Metafor - doc:user:elements:volumesULiege - Aerospace & Mechanical Engineering
http://metafor.ltas.ulg.ac.be/dokuwiki/
2026-05-15T00:31:35+00:00Metafor
http://metafor.ltas.ulg.ac.be/dokuwiki/
http://metafor.ltas.ulg.ac.be/dokuwiki/_media/logo.pngtext/html2016-03-30T13:23:04+00:00Anonymous (anonymous@undisclosed.example.com)Continuous orthotropic damage
http://metafor.ltas.ulg.ac.be/dokuwiki/doc/user/elements/volumes/continuousanisodamage?rev=1459344184&do=diff
Continuous orthotropic damage
The ContinousAnisoDamage class manages the continuous orthotropic damage evolution laws. When defining a new law, the evolution of the damage variable $\delta H$ must be defined, and so must be its derivatives with respect to pressure, plastic strain and damage.$D$$$
\dot D = \left(\dfrac{\tilde\sigma_{eq}^2 R_\nu}{2ES}\right)^s |D^{pl}| \mbox{ if } \varepsilon^{pl} > \varepsilon^{pl}_D
$$$|D^{pl}|$$D^{pl}$$D^{pl}$$$
R_\nu = \dfrac{2}{3}\left(1+\nu\right) + 3\left(…text/html2021-04-09T09:35:13+00:00Anonymous (anonymous@undisclosed.example.com)Continuous isotropic damage
http://metafor.ltas.ulg.ac.be/dokuwiki/doc/user/elements/volumes/continuousdamage?rev=1617960913&do=diff
Continuous isotropic damage
The ContinousDamage class manages all continuous damage evolution laws. When a new law is defined, the evolution of the damage variable $\delta D$ must be defined, and so must be its derivatives with respect to pressure, plastic strain and damage.$$
\dot D = \left(\dfrac{\bar \sigma^2 R_\nu}{2ES\left(1-D\right)^2}\right)^s \dot \varepsilon^{pl} \mbox{, if } \varepsilon^{pl} > \varepsilon^{pl}_D \mbox{, and } \eta > \eta_D
$$$$
R_\nu = \dfrac{2}{3}\left(1+\nu\right) +…text/html2018-11-13T16:38:42+00:00Anonymous (anonymous@undisclosed.example.com)Damage
http://metafor.ltas.ulg.ac.be/dokuwiki/doc/user/elements/volumes/damage?rev=1542127122&do=diff
Damage
The Damage class manages all damage evolution laws. When defining a new law, the following must be defined:
* The stress associated to damage which is taken into account in the plastic criterion $ \sigma_{damage} $
* The evolution of the damage variable $ D $
* $\omega $$ \sigma_{damage}$$$
\sigma_{damage}=K\left[\dfrac{\dot{\bar{\varepsilon}}^{vp}\bar{\sigma}\left[1-D\right]}{\bar{\sigma}+p\dfrac{\partial f}{\partial p}}\right]^{m}\left[\bar{\varepsilon}^{vp}\right]^{n}
$$$ \omega…text/html2018-11-27T07:42:50+00:00Anonymous (anonymous@undisclosed.example.com)Methods to integrate stresses
http://metafor.ltas.ulg.ac.be/dokuwiki/doc/user/elements/volumes/elements_formulation?rev=1543304570&do=diff
Methods to integrate stresses
Following the classical approach (Cauchy stresses and out of conservative schemes), stresses over an element can be computed using 4 different methods.
Standard formulation
When using the standard formulation (CAUCHYMECHVOLINTMETH = VES_CMVIM_STD$$ F^{int} = \underbrace{\int_{V(t)}{ [B]^{T} {s} \ } dV}_{4 \ integration \ points \ in \ 2D - 8 \ in \ 3D} +
\underbrace{\int_{V(t)}{ p [B]^{T} {I} \ } dV}_{1 \ integration \ points} $$$s$$[B]^T$text/html2017-12-01T11:11:05+00:00Anonymous (anonymous@undisclosed.example.com)"Fluid" materials
http://metafor.ltas.ulg.ac.be/dokuwiki/doc/user/elements/volumes/fluid_iso_hypo_materials?rev=1512126665&do=diff
"Fluid" materials
FluidHypoMaterial
Description
Material law describing a non viscous fluid.
Stresses are computed with
$$
\sigma_{ij} = s_{ij} + p\delta_{ij}
$$
with $ s_{ij} = 0 $ in a non viscous fluid.
The equation which associates pressure and volume is
$$
dp = K \frac{dV}{V}
$$
where $K$ is the bulk modulus.
NortonHoffHypoMaterial$$
\sigma_{ij} = s_{ij} + p \delta_{ij}
$$$p$$ s_{ij} $$ s_{ij} $$ D_{ij} $$$ s_{ij} = 2 \mu D_{ij} \left( \sqrt{3} \ \sqrt{\frac{2}{3} D_{wz}.D_{wz}} …text/html2016-03-30T13:23:04+00:00Anonymous (anonymous@undisclosed.example.com)Grain Size
http://metafor.ltas.ulg.ac.be/dokuwiki/doc/user/elements/volumes/grainsize?rev=1459344184&do=diff
Grain Size
The GrainSize class manages the laws estimating the stress based on the size of grains and the laws governing the evolution of their size. When this size is taken into account, both laws must be defined (the stress due to grain size is taken into account in the plastic criterion).$$
\sigma_d =K\,d^p\,\left (\dot{\bar{\varepsilon}}^{pl} \right )^m\,\left (\bar{\varepsilon}^{pl} \right )^n
$$$$
\dot{d}=\dfrac{\alpha_1}{d^Q}+\dfrac{\alpha_2 \dot{\bar{\varepsilon}}^{pl}}{d^R}
$$$K $$m $$…text/html2016-03-30T13:23:04+00:00Anonymous (anonymous@undisclosed.example.com)Gravity
http://metafor.ltas.ulg.ac.be/dokuwiki/doc/user/elements/volumes/gravite?rev=1459344184&do=diff
Gravity
In Metafor, gravity is introduced with a ElementProperties on volume or shell elements, using the codes GRAVITY_X, GRAVITY_Y or GRAVITY_Z.text/html2026-01-15T13:12:46+00:00Anonymous (anonymous@undisclosed.example.com)Deviatoric Potentials
http://metafor.ltas.ulg.ac.be/dokuwiki/doc/user/elements/volumes/hyper_dev_potential?rev=1768482766&do=diff
Deviatoric Potentials
This section contains all material laws which allow to define the deviatoric part of the strain-energy density function $W_{dev}$
Isotropic Elastic Potentials
The ElasticPotential material law regroups elastic isotropic deviatoric strain-energy density functions as
$$
W_{dev} = W^e_{dev}\left(\bar{I}_1, \bar{I}_2, \bar{I}_3\right) = W^e_{dev}\left(\bar{I}_1, \bar{I}_2, J\right)
$$$$
\bar{I}_1 = \text{tr}\bar{\mathbf{B}} = \text{tr}\bar{\mathbf{C}} = \bar{\mathbf{F}}:\ba…text/html2026-01-15T12:15:35+00:00Anonymous (anonymous@undisclosed.example.com)Function Based Materials
http://metafor.ltas.ulg.ac.be/dokuwiki/doc/user/elements/volumes/hyper_functionbased?rev=1768479335&do=diff
Function Based Materials
FunctionBasedHyperMaterial
Description
Hyperelastic law, using a Cauchy stress tensor $\boldsymbol{\sigma}$, stress in the current configuration.
(Quasi-)incompressibility is treated by a volumetric/deviatoric multiplicative split of the deformation gradient, i.e. $\bar{\mathbf{F}} = J^{-1/3}\mathbf{F}$$\bar{\mathbf{B}} =\bar{\mathbf{F}}\bar{\mathbf{F}}^T $$\psi$$\psi_{e}$$\psi_{vol}$$$
\psi = \sum_{i=1}^{N_{e}}\psi_{e}^{(i)} + \sum_{i=1}^{N_{vol}}\psi_{vol}^{(i)} =…text/html2025-11-14T10:33:38+00:00Anonymous (anonymous@undisclosed.example.com)Inelastic Potentials
http://metafor.ltas.ulg.ac.be/dokuwiki/doc/user/elements/volumes/hyper_inel_potential?rev=1763116418&do=diff
Inelastic Potentials
The InelasticPotential material law regroups all the inelastic contributions $\mathbf{F}^{in}$ to the total deformation gradient $\mathbf{F}$. The law is responsible for the computation of the elastic part $\mathbf{F}^{in}$ of the total deformation gradient and associated elastic volume variation $J^e$$$
\mathbf{F}^e = \mathbf{F} \left(\mathbf{F}^{in}\right)^{-1} \hspace{.3cm} \text{and} \hspace{.3cm} J^e = \frac{J}{J^{in}}
$$$$
\mathbf{F}^{in} = \mathbf{F}^{th} = \left( 1…text/html2026-01-16T14:36:18+00:00Anonymous (anonymous@undisclosed.example.com)Hyperelastic materials
http://metafor.ltas.ulg.ac.be/dokuwiki/doc/user/elements/volumes/hyper_materials?rev=1768574178&do=diff
Hyperelastic materials
NeoHookeanHyperMaterial
Description
Neo-Hookean hyperelastic law, using a Cauchy stress tensor $\boldsymbol{\sigma}$, stress in the current configuration.
(Quasi-)incompressibility is treated by a volumetric/deviatoric multiplicative split of the deformation gradient, i.e. $\bar{\mathbf{F}} = J^{-1/3}\mathbf{F}$$\bar{\mathbf{b}} =\bar{\mathbf{F}}\bar{\mathbf{F}}^T $$$
W\left(I_1,I_2,J\right) = \bar{W}\left(\bar{I_1},\bar{I_2}\right) + K f\left(J\right) = C_1\left(\…text/html2025-09-29T12:34:25+00:00Anonymous (anonymous@undisclosed.example.com)Viscoelastic laws
http://metafor.ltas.ulg.ac.be/dokuwiki/doc/user/elements/volumes/hyper_viscoelastic?rev=1759149265&do=diff
Viscoelastic laws
The HyperFunction class manages hyperelastic laws, when IsoViscoElasticFunction manages a combination of HyperFunctions to create a viscoelastic law.
OgdenHyperFunction
Description
Ogden hyperelastic law.
The deviatoric potential is computed based on a Cauchy tensor with a unit determinant:$$
U^{dev}= \sum_i^3 \sum_j^3 \frac{\mu_j}{a_j} \left(\lambda_i^{\frac{1}{2}a_j}-1\right)
$$$ \lambda_i $$ \hat{C} $$ \mu_1 $$ \mu_2 $$ \mu_3 $$ a_1 $$ a_2 $$ a_3 $$$
U^{dev}= \frac{1}{4…text/html2025-11-14T10:34:20+00:00Anonymous (anonymous@undisclosed.example.com)Volumic Potentials
http://metafor.ltas.ulg.ac.be/dokuwiki/doc/user/elements/volumes/hyper_vol_potential?rev=1763116460&do=diff
Volumic Potentials
The VolumicPotential material law regroups all the functions $\mathcal{f}(J)$ such that the volumetric part of the strain-energy density function $W_{vol}$ can be expressed as
$$
W_{vol} = k_0\mathcal{f}(J)
$$
with the compression modulus $k_0$ defined on the material level.
QuadraticVolumicPotential
$$
\mathcal{f}(J) = \frac{1}{2}\left(J-1\right)^2
$$$$
\mathcal{f}(J) = \frac{1}{2}\left(\text{ln}J\right)^2
$$$$
\mathcal{f}(J) = \frac{1}{2}\left(J-1\right)^2 + \frac{1}{2}\le…text/html2026-01-15T09:26:59+00:00Anonymous (anonymous@undisclosed.example.com)Traditional Materials
http://metafor.ltas.ulg.ac.be/dokuwiki/doc/user/elements/volumes/iso_hypo_materials?rev=1768469219&do=diff
Traditional Materials
The orthotropic frame is a reference frame which is tied to the matter. It can be used to get stresses in a frame which is initially along given directions (for example, axial stresses on a sheet metal), or for anisotropic reasons. By default, the fame is aligned on the global one. $\Delta t$$$
\begin{cases}
p^{1} = p^{0} + 3K {\Delta\epsilon}_{ii} \\
s^{1}_{ij} = s^{0}_{ij} + 2G {\Delta\hat{\epsilon}}_{ij} + \eta \frac{{\Delta\hat{\epsilon}}_{ij}}{\Delta t}
\end{cases}
…text/html2020-07-08T08:16:28+00:00Anonymous (anonymous@undisclosed.example.com)Isotropic hardening
http://metafor.ltas.ulg.ac.be/dokuwiki/doc/user/elements/volumes/isohard?rev=1594196188&do=diff
Isotropic hardening
The IsotropicHardening class manages all isotropic hardening laws in Metafor, which are described below.
LinearIsotropicHardening
Description
Linear isotropic hardening
$$
\sigma_{vm} = \sigma^{el} + h\, \bar{\varepsilon}^{vp}
$$
Parameters
Name $\sigma^{el}$$h $$h = \frac{E E_T}{E - E_T} $$E$$E_T$$$
\sigma_{vm} = \sigma^{el} + Q\left(1-\exp\left(-\xi \bar{\varepsilon}^{vp}\right)\right)
$$$\sigma^{el}$$Q $$\xi$$$
\sigma_…text/html2022-06-16T13:06:24+00:00Anonymous (anonymous@undisclosed.example.com)Kinematic hardening
http://metafor.ltas.ulg.ac.be/dokuwiki/doc/user/elements/volumes/kinehard?rev=1655384784&do=diff
Kinematic hardening
The KinematicHardening class manages the kinematic hardening evolution laws.
DruckerPragerKinematicHardening
Description
Drucker-Prager linear kinematic hardening.
$$ \dot{X}_{ij}^{dp} = \dfrac{2}{3}\, h\,D_{ij}^{vp}$$
Parameters
Name Metafor Code Dependency $h $$$ \dot{X}_{ij}^{af} = \dfrac{2}{3}\, h\,D_{ij}^{vp} - b\, \dot{\bar{\varepsilon}}\, X_{ij}^{af} $$$h $$b $$$ \dot{X}_{ij}^{cf} = \dfrac{2}{3}\, h\,D_{ij}^{vp} - b\, \dot{\bar{\varepsil…text/html2016-03-30T13:23:04+00:00Anonymous (anonymous@undisclosed.example.com)Continuous orthotropic damage
http://metafor.ltas.ulg.ac.be/dokuwiki/doc/user/elements/volumes/ortho_continuousdamage?rev=1459344184&do=diff
Continuous orthotropic damage
The ContinousDamage class manages all continuous damage evolution laws. When a new law is defined, the evolution of the damage variable $ \Delta D $ must be defined, and so must be its derivatives with respect to pressure, plastic strain and damage.$$
\begin{eqnarray*}
W_{\rm D} &=& \dfrac{1}{2}\Biggl(
\dfrac{\sigma_{11}^2}{E_1\,(1-d_{11})}
-2\,\dfrac{\nu_{12}}{E_1}\,\sigma_{11}\,\sigma_{22}
-2\,\dfrac{\nu_{13}}{E_1}\,\sigma_{11}\,\sigma_{33}
\\
&& +\dfrac{\sigma_{…text/html2025-07-22T09:56:06+00:00Anonymous (anonymous@undisclosed.example.com)Orthotropic materials
http://metafor.ltas.ulg.ac.be/dokuwiki/doc/user/elements/volumes/ortho_hypo_materials?rev=1753178166&do=diff
Orthotropic materials
ElastOrthoHypoMaterial
Description
Linear elastic orthotropic material.
The strain-stress relation in the orthotropic frame is written as:
$$
\left[
\begin{array}{c}
\varepsilon_{11} \\
\varepsilon_{22} \\
\varepsilon_{33} \\
\varepsilon_{23} \\
\varepsilon_{31} \\
\varepsilon_{12}
\end{array}
\right]
=
\left[
\begin{array}{cccccc}
\frac{1}{E_{1}} & -\frac{\nu_{12}}{E_{1}} & -\frac{\nu_{13}}{E_{1}} & 0 & 0 & 0 \\
-\frac{\nu_{12}}{E…text/html2016-03-30T13:23:04+00:00Anonymous (anonymous@undisclosed.example.com)Plastic criteria
http://metafor.ltas.ulg.ac.be/dokuwiki/doc/user/elements/volumes/ortho_plasticity_criterion?rev=1459344184&do=diff
Plastic criteria
The PlasticCriterion class manages the possibility to replace the default Von Mises plastic criterion by another one, described below.
Comp1DirPlasticCriterion
Description
Plastic criterion for orthotropic composite plies with unidirectional fibers. Also used with woven fibers.$$
\overline{\sigma}
= \sqrt{\sigma_{12}^2+\sigma_{13}^2+\sigma_{23}^2
+a^2\, \sigma_{22}^2
+b^2\, \sigma_{33}^2}
$$text/html2016-03-30T13:23:04+00:00Anonymous (anonymous@undisclosed.example.com)Plastic criteria
http://metafor.ltas.ulg.ac.be/dokuwiki/doc/user/elements/volumes/plasticity_criterion?rev=1459344184&do=diff
Plastic criteria
The PlasticCriterion class manages the possibility to replace the default Von Mises plastic criterion by another one, described below.
VonMisesPlasticCriterion
Description
Isotropic plastic criterion (default in Metafor)
$$
\sqrt{\frac{3}{2}s_{ij}s_{ij}} - (\sigma_{vm} + \sigma_{visq} + \sigma_{grainSize} + ...) = 0
$$
Parameters
$$
\begin{multline}
\sqrt{\frac{1}{2}} \sqrt{F (s_{22}-s_{33})^2 + G (s_{33}-s_{11})^2 + H (s_{11}-s_{22})^2 + 2 (L s_{13}^2 + M s_{23}^2 + N s…text/html2016-03-30T13:23:04+00:00Anonymous (anonymous@undisclosed.example.com)Element failure
http://metafor.ltas.ulg.ac.be/dokuwiki/doc/user/elements/volumes/rupture?rev=1459344184&do=diff
Element failure
Volume element can be deactivated using a failure criterion. This criterion is applied on the FieldApplicator of volume elements. The criterion is defined as:
rc = NamemRuptureCriterion()
rc.put(param, value)
rc.depend(param, fct, Field1D(Lock))
...
app = FieldApplicator(no) # association to the FieldApplicator number no
app.push(1, SIDE_ID)
app.addRuptureCriterion(rc)text/html2022-07-14T12:32:34+00:00Anonymous (anonymous@undisclosed.example.com)Failure criteria
http://metafor.ltas.ulg.ac.be/dokuwiki/doc/user/elements/volumes/rupturecritere?rev=1657801954&do=diff
Failure criteria
RuptureCriterion
Description
RuptureCriterion manages various failure criteria.
The critical value C (RUPT_CRIT_VALUE) of a variable above which the element is broken.
The type of failure (RUPT_TYPE_CRIT) are defined in the table below : $$ C = \int_0^{\overline{\varepsilon}^p} \sigma_1 d\overline{\varepsilon}^p$$$$ C = \int_0^{\overline{\varepsilon}^p} \frac{\sigma_1}{\overline{\sigma}} d\overline{\varepsilon}^p$$$$ C = \int_0^{\overline{\varepsilon}^p} \frac{2\sigm…text/html2023-12-01T09:42:12+00:00Anonymous (anonymous@undisclosed.example.com)General Points
http://metafor.ltas.ulg.ac.be/dokuwiki/doc/user/elements/volumes/start?rev=1701423732&do=diff
General Points
Definition of a material law
These laws are usually referenced by materials to define a hardening type of a viscosity function. Examples of some available laws for isotropic hardening can be found in Isotropic hardening.
lawno = lawset.define (numero, type)
lawno = lawset(numero)
lawno.put(param, value)
lawno.depend(param, fct, Key(Lock)))
...text/html2016-03-30T13:23:04+00:00Anonymous (anonymous@undisclosed.example.com)Cohesion degree
http://metafor.ltas.ulg.ac.be/dokuwiki/doc/user/elements/volumes/thixo_burgoscohesionmatlaw?rev=1459344184&do=diff
Cohesion degree
The CohesionMatLaw class manages all cohesion degree evolution laws, specific to thixotropic materials. These laws are described below.
:!: Careful: Only works if used with thixotropic materials (ThixoEvpIsoHHypoMaterial or ThixoTmEvpIsoHHypoMaterial$$
d \lambda / dt = a (1 - \lambda)^{1+e} - b \lambda e^{c \dot{\bar{\epsilon}}^{vp} } (\dot{\bar{\epsilon}}^{vp})^d
$$$ a $$ b $$ c $$ d $$ e $$$
\lambda =\lambda_e + ( \lambda_0 - \lambda_e) e^{F(\lambda) \Delta t}
$$$$
F(\lambd…text/html2025-07-22T09:56:40+00:00Anonymous (anonymous@undisclosed.example.com)Thixotropic materials
http://metafor.ltas.ulg.ac.be/dokuwiki/doc/user/elements/volumes/thixo_iso_hypo_materials?rev=1753178200&do=diff
Thixotropic materials
ThixoEvpIsoHHypoMaterial
Description
Elasto-visco-plastic law with nonlinear hardening, temperature set in a way specific for thixotropic materials.
Stresses are integrated with a radial return method. The stiffness tangent matrix is analytic and numerical$$
f=\overline{\sigma}-\sigma_{yield}=0
$$$ \overline{\sigma}$$ \sigma_{yield} $$\sigma_{yield}$$\sigma_{yield}$text/html2016-03-30T13:23:04+00:00Anonymous (anonymous@undisclosed.example.com)Isotropic hardening
http://metafor.ltas.ulg.ac.be/dokuwiki/doc/user/elements/volumes/thixo_isohard?rev=1459344184&do=diff
Isotropic hardening
The IsotropicHardening class manages all isotropic hardening laws in Metafor. The laws developed for thixotropic materials are are described below.
ShimaOyaneIsotropicHardening
Description
Isotropic hardening, specific for thixotropic materials. Shima and Oyane extended laws, only taking one internal parameter into account, the [doc:user:elements:volumes:thixo_scheilliquidfractionmatlaw|liquid fraction]], either full ($ f_l $$$
\sigma_{vm} = \sigma_{vm}^{sol} (1-f_l)^{h_2…text/html2016-03-30T13:23:04+00:00Anonymous (anonymous@undisclosed.example.com)Liquid fraction
http://metafor.ltas.ulg.ac.be/dokuwiki/doc/user/elements/volumes/thixo_scheilliquidfractionmatlaw?rev=1459344184&do=diff
Liquid fraction
The class LiquidFractionMatLaw manages all liquid fraction evolution laws, specific to thixotropic materials. These laws are described below.
:!: Careful: Only works if used with thixotropic materials (ThixoEvpIsoHHypoMaterial or ThixoTmEvpIsoHHypoMaterial$$
f_l = \left( \frac{T-T_s}{T_l-T_s} \right) ^{\frac{1}{r-1}}
$$$ T_l $$ T_l $$ r $$ f_l^{eff} $$ f_l $$f_l^{eff} $$ \lambda $$$
f_l^{eff} = f_l [1-\lambda(1-f_l)]
$$text/html2016-03-30T13:23:04+00:00Anonymous (anonymous@undisclosed.example.com)Yield Stress
http://metafor.ltas.ulg.ac.be/dokuwiki/doc/user/elements/volumes/thixo_yield_stress?rev=1459344184&do=diff
Yield Stress
The class YieldStress manages the yield stress used in the plastic criterion, whether plastic (isotropic hardening), visco-plastic (Perzyna as additive, Cowper-Symonds as multiplicative or ZerilliArmstrong, JohnsonCook, ... as flow stress models)$$
\sigma_{yield} = \sigma_{yield} (\bar{\varepsilon}^{vp}, \dot{\bar{\varepsilon}}^{vp}, grainSize, ...)
$$$ \lambda $$ f_{l} $$ f_{l}^{eff} $$ m_5 $$ f_{l} $$ m_5=0 $$ f_{l}^{eff} $$ m_5=1 $$$
\sigma_{yield}= \sigma_{isoH} + \sigma_{vis…text/html2024-10-22T12:15:33+00:00Anonymous (anonymous@undisclosed.example.com)User defined materials
http://metafor.ltas.ulg.ac.be/dokuwiki/doc/user/elements/volumes/user_defined_materials?rev=1729599333&do=diff
User defined materials
This section explains how any user can define its own constitutive equation in Metafor (usermat or user-defined feature).
The idea is to create a Python class (e.g., in the input file) that derives from the C++ class `PythonHyperMaterial` and overwrites the following functions:text/html2025-04-23T10:05:55+00:00Anonymous (anonymous@undisclosed.example.com)Volume element
http://metafor.ltas.ulg.ac.be/dokuwiki/doc/user/elements/volumes/volumeelement?rev=1745402755&do=diff
Volume element
Introduction
In this section, Metafor volume element are described. A FieldApplicator interaction is associated to them.
Volume[2|3]DElement
Description
Volume2DElement and Volume3DElement are basic elements in Metafor. Volume2DElement is a quadrangle with 4 nodes in 2D, while $n$$d$$(n+1)^{d}$$n=1$$d=2$$\theta$$(m+1)^d$$m$$J_e$$J_{e,aej}$$J_I$$J_I$text/html2016-03-30T13:23:04+00:00Anonymous (anonymous@undisclosed.example.com)Volume interaction
http://metafor.ltas.ulg.ac.be/dokuwiki/doc/user/elements/volumes/volumeinteraction?rev=1459344184&do=diff
Volume interaction
Generating volume elements on a mesh is done with a specific Interaction called FieldApplicator:
app = FieldApplicator(no)
app.push(gObject1)
app.push(gObject2)
...
app.addProperty(prp) # association of an ElementProperties
app.addRuptureCriterion(rc) # failure criterion (optional)
interactionset.add(app) # the interaction is added in InteractionSettext/html2025-03-11T15:56:10+00:00Anonymous (anonymous@undisclosed.example.com)Yield Stress
http://metafor.ltas.ulg.ac.be/dokuwiki/doc/user/elements/volumes/yield_stress?rev=1741708570&do=diff
Yield Stress
The class YieldStress manages the yield stress used in the plastic criterion, whether plastic (isotropic hardening), visco-plastic (Perzyna as additive, Cowper-Symonds as multiplicative or ZerilliArmstrong, JohnsonCook, ... as flow stress models)$$
\sigma_{yield} = \sigma_{yield} (\bar{\varepsilon}^{vp}, \dot{\bar{\varepsilon}}^{vp}, grainSize, ...)
$$$$
\sigma_{yield} = \sigma_{isoHard}( \bar{\varepsilon}^{vp})
$$$$
\sigma_{yield} = \sigma_{isoHard}( \bar{\varepsilon}^{vp}) …