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--- doc:user:elements:volumes:rupturecritere [2016/03/30 15:23] – external edit 127.0.0.1
+++ doc:user:elements:volumes:rupturecritere [2017/04/05 09:21] – [OneParameterRuptureCriterion] canales
@@ Line 1: / Line 1: @@
-====== Failure criterion ======
+====== Failure criteria ======
 ===== RuptureCriterion =====
@@ Line 25: / Line 25: @@
 for a criterion based on a critical value of the equivalent plastic strain.
+===== OneParameterRuptureCriterion =====
+=== Description ===
+Four simple rupture criteria are 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**
+^          Name      ^  Metafor Code  ^ Dependency         ^
+|Criterion  |  ''RUPT_OP_LAW''  |          -         |
 ===== BaoRuptureCriterion =====
@@ Line 169: / Line 188: @@
 |$A $  |  ''RUPT_MPSTRAIN_CL''  |          -         |
 |$B $  |  ''RUPT_MPSTRAIN_TL''  |          -         |
+===== BaiRuptureCriterion =====
+=== Description ===
+Bai and Wierzbicki rupture criterion [[doc:user:elements:volumes:rupturecritere#References|[7]]]. The element is broken if the variable C, defined below, reaches a critical value:
+$$
+ C = \int_0^{\overline{\varepsilon}^p}\dfrac{d\overline{\varepsilon}^{p}}{\overline{\varepsilon}^p_f (\eta,\overline{\theta})}
+$$
+where $\overline{\varepsilon}^p_f (\eta,\overline{\theta})$ is defined as:
+$$\overline{\varepsilon}^p_f (\eta,\overline{\theta}) = \left[ \frac{1}{2}\left( D_1e^{-D_2\eta}+D_5e^{-D_6\eta} \right)-D_3e^{-D_4\eta} \right]\overline{\theta}^2 + \frac{1}{2}\left( D_1e^{- D_2\eta}-D_5e^{-D_6\eta} \right)\overline{\theta}+D_3e^{-D_4\eta}$$
+=== Parameters ===
+^          Name      ^  Metafor Code  ^ Dependency         ^
+|$D_1$  |  ''RUPT_BAI_D1''  |          -         |
+|$D_2$  |  ''RUPT_BAI_D2''  |          -         |
+|$D_3$  |  ''RUPT_BAI_D3''  |          -         |
+|$D_4$  |  ''RUPT_BAI_D4''  |          -         |
+|$D_5$  |  ''RUPT_BAI_D5''  |          -         |
+|$D_6$  |  ''RUPT_BAI_D6''  |          -         |
+|$\eta_{cutoff}$  |  ''RUPT_BAI_CUTOFF''  |          -         |
+===== LouRuptureCriterion =====
+=== Description ===
+Lou, Yoon and Huh rupture criterion [[doc:user:elements:volumes:rupturecritere#References|[8]]]. The element is broken if the variable K, defined below, reaches a critical value:
+$$
+ K = \int_0^{\overline{\varepsilon}^p}\dfrac{d\overline{\varepsilon}^{p}}{\overline{\varepsilon}^p_f (\eta,\overline{\theta})}
+$$
+where $\overline{\varepsilon}^p_f$ is defined as:
+$$
+\overline{\varepsilon}^p_f = D_3\left( \frac{2}{\sqrt{L^2+3}} \right)^{-D_1} \left( \left\langle \frac{1}{1+C}
+\left[ \eta+\frac{3-L}{3\sqrt{L^2+3}}+C \right] \right\rangle \right)^{-D_2}
+$$
+with,
+$$
+L = \frac{3 \tan\left( \theta \right) - \sqrt{3}}{\tan \left( \theta \right) + \sqrt{3}}
+$$
+where $D_1$, $D_2$ and $D_3$ 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.
+=== Parameters ===
+^          Name      ^  Metafor Code  ^ Dependency         ^
+|$D_1$  |  ''RUPT_LOU_D1''  |          -         |
+|$D_2$  |  ''RUPT_LOU_D2''  |          -         |
+|$D_3$  |  ''RUPT_LOU_D3''  |          -         |
+|$C$    |  ''RUPT_LOU_C''  |          -         |
 ===== References =====
@@ Line 183: / Line 252: @@
 [6]
+[7] [[http://www.sciencedirect.com/science/article/pii/S0749641907001246|Bai I, Wierzbicki T. A new model of metal plasticity and fracture with pressure and Lode dependence. International Journal of Plasticity 2008;24:1071-1096.]]
+[8] [[http://www.sciencedirect.com/science/article/pii/S0749641913001617|Lou Y, Yoon JW, Huh H. Modeling of shear ductile fracture considering a changeable cut-off value for stress triaxiality. International Journal of Plasticity 2014;54:56-80.]]