# Metafor

ULiege - Aerospace & Mechanical Engineering

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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 