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doc:user:elements:volumes:ortho_hypo_materials

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doc:user:elements:volumes:ortho_hypo_materials [2020/12/08 11:01] – [OrthoElastHypoMaterial] bomandoc:user:elements:volumes:ortho_hypo_materials [2025/07/22 11:56] (current) – [DamageEpIsoHOrthoHypoMaterial] papeleux
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 === Description === === Description ===
  
-Linear orthotropic material.+Linear elastic orthotropic material.
  
 The strain-stress relation in the orthotropic frame is written as: The strain-stress relation in the orthotropic frame is written as:
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 $$ $$
  
-===== Parameters ===+=== Parameters ===
  
 ^   Name                                             ^     Metafor Code     ^ ^   Name                                             ^     Metafor Code     ^
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 | Orthotropic axis                                    |    ''ORTHO_AX2_Y''       | | Orthotropic axis                                    |    ''ORTHO_AX2_Y''       |
 | Orthotropic axis                                    |    ''ORTHO_AX2_Z''       | | Orthotropic axis                                    |    ''ORTHO_AX2_Z''       |
 +| Orthotropic axis initialized by mesh construction \\ boolean : True - False (def) \\ override OrthoAxis definition  | ''ORTHO_INIT_AS_JACO'' | 
  
 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. 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.
 +
 +===== TmElastOrthoHypoMaterial =====
 +:!: Metafor version >=3536
 +=== Description ===
 +Linear thermoelastic orthotropic material with orthotropic thermal conduction law.
 +
 +Thermal conduction writes in the orthotropic frame
 +$$
 +\boldsymbol{K}~\nabla T = \left[
 +  \begin{array}{c c c}
 +     K_1 & 0 & 0 \\
 +     0 & K_2 & 0 \\
 +     0 & 0 & K_3 
 +  \end{array}
 +\right] \nabla T,
 +$$
 +where $\boldsymbol{K}$ is the orthotropic conduction matrix (in material axes) and $\nabla T$ is the temperature gradient.
 +
 +Linear thermoelasticity in the orthotropic frame writes
 +$$
 +\boldsymbol{\sigma} = \boldsymbol{\sigma}_0 + \mathbb{H} : (\boldsymbol{\varepsilon} - \boldsymbol{\varepsilon}^{th}) =  \boldsymbol{\sigma}_0 + \mathbb{H} : (\boldsymbol{\varepsilon} - \boldsymbol{\alpha} \Delta T),
 +$$
 +with stress tensor $\boldsymbol{\sigma}$, initial stress tensor $\boldsymbol{\sigma}_0$, Hooke's tensor $\mathbb{H}$, strain tensor (mechanical) $\boldsymbol{\varepsilon}$, and thermal strain tensor $\boldsymbol{\varepsilon}^{th}$, which is the product of the temperature variation $\Delta T$ and the thermal expansion (symmetric) tensor $\boldsymbol{\alpha}$.
 +
 +Thermoelastic dissipation term $\dot{W}^{te}$ is given by the general (anisotropic) relation
 +$$
 +\dot{W}^{te} = -\eta_{te} \left(\sum_{i=1}^3 \sum_{j=1}^3 \mathbb{H}_{ijkl} \alpha_{kl} \right)T \frac{\dot{J}}{J},
 +$$
 +with fraction of heat dissipated thermoelastic energy $\eta_{te}$ and determinant of the Jacobian matrix $J$.
 +
 +=== Parameters ===
 +^   Name                                             ^     Metafor Code     ^  Dependency ^
 +| Density                              |   ''MASS_DENSITY''       |  ''TO/TM''   |
 +| Young Modulus $E_1$                |  ''YOUNG_MODULUS_1''   |  ''TO/TM''   |
 +| Young Modulus $E_2$                |  ''YOUNG_MODULUS_2''   |  ''TO/TM''   |
 +| Young Modulus $E_3$                |  ''YOUNG_MODULUS_3''   |  ''TO/TM''   |
 +| Poisson ratio $\nu_{12}$    |  ''POISSON_RATIO_12''  |  ''TO/TM''   |
 +| Poisson ratio $\nu_{13}$    |  ''POISSON_RATIO_13''  |  ''TO/TM''   |
 +| Poisson ratio $\nu_{23}$    |  ''POISSON_RATIO_23''  |  ''TO/TM''   |
 +| Shear modulus $G_{12}$      |  ''SHEAR_MODULUS_12''  |  ''TO/TM''   |
 +| Shear modulus $G_{13}$      |  ''SHEAR_MODULUS_13''  |  ''TO/TM''   |
 +| Shear modulus $G_{23}$      |  ''SHEAR_MODULUS_23''  |  ''TO/TM''   |
 +| 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''       |  -   |
 +| Orthotropic axis initialized by mesh construction \\ boolean : True - False (def) \\ override OrthoAxis definition  | ''ORTHO_INIT_AS_JACO'' |      -       | 
 +| Thermal Expansion $\alpha_1$                |  ''THERM_EXPANSION_1''   |  ''TO/TM''   |
 +| Thermal Expansion $\alpha_2$                |  ''THERM_EXPANSION_2''   |  ''TO/TM''   |
 +| Thermal Expansion $\alpha_3$                |  ''THERM_EXPANSION_3''   |  ''TO/TM''   |
 +| Conductivity $K_1$                |  ''CONDUCTIVITY_1''   |  ''TO/TM''   |
 +| Conductivity $K_2$                |  ''CONDUCTIVITY_2''   |  ''TO/TM''   |
 +| Conductivity $K_3$                |  ''CONDUCTIVITY_3''   |  ''TO/TM''   |
 +| Heat Capacity $C_p$                |  ''HEAT_CAPACITY''   |  ''TO/TM''   |
 +| Dissipated thermoelastic power fraction $\eta_e$               |  ''DISSIP_TE''   |  -   |
 +| Dissipated (visco)plastic power fraction (Taylor-Quinney factor)                |  ''DISSIP_TQ''   |  -   |
  
 ===== EpIsoHOrthoHypoMaterial ===== ===== EpIsoHOrthoHypoMaterial =====
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 where $\overline{\sigma}$ is an equivalent stress, specific to orthotropic materials. See for example the [[doc:user:elements:volumes:isohard#comp1dirplasticcriterion|criterion]] for long-fiber composites.  where $\overline{\sigma}$ is an equivalent stress, specific to orthotropic materials. See for example the [[doc:user:elements:volumes:isohard#comp1dirplasticcriterion|criterion]] for long-fiber composites. 
  
-===== Parameters ===+=== Parameters ===
  
 ^   Name                                             ^     Metafor Code     ^ ^   Name                                             ^     Metafor Code     ^
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 | Orthotropic axis                                    |    ''ORTHO_AX2_Y''       | | Orthotropic axis                                    |    ''ORTHO_AX2_Y''       |
 | Orthotropic axis                                    |    ''ORTHO_AX2_Z''       | | Orthotropic axis                                    |    ''ORTHO_AX2_Z''       |
 +| Orthotropic axis initialized by mesh construction \\ boolean : True - False (def) \\ override OrthoAxis definition  | ''ORTHO_INIT_AS_JACO'' |
 +
 +===== TmEpIsoHOrthoHypoMaterial =====
 +:!: Metafor version >=3536
 +=== Description ===
 +Thermomechanical elastoplastic orthotropic material with isotropic hardening. The thermal part of the law is similar to the one of the [[#orthoelasthypomaterial|linear thermoelastic orthotropic material]].
 +
 +=== Parameters ===
 +^   Name                                             ^     Metafor Code     ^  Dependency ^
 +| Density                              |   ''MASS_DENSITY''       |  ''TO/TM''   |
 +| Young Modulus $E_1$                |  ''YOUNG_MODULUS_1''   |  ''TO/TM''   |
 +| Young Modulus $E_2$                |  ''YOUNG_MODULUS_2''   |  ''TO/TM''   |
 +| Young Modulus $E_3$                |  ''YOUNG_MODULUS_3''   |  ''TO/TM''   |
 +| Poisson ratio $\nu_{12}$    |  ''POISSON_RATIO_12''  |  ''TO/TM''   |
 +| Poisson ratio $\nu_{13}$    |  ''POISSON_RATIO_13''  |  ''TO/TM''   |
 +| Poisson ratio $\nu_{23}$    |  ''POISSON_RATIO_23''  |  ''TO/TM''   |
 +| Shear modulus $G_{12}$      |  ''SHEAR_MODULUS_12''  |  ''TO/TM''   |
 +| Shear modulus $G_{13}$      |  ''SHEAR_MODULUS_13''  |  ''TO/TM''   |
 +| Shear modulus $G_{23}$      |  ''SHEAR_MODULUS_23''  |  ''TO/TM''   |
 +| 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''       |  -   |
 +| Orthotropic axis initialized by mesh construction \\ boolean : True - False (def) \\ override OrthoAxis definition  | ''ORTHO_INIT_AS_JACO'' |      -       | 
 +| Thermal Expansion $\alpha_1$                |  ''THERM_EXPANSION_1''   |  ''TO/TM''   |
 +| Thermal Expansion $\alpha_2$                |  ''THERM_EXPANSION_2''   |  ''TO/TM''   |
 +| Thermal Expansion $\alpha_3$                |  ''THERM_EXPANSION_3''   |  ''TO/TM''   |
 +| Conductivity $K_1$                |  ''CONDUCTIVITY_1''   |  ''TO/TM''   |
 +| Conductivity $K_2$                |  ''CONDUCTIVITY_2''   |  ''TO/TM''   |
 +| Conductivity $K_3$                |  ''CONDUCTIVITY_3''   |  ''TO/TM''   |
 +| Heat Capacity $C_p$                |  ''HEAT_CAPACITY''   |  ''TO/TM''   |
 +| Dissipated thermoelastic power fraction $\eta_e$               |  ''DISSIP_TE''   |  -   |
 +| Dissipated (visco)plastic power fraction (Taylor-Quinney factor)                |  ''DISSIP_TQ''   |  -   |
 ===== DamageEpIsoHOrthoHypoMaterial ===== ===== DamageEpIsoHOrthoHypoMaterial =====
  
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 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 [[doc:user:elements:volumes:ortho_continuousdamage|basic laws]] 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 [[doc:user:elements:volumes:ortho_continuousdamage|basic laws]]
  
-===== Parameters ===+=== Parameters ===
  
 ^   Name                                             ^     Metafor Code     ^ ^   Name                                             ^     Metafor Code     ^
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 | Orthotropic axis                                    |    ''ORTHO_AX2_Y''       | | Orthotropic axis                                    |    ''ORTHO_AX2_Y''       |
 | Orthotropic axis                                    |    ''ORTHO_AX2_Z''       | | Orthotropic axis                                    |    ''ORTHO_AX2_Z''       |
 +| Orthotropic axis initialized by mesh construction \\ boolean : True - False (def) \\ override OrthoAxis definition  | ''ORTHO_INIT_AS_JACO'' |      -       | 
doc/user/elements/volumes/ortho_hypo_materials.1607421703.txt.gz · Last modified: by boman
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