12}}{E_2} & \frac{1}{E_2} & \frac{-\nu_{23}}{E_3} & 0 & 0 & 0 \\ \frac{-\nu_{13}}{E_3} & \frac{-\nu_{23}}{E_3} & \frac{1}{E_3} & 0 & 0 & 0 \\ 0 & 0 & 0 & \frac{1}{G_{12}} & 0 & 0 \\ 0 & 0 & 0 & 0 & \frac{1}{G_{13}} & 0 \\ 0 & 0 & 0 & 0 & 0 & \frac{1}{G_{23}} \end{bmatrix} \]
from the following independent parameters:
| Parameter | Description |
|---|---|
| \( E_1 \) | Young's modulus effective in \( x_1 \) - direction |
| \( E_2 \) | Young's modulus effective in \( x_2 \) - direction |
| \( E_3 \) | Young's modulus effective in \( x_3 \) - direction |
| \( \nu_{12} \) | Poisson's ratio effective between \( x_1 \) and \( x_2 \) - direction |
| \( \nu_{13} \) | Poisson's ratio effective between \( x_1 \) and \( x_3 \) - direction |
| \( \nu_{23} \) | Poisson's ratio effective between \( x_2 \) and \( x_3 \) - direction |
| \( G_{12} \) | Shear modulus effective between \( x_1 \) and \( x_2 \) - direction |
| \( G_{13} \) | Shear modulus effective between \( x_1 \) and \( x_3 \) - direction |
| \( G_{23} \) | Shear modulus effective between \( x_2 \) and \( x_3 \) - direction |
| Matrix6d Marmot::ContinuumMechanics::Elasticity::Orthotropic::stiffnessTensor | ( | const double | E1, |
| const double | E2, | ||
| const double | E3, | ||
| const double | nu12, | ||
| const double | nu23, | ||
| const double | nu13, | ||
| const double | G12, | ||
| const double | G23, | ||
| const double | G31 | ||
| ) |
Computes the orthotropic stiffness tensor \( \mathbb{C} \) as inverse of the orthotropic compliance tensor \( \mathbb{C}^{-1} \).