doc:user:elements:volumes:ortho_hypo_materials
Differences
This shows you the differences between two versions of the page.
Both sides previous revisionPrevious revisionNext revision | Previous revisionNext revisionBoth sides next revision | ||
doc:user:elements:volumes:ortho_hypo_materials [2013/07/11 15:46] – [DamageEpIsoHOrthoHypoMaterial] joris | doc:user:elements:volumes:ortho_hypo_materials [2015/01/26 12:11] – joris | ||
---|---|---|---|
Line 1: | Line 1: | ||
+ | ====== Orthotropic materials ====== | ||
+ | ===== OrthoElastHypoMaterial ===== | ||
+ | |||
+ | === Description === | ||
+ | |||
+ | Linear orthotropic material. | ||
+ | |||
+ | The strain-stress relation in the orthotropic frame is written as: | ||
+ | |||
+ | |||
+ | $$ | ||
+ | \left[ | ||
+ | \begin{array}{c} | ||
+ | \varepsilon_{11} \\ | ||
+ | \varepsilon_{22} \\ | ||
+ | \varepsilon_{33} \\ | ||
+ | \varepsilon_{23} \\ | ||
+ | \varepsilon_{31} \\ | ||
+ | \varepsilon_{12} | ||
+ | \end{array} | ||
+ | \right] | ||
+ | = | ||
+ | \left[ | ||
+ | \begin{array}{cccccc} | ||
+ | \frac{1}{E_{1}} & -\frac{\nu_{12}}{E_{1}} & -\frac{\nu_{13}}{E_{1}} & 0 & 0 & 0 \\ | ||
+ | -\frac{\nu_{12}}{E_{1}} & \frac{1}{E_{2}} & -\frac{\nu_{23}}{E_{2}} & 0 & 0 & 0 \\ | ||
+ | -\frac{\nu_{13}}{E_{1}} & -\frac{\nu_{23}}{E_{2}} & \frac{1}{E_{3}} & 0 & 0 & 0 \\ | ||
+ | 0 & 0 & 0 & \frac{1}{2\, | ||
+ | 0 & 0 & 0 & 0 & \frac{1}{2\, | ||
+ | 0 & 0 & 0 & 0 & 0 & \frac{1}{2\, | ||
+ | \end{array} | ||
+ | \right] | ||
+ | \left[ | ||
+ | \begin{array}{c} | ||
+ | \sigma_{11} \\ | ||
+ | \sigma_{22} \\ | ||
+ | \sigma_{33} \\ | ||
+ | \sigma_{23} \\ | ||
+ | \sigma_{31} \\ | ||
+ | \sigma_{12} | ||
+ | \end{array} | ||
+ | \right] | ||
+ | $$ | ||
+ | |||
+ | ===== Parameters === | ||
+ | |||
+ | ^ | ||
+ | | Density | ||
+ | | Young Modulus $E_1$ | '' | ||
+ | | Young Modulus $E_2$ | '' | ||
+ | | Young Modulus $E_3$ | '' | ||
+ | | Poisson ratio $\nu_{12}$ | ||
+ | | Poisson ratio $\nu_{13}$ | ||
+ | | Poisson ratio $\nu_{23}$ | ||
+ | | Shear modulus $G_{12}$ | ||
+ | | Shear modulus $G_{13}$ | ||
+ | | Shear modulus $G_{23}$ | ||
+ | | Objectivity method | ||
+ | | Orthotropic axis | '' | ||
+ | | Orthotropic axis | '' | ||
+ | | Orthotropic axis | '' | ||
+ | | Orthotropic axis | '' | ||
+ | | Orthotropic axis | '' | ||
+ | | Orthotropic axis | '' | ||
+ | |||
+ | Only the first two orthotropic axes are computed using '' | ||
+ | |||
+ | ===== EpIsoHOrthoHypoMaterial ===== | ||
+ | |||
+ | === Description === | ||
+ | |||
+ | Elastoplastic orthotropic material with isotropic hardening. | ||
+ | |||
+ | The elastic part follows the same relation as the [[# | ||
+ | |||
+ | As in the isotropic case, the yield stress verifies the constraint: | ||
+ | |||
+ | $$ | ||
+ | f=\overline{\sigma}-\sigma_{yield}=0 | ||
+ | $$ | ||
+ | |||
+ | where $\overline{\sigma}$ is an equivalent stress, specific to orthotropic materials. See for example the [[doc: | ||
+ | |||
+ | ===== Parameters === | ||
+ | |||
+ | ^ | ||
+ | | Density | ||
+ | | Young Modulus $E_1$ | '' | ||
+ | | Young Modulus $E_2$ | '' | ||
+ | | Young Modulus $E_3$ | '' | ||
+ | | Poisson ratio $\nu_{12}$ | ||
+ | | Poisson ratio $\nu_{13}$ | ||
+ | | Poisson ratio $\nu_{23}$ | ||
+ | | Shear modulus $G_{12}$ | ||
+ | | Shear modulus $G_{13}$ | ||
+ | | Shear modulus $G_{23}$ | ||
+ | | Number of the material law which defines the yield stress $\sigma_{yield}$ | ||
+ | | Number of the plastic criterion | ||
+ | | Objectivity method \\ (Jaumann = 0, GreenNaghdi = 1)| '' | ||
+ | | Orthotropic axis | '' | ||
+ | | Orthotropic axis | '' | ||
+ | | Orthotropic axis | '' | ||
+ | | Orthotropic axis | '' | ||
+ | | Orthotropic axis | '' | ||
+ | | Orthotropic axis | '' | ||
+ | ===== DamageEpIsoHOrthoHypoMaterial ===== | ||
+ | |||
+ | === Description === | ||
+ | |||
+ | Elastoplastic orthotropic material with isotropic hardening and damage. | ||
+ | |||
+ | The elastoplastic part has the same characteristics as the [[# | ||
+ | |||
+ | The damage part consists in a material softening governed by one or several damage variables $d_{ij}$, whose value is included between 0 and 1. Typically, a modulus equal to $E_i$ before damage becomes $(1-d_i)\, | ||
+ | |||
+ | ===== Parameters === | ||
+ | |||
+ | ^ | ||
+ | | Density | ||
+ | | Young Modulus $E_1$ | '' | ||
+ | | Young Modulus $E_2$ | '' | ||
+ | | Young Modulus $E_3$ | '' | ||
+ | | Poisson ratio $\nu_{12}$ | ||
+ | | Poisson ratio $\nu_{13}$ | ||
+ | | Poisson ratio $\nu_{23}$ | ||
+ | | Shear modulus $G_{12}$ | ||
+ | | Shear modulus $G_{13}$ | ||
+ | | Shear modulus $G_{23}$ | ||
+ | | Number of the material law which defines the yield stress $\sigma_{yield}$ | ||
+ | | Number of the plastic criterion | ||
+ | | Number of the damage law | '' | ||
+ | | Maximal value of damage variables (failure) | ||
+ | | Objectivity method \\ (Jaumann = 0, GreenNaghdi = 1)| '' | ||
+ | | Orthotropic axis | '' | ||
+ | | Orthotropic axis | '' | ||
+ | | Orthotropic axis | '' | ||
+ | | Orthotropic axis | '' | ||
+ | | Orthotropic axis | '' | ||
+ | | Orthotropic axis | '' |
doc/user/elements/volumes/ortho_hypo_materials.txt · Last modified: 2020/12/08 11:01 by boman