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commit:futur:cristian [2016/11/23 16:06] – [LemaitreChabocheContinuousDamage] canales | commit:futur:cristian [2017/04/05 15:46] – canales | ||
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- | ====== Commit | + | ====== Commit |
+ | ===== EvpMixtHHypoMaterial ===== | ||
+ | Extension of the mixed hardening framework developed in '' | ||
- | ===== ContinuousDamageEvpIsoHHypoMaterial | + | ===== Kinematic hardening models |
- | * Introduction | + | Extension |
- | * The respective documentation page has been updated: [[doc: | + | |
- | ===== Fracture criteria ===== | + | |
- | * Introduction of the Lode parameter ($\overline{\theta}$) as a new field available at Gauss points, which has been denoted as '' | + | |
- | $$ \overline{\theta} = 1 - \frac{6\theta}{\pi} = 1 - \frac{2}{\pi}\arccos{\left( \frac{r}{\overline{\sigma}} \right)^3} $$ | + | |
- | where $\theta$ is the Lode angle, $r$ is the third invariant of the deviatoric stress tensor and $\overline{\sigma}$ is the equivalent stress. The Lode paramater ($\overline{\theta}$) is a normalized version of the Lode angle ($\theta$), which values are always between -1 and 1. This stress state variable will permit the definition of more advanced fracture criteria and damage models. | + | |
- | * '' | + | |
- | * '' | + | |
- | * '' | + | |
- | * The respective documentation page has been updated: [[doc: | + | |
- | ===== Parasolid ===== | + | * '' |
- | * A new repository ('' | + | * '' |
- | ===== Fracture | + | ===== YoshidaUemori02KinematicHardening |
+ | Nonlinear kinematic hardening adapted from the two-surface developed by [[http:// | ||
- | ==== New field at Gauss points - Lode parameter ==== | + | $$ \dot{X}_{ij}^{yu} = C \left( \dfrac{2}{3}\,a\,D_{ij}^{vp} - \left( \dfrac{\overline{X}_{ij}^{yu}}{\overline{\sigma}} \right)^{\zeta-1}\, \dot{\bar{\varepsilon}}\, X_{ij}^{yu} |
- | Classically, | + | |
- | $$ \overline{\theta} = 1 - \frac{6\theta}{\pi} = 1 - \frac{2}{\pi}\arccos{\left( \frac{r}{\overline{\sigma}} \right)^3} $$ | + | |
- | where $\theta$ is the Lode angle, $r$ is the third invariant of the deviatoric stress tensor and $\overline{\sigma}$ is the equivalent stress. The Lode paramater ($\overline{\theta}$) is a normalized version of the Lode angle ($\theta$), which values are always between -1 and 1. This stress state variable has been added as '' | + | |
- | ==== Rupture criteria ==== | + | where $\overline{X}_{yu}^{ij}$ and $\overline{\sigma}$ are the equivalent backstress and the equivalent stress, respectively, |
- | === IndependantInternalFieldID === | + | |
+ | ===== Cleaning ===== | ||
+ | I have made a tab cleaning service (~60 files). | ||
- | === OneParameterRuptureCriterion | + | ===== Fichiers ajoutés/ |
- | Here, four simple rupture criteria were gathered in one single family. In order to selected one of the criteria the parameter '' | + | |
- | //Cockroft and Latham criterion // | + | < |
- | $$ C = \int_0^{\overline{\varepsilon}^p} \frac{\sigma_1}{\overline{\sigma}} | + | [a]: YoshidaUemori02KinematicHardening.cpp |
- | //Brozzo criterion// | + | [a]: YoshidaUemori02KinematicHardening.h |
- | $$ C = \int_0^{\overline{\varepsilon}^p} \frac{2\sigma_1}{3(\sigma_1-p)} | + | [r]: |
- | //Ayada criterion// | + | </code> |
- | $$ C = \int_0^{\overline{\varepsilon}^p} \frac{p}{\overline{\sigma}} | + | |
- | //Rice and Tracey criterion// | + | |
- | $$ C = \int_0^{\overline{\varepsilon}^p} \exp\left(\frac{3}{2} \frac{p}{\overline{\sigma}}\right) | + | |
- | // | + | |
- | ^ Name ^ Metafor Code ^ Dependency | + | |
- | |Criterion | + | |
- | === BaiRuptureCriterion | + | ===== Cas tests ajoutés/supprimés |
- | Bai and Wierzbicki \cite{bai2010, | + | |
- | $$\overline{\varepsilon}^p_f (\eta, | + | |
- | In addition, a constant cut-off value for stress triaxiality $\eta_{cutoff}$ has been implemented. This means that there is no damage accumulation when $\eta$ is below this value, as proposed by Bao and Wierzbicki \cite{bao2005}. | + | |
- | Then, the element is broken if the variable C reaches a critical value: | + | |
- | $$ | + | |
- | C = \int_0^{\overline{\varepsilon}^p}\dfrac{d\overline{\varepsilon}^{p}}{\overline{\varepsilon}^p_f (\eta, | + | |
- | $$ | + | |
- | // | + | |
- | ^ Name ^ Metafor Code ^ Dependency | + | |
- | |$D_1$ | + | |
- | |$D_2$ | + | |
- | |$D_3$ | + | |
- | |$D_4$ | + | |
- | |$D_5$ | + | |
- | |$D_6$ | + | |
- | |$\eta_{cutoff}$ | + | |
- | + | ||
- | === LouRuptureCriterion === | + | |
- | Lou et al. \cite{lou2014} has been recently developed a model based on the underlying mechanisms leading to fracture in shear dominated processes. This model also includes a variable cut-off value for $\eta$, which depends on the value of the Lode angle. This fracture model is defined as, | + | |
- | $$ | + | |
- | \overline{\varepsilon}^p_f = c_3\left( \frac{2}{\sqrt{L^2+3}} \right)^{-c_1} \left( \left\langle \frac{1}{1+C} | + | |
- | \left[ \eta+\frac{3-L}{3\sqrt{L^2+3}}+C \right] \right\rangle \right)^{-c_2} | + | |
- | $$ | + | |
- | + | ||
- | with, | + | |
- | $$ | + | |
- | L = \frac{3 \tan\left( \theta \right) - \sqrt{3}}{\tan \left( \theta \right) + \sqrt{3}} | + | |
- | $$ | + | |
- | where $c_1$, $c_2$ and $c_3$ are material parameters. $L$ corresponds to an alternative definition of the Lode angle and the $\left\langle \bullet \right\rangle$ symbol denotes the MacAuley brackets. If the constant $C$ is fixed to $1/3$, as proposed by the authors, the Lode dependent cut-off value for damage accumulation is below $-1/3$ for any set of $\eta$ and $L$. | + | |
- | + | ||
- | // | + | |
- | ^ Name ^ Metafor Code ^ Dependency | + | |
- | |$D_1$ | + | |
- | |$D_2$ | + | |
- | |$D_3$ | + | |
- | |$C$ | '' | + | |
- | + | ||
- | ==== Continuous damage mechanics ==== | + | |
- | + | ||
- | === Lemaitre-Chaboche model === | + | |
- | The classical Lemaitre-Chaboche model has been extended in order to include a limit value of stress triaxility ($\eta_{threshold}$) below which there is no damage growth as proposed by \cite{bouchard2011}. | + | |
- | + | ||
- | // | + | |
- | ^ Name ^ Metafor Code ^ Dependency | + | |
- | |$\eta_{threshold}$ ($=-10$ by default) | + | |
- | + | ||
- | === Micro-Crack Closure Effect - MCCE === | + | |
- | In the continuous damage mechanics framework, damage is considered to soften the material by a weakening function $w(D)$. In the 1D case, the effect of this function is represented as: | + | |
- | $$\sigma^* = \frac{\sigma}{w(D)}$$ | + | |
- | with, | + | |
- | $$ | + | |
- | w(D) = \left\{ | + | |
- | | + | |
- | 1-D & | + | |
- | 1-hD & | + | |
- | | + | |
- | | + | |
- | $$ | + | |
- | where $\sigma$ is the flow stress of undamaged material and $h$ is a material parameter ($0 < h < 1$), which accounts for the MCCE. | + | |
- | In order to take into account the micro-crack closure effect (distinction of the weakening effect of damage under compressive and tensile stress states) in our continuous damage framework, I included a new parameter to be defined in the "" | + | |
- | + | ||
- | // | + | |
- | ^ Name ^ Metafor Code ^ Dependency | + | |
- | |$h$ ($=1$ by default) | + | |
- | + | ||
- | ==== References ==== | + | |
- | + | ||
- | ===== Miscellaneous ===== | + | |
- | * I replaced some " | + | |
- | * '' | + | |
- | ===== Divers ===== | + | |
- | * GiD importer | + | |
- | * Lagamine importer | + | |
- | + | ||
- | ===== Yield criteria | + | |
- | * '' | + | |
- | * '' | + | |
- | * '' | + | |
- | * '' | + | |
- | * '' | + | |
- | * '' | + | |
- | * '' | + | |
- | * '' | + | |
- | * '' | + | |
+ | < | ||
+ | [a]: Hill48v2IsoMixHard.py | ||
+ | [a]: Hill48v2MixHard.py | ||
+ | [a]: YoshidaUemori02CinHEp.py | ||
+ | [r]: | ||
+ | </ | ||
+ | --- // |
commit/futur/cristian.txt · Last modified: 2017/04/05 15:54 by canales