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Functions for the description of transversely isotropic elastic behavior. More...
Functions | |
| Matrix6d | complianceTensor (const double E1, const double E2, const double nu12, const double nu23, const double G12) |
| Matrix6d | stiffnessTensor (const double E1, const double E2, const double nu12, const double nu23, const double G12) |
Functions for the description of transversely isotropic elastic behavior.
| Matrix6d Marmot::ContinuumMechanics::Elasticity::TransverseIsotropic::complianceTensor | ( | const double | E1, |
| const double | E2, | ||
| const double | nu12, | ||
| const double | nu23, | ||
| const double | G12 | ||
| ) |
Computes the transversely isotropic compliance tensor:
\[ \displaystyle \mathbb{ C }^{-1} = \begin{bmatrix} \frac{1}{E_1} & \frac{-\nu_{12}}{E_1} & \frac{-\nu_{12}}{E_1} & 0 & 0 & 0 \\ \frac{-\nu_{12}}{E_1} & \frac{1}{E_2} & \frac{-\nu_{23}}{E_2} & 0 & 0 & 0 \\ \frac{-\nu_{12}}{E_1} & \frac{-\nu_{12}}{E_2} & \frac{1}{E_2} & 0 & 0 & 0 \\ 0 & 0 & 0 & \frac{1}{G_{12}} & 0 & 0 \\ 0 & 0 & 0 & 0 & \frac{1}{G_{12}} & 0 \\ 0 & 0 & 0 & 0 & 0 & \frac{1}{G_{23}} \end{bmatrix} \]
The isotropic plane is defined with respect to the \( x_2 \) and \( x_3 \) axes of a local coordinate system. It is computed from the young's modulus \( E_1 \), the shear modulus \( G_{12} \) and poisson's ratio \( \nu_{12} \) effective out of the isotropic plane and the in - plane young's modulus \( E_2 \) and poisson's ratio \( \nu_{23} \).
The in - plane shear modulus \( G_{23} \) can be expressed by
\[ \displaystyle G_{23} = \frac{E_2}{2\,(1 + \nu_{23})} \]
| Matrix6d Marmot::ContinuumMechanics::Elasticity::TransverseIsotropic::stiffnessTensor | ( | const double | E1, |
| const double | E2, | ||
| const double | nu12, | ||
| const double | nu23, | ||
| const double | G12 | ||
| ) |
Computes the transversely isotropic stiffness tensor \( \mathbb{C} \) as inverse of the transversely isotropic compliance tensor \( \mathbb{C}^{-1} \).