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doc:user:elements:volumes:ortho_hypo_materials

Orthotropic materials

ElastOrthoHypoMaterial

Description

Linear orthotropic material.

The strain-stress relation in the orthotropic frame is written as:

$$ \left[ \begin{array}{c} \varepsilon_{11} \\ \varepsilon_{22} \\ \varepsilon_{33} \\ \varepsilon_{23} \\ \varepsilon_{31} \\ \varepsilon_{12} \end{array} \right] = \left[ \begin{array}{cccccc} \frac{1}{E_{1}} & -\frac{\nu_{12}}{E_{1}} & -\frac{\nu_{13}}{E_{1}} & 0 & 0 & 0 \\ -\frac{\nu_{12}}{E_{1}} & \frac{1}{E_{2}} & -\frac{\nu_{23}}{E_{2}} & 0 & 0 & 0 \\ -\frac{\nu_{13}}{E_{1}} & -\frac{\nu_{23}}{E_{2}} & \frac{1}{E_{3}} & 0 & 0 & 0 \\ 0 & 0 & 0 & \frac{1}{2\,G_{23}} & 0 & 0 \\ 0 & 0 & 0 & 0 & \frac{1}{2\,G_{13}} & 0 \\ 0 & 0 & 0 & 0 & 0 & \frac{1}{2\,G_{12}} \end{array} \right] \left[ \begin{array}{c} \sigma_{11} \\ \sigma_{22} \\ \sigma_{33} \\ \sigma_{23} \\ \sigma_{31} \\ \sigma_{12} \end{array} \right] $$

Parameters

Name Metafor Code
Density MASS_DENSITY
Young Modulus $E_1$ YOUNG_MODULUS_1
Young Modulus $E_2$ YOUNG_MODULUS_2
Young Modulus $E_3$ YOUNG_MODULUS_3
Poisson ratio $\nu_{12}$ POISSON_RATIO_12
Poisson ratio $\nu_{13}$ POISSON_RATIO_13
Poisson ratio $\nu_{23}$ POISSON_RATIO_23
Shear modulus $G_{12}$ SHEAR_MODULUS_12
Shear modulus $G_{13}$ SHEAR_MODULUS_13
Shear modulus $G_{23}$ SHEAR_MODULUS_23
Objectivity method
(Jaumann = 0, GreenNaghdi = 1)
OBJECTIVITY
Orthotropic axis ORTHO_AX1_X
Orthotropic axis ORTHO_AX1_Y
Orthotropic axis ORTHO_AX1_Z
Orthotropic axis ORTHO_AX2_X
Orthotropic axis ORTHO_AX2_Y
Orthotropic axis ORTHO_AX2_Z

Only the first two orthotropic axes are computed using ORTHO_AX{1,2}_{X,Y,Z}, the third one being computed as the cross product of the first two.

EpIsoHOrthoHypoMaterial

Description

Elastoplastic orthotropic material with isotropic hardening.

The elastic part follows the same relation as the linear orthotropic material.

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 criterion for long-fiber composites.

Parameters

Name Metafor Code
Density MASS_DENSITY
Young Modulus $E_1$ YOUNG_MODULUS_1
Young Modulus $E_2$ YOUNG_MODULUS_2
Young Modulus $E_3$ YOUNG_MODULUS_3
Poisson ratio $\nu_{12}$ POISSON_RATIO_12
Poisson ratio $\nu_{13}$ POISSON_RATIO_13
Poisson ratio $\nu_{23}$ POISSON_RATIO_23
Shear modulus $G_{12}$ SHEAR_MODULUS_12
Shear modulus $G_{13}$ SHEAR_MODULUS_13
Shear modulus $G_{23}$ SHEAR_MODULUS_23
Number of the material law which defines the yield stress $\sigma_{yield}$ YIELD_NUM
Number of the plastic criterion PLASTICCRITERION_NUM
Objectivity method
(Jaumann = 0, GreenNaghdi = 1)
OBJECTIVITY
Orthotropic axis ORTHO_AX1_X
Orthotropic axis ORTHO_AX1_Y
Orthotropic axis ORTHO_AX1_Z
Orthotropic axis ORTHO_AX2_X
Orthotropic axis ORTHO_AX2_Y
Orthotropic axis ORTHO_AX2_Z

DamageEpIsoHOrthoHypoMaterial

Description

Elastoplastic orthotropic material with isotropic hardening and damage.

The elastoplastic part has the same characteristics as the elastoplastic orthotropic material

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 $(1-d_i)\,E_i$ once damage appears, but not always. The way damage is induced depends on the law defined by the parameter DAMAGE_NUM. See for example the basic laws

Parameters

Name Metafor Code
Density MASS_DENSITY
Young Modulus $E_1$ YOUNG_MODULUS_1
Young Modulus $E_2$ YOUNG_MODULUS_2
Young Modulus $E_3$ YOUNG_MODULUS_3
Poisson ratio $\nu_{12}$ POISSON_RATIO_12
Poisson ratio $\nu_{13}$ POISSON_RATIO_13
Poisson ratio $\nu_{23}$ POISSON_RATIO_23
Shear modulus $G_{12}$ SHEAR_MODULUS_12
Shear modulus $G_{13}$ SHEAR_MODULUS_13
Shear modulus $G_{23}$ SHEAR_MODULUS_23
Number of the material law which defines the yield stress $\sigma_{yield}$ YIELD_NUM
Number of the plastic criterion PLASTICCRITERION_NUM
Number of the damage law DAMAGE_NUM
Maximal value of damage variables (failure) DAMAGE_MAX
Objectivity method
(Jaumann = 0, GreenNaghdi = 1)
OBJECTIVITY
Orthotropic axis ORTHO_AX1_X
Orthotropic axis ORTHO_AX1_Y
Orthotropic axis ORTHO_AX1_Z
Orthotropic axis ORTHO_AX2_X
Orthotropic axis ORTHO_AX2_Y
Orthotropic axis ORTHO_AX2_Z
doc/user/elements/volumes/ortho_hypo_materials.txt · Last modified: 2020/12/08 11:01 by boman