Differences

This shows you the differences between two versions of the page.

--- doc:user:elements:volumes:plasticity_criterion [2013/07/11 14:48] – created joris
+++ doc:user:elements:volumes:plasticity_criterion [2016/03/30 15:23] (current) – external edit 127.0.0.1
@@ Line 1: / Line 1: @@
+====== 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 ===
+ néant
+===== Hill48PlasticCriterion =====
+=== Description ===
+Second order orthotropic plastic criterion
+$$
+\begin{multline}
+\sqrt{\frac{1}{2}} \sqrt{F (s_{22}-s_{33})^2 + G (s_{33}-s_{11})^2  + H (s_{11}-s_{22})^2  + 2 (L s_{13}^2 + M s_{23}^2 + N s_{12}^2) } \\- (\sigma_{vm} + \sigma_{visq} + \sigma_{grainSize} + ...) = 0
+\end{multline}
+$$
+where stresses are defined in an orthotropic frame.
+=== Parameters ===
+^   Name                                             ^     Metafor Code     ^  Dependency ^
+|  $F$                                        |  ''HILL48_F''  |  néant             |
+|  $G$                                        |  ''HILL48_G''  |  néant             |
+|  $H$                                        |  ''HILL48_H''  |  néant             |
+|  $L$                                        |  ''HILL48_L''  |  néant             |
+|  $M$                                        |  ''HILL48_M''  |  néant             |
+|  $N$                                        |  ''HILL48_N''  |  néant             |
+=== Parameter estimation (for sheet metal) ===
+For sheet metal, the anisotropic parameters can be estimated based on tensile tests (plastic strain of around 10%). Strains are measured along the width ( $\varepsilon_{t}$ ) and the thickness ( $\varepsilon_{e}$ ). The plastic anisotropy coefficient is then defined as :
+ $r = \frac{\varepsilon_{t}}{\varepsilon_{e}}$
+This test is done in samples cut along the 0, 45 and 90 degrees axes to define  $r_{0}$  ,  $_{45}$  ,  $r_{90}$ .
+A planar average is then defined as :
+ $r_{moy} = \frac{r_{0} + 2 r_{45} + r_{90}}{4}$
+Based on tensile tests, it is not possible to estimate shear through the thickness, so L and M parameters are considered equal to 3.
+    *  $F = \frac{2}{1+r_0}\frac{r_{0}}{r_{90}}$
+    *  $G = \frac{2}{1+r_0}$
+    *  $H = \frac{2r_{0}}{1+r_0}$
+    *  $L = 3$
+    *  $M = 3$
+    *  $N = \frac{1+2r_{45}}{1+r_0}\frac{r_{0}+r_{90}}{r_{90}}$