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--- doc:user:elements:volumes:ortho_hypo_materials [2014/10/01 16:56] – joris
+++ doc:user:elements:volumes:ortho_hypo_materials [2024/12/09 14:37] (current) – [TmElastOrthoHypoMaterial] vanhulle
@@ Line 1: / Line 1: @@
 ====== Orthotropic materials ======
-===== OrthoElastHypoMaterial =====
+===== ElastOrthoHypoMaterial =====
 === Description ===
-Linear orthotropic material.
+Linear elastic orthotropic material.
 The strain-stress relation in the orthotropic frame is written as:
@@ Line 44: / Line 44: @@
 $$
-===== Parameters ===
+=== Parameters ===
 ^   Name                                             ^     Metafor Code     ^
@@ Line 65: / Line 65: @@
 | Orthotropic axis                                    |    ''ORTHO_AX2_Z''       |
-Only the first two orthotropic axes are calculated using ''ORTHO_AX{1,2}_{X,Y,Z}'', the third one being calculated as the cross product of the first two.
+Only the first two orthotropic axes are computed using ''ORTHO_AX{1,2}_{X,Y,Z}'', the third one being computed as the cross product of the first two.
+===== TmElastOrthoHypoMaterial =====
+:!: Metafor version >=3536
+=== Description ===
+Linear thermoelastic orthotropic material with orthotropic thermal conduction law.
+Thermal conduction writes in the orthotropic frame
+$$
+\boldsymbol{K}~\nabla T = \left[
+  \begin{array}{c c c}
+     K_1 & 0 & 0 \\
+& K_2 & 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''       |  -   |
+| 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 =====
@@ Line 83: / Line 141: @@
 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     ^
@@ Line 105: / Line 163: @@
 | Orthotropic axis                                    |    ''ORTHO_AX2_Y''       |
 | Orthotropic axis                                    |    ''ORTHO_AX2_Z''       |
+===== 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''       |  -   |
+| 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 =====
@@ Line 115: / Line 209: @@
 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     ^