• Introduction of the Micro-Crack Closure Effect (MCCE) by means of the DAMAGE_MCCE parameter. This new parameter makes the distinction of the weakening effect of damage under compressive ($\eta<0$) and tensile ($\eta\ge 0$) stress states. In this first attempt, the distinction between stress states depends solely on the stress triaxiality ratio. It is no mandatory to include this parameter when using the ContinuousDamageEvpIsoHHypoMaterial and it takes a default value equal to $1.0$ (no MCCE).
• The respective documentation page has been updated: Doc Traditional Materials.

• Introduction of the Lode parameter ($\overline{\theta}$) as a new field available at Gauss points, which has been denoted as IF_LODE_PARAMETER. This variable is defined 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.

• BaiRuptureCriterion: Fracture criterion that takes into account $\eta$ and $\overline{\theta}$ into its formulation.
• LouRuptureCriterion: Fracture criterion that takes into account $\eta$ and $\overline{\theta}$ into its formulation. Specially developed for shear-dominated fracture.
• OneParameterRuptureCriterion: Family of simple fracture criteria i.e., Cockroft and Latham, Brozzo, Ayada and Rice and Tracey models.
• The respective documentation page has been updated: Doc Failure Criteria.

• A new repository (mtParasolid/tests/numisheet) has been created to include recently developed Numisheet benchmark tests. Two tests have been included by the moment: Square Cup Deep-drawing (Numisheet1993) and Cross-shaped Cup Deep-drawing (Numisheet2011).

Classically, the sensitivity of the damage accumulation to the stress states has been solely introduced by means of the stress triaxiality ratio ($\eta=p/\overline{\sigma}$). Thanks to the experimental observations performed by Bao and Wierzbicki \cite{bao2004a,bao2004b} and Barsoum and Faleskog \cite{barsoum2007} the influence of the Lode angle (related to the third invariant of the stress tensor) on damage was putted in evidence, where non-smooth fracture locus were exhibited for low levels of triaxiality (shear dominated fracture). This clearly contrast with the formulation followed by former damage models. $$ \overline{\theta} = 1 - \frac{6\theta}{\pi} = 1 - \frac{2}{\pi}\arccos{\left( \frac{r}{\overline{\sigma}} \right)^3} $$ 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 IF_LODE_PARAMETER and has been used to implement new rupture criteria.

Here, four simple rupture criteria were gathered in one single family. In order to selected one of the criteria the parameter RUPT_OP_LAW (only parameter in this criterion) need to be defined as: COCKROFT, BROZZO, AYADA or RICE. Then, the element is broken if the variable C reaches a critical value, which is defined in each case as:

Cockroft and Latham criterion $$ C = \int_0^{\overline{\varepsilon}^p} \frac{\sigma_1}{\overline{\sigma}} d\overline{\varepsilon}^p$$ Brozzo criterion $$ C = \int_0^{\overline{\varepsilon}^p} \frac{2\sigma_1}{3(\sigma_1-p)} d\overline{\varepsilon}^p$$ Ayada criterion $$ C = \int_0^{\overline{\varepsilon}^p} \frac{p}{\overline{\sigma}} d\overline{\varepsilon}^p$$ Rice and Tracey criterion $$ C = \int_0^{\overline{\varepsilon}^p} \exp\left(\frac{3}{2} \frac{p}{\overline{\sigma}}\right) d\overline{\varepsilon}^p$$ Parameters

Bai and Wierzbicki \cite{bai2010,bai2008} proposed a fracture model based on the experimental observations of non-smooth fracture locus previously done by Bao and Wierzbicki \cite{bao2004a,bao2004b}. In this model, the influence of stress triaxiality on damage is represented by a series of exponential functions, leading to higher fracture strains for lower triaxialities. Furthermore, the effect of the Lode parameter is included by means of a quadratic function. $$\overline{\varepsilon}^p_f (\eta,\overline{\theta}) = \left[ \frac{1}{2}\left( D_1e^{-D_2\eta}+D_5e^{-D_6\eta} \right)-D_3e^{-D_4\eta} \right]\overline{\theta}^2 + \frac{1}{2}\left( D_1e^{- D_2\eta}-D_5e^{-D_6\eta} \right)\overline{\theta}+D_3e^{-D_4\eta}$$ 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: $$ C = \int_0^{\overline{\varepsilon}^p}\dfrac{d\overline{\varepsilon}^{p}}{\overline{\varepsilon}^p_f (\eta,\overline{\theta})} $$ Parameters

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 $L$.

Parameters

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}.

Parameters

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, $$ w(D) = \left\{ \begin{array}{ll} 1-D &\mbox{if } \eta \geq 0\\ 1-hD &\mbox{if } \eta < 0\\ \end{array} \right. $$ 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 ““ContinuousDamageEvpIsoHHypoMaterial”” description.

Parameters

• I replaced some “tabs” by “4 spaces” that were still in the source files (37 files).
• toolbox.lagamine: I added an interface to import tests (mesh and boundary conditions) from the FE code Lagamine (MSM group @ ArGEnCo).

• GiD importer
• Lagamine importer

• DruckerPlasticCriterion
• HosfordPlasticCriterion
• Barlat0413pOrthoPlasticCriterion
• Barlat0418pOrthoPlasticCriterion
• CazacuBarlat01OrthoPlasticCriterion
• CazacuBarlat04IsotropicPlasticCriterion
• CazacuBarlat04OrthoPlasticCriterion
• CazacuBarlat06IsotropicPlasticCriterion
• CazacuBarlat06OrthoPlasticCriterion