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--- doc:user:elements:volumes:rupturecritere [2016/10/09 00:29] – [IFRuptureCriterion] canales
+++ doc:user:elements:volumes:rupturecritere [2017/04/05 09:21] – [OneParameterRuptureCriterion] canales
@@ Line 1: / Line 1: @@
-====== Failure criterion ======
+====== Failure criteria ======
 ===== RuptureCriterion =====
@@ Line 39: / Line 39: @@
 //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//
+**Parameters**
 ^          Name      ^  Metafor Code  ^ Dependency         ^
 |Criterion  |  ''RUPT_OP_LAW''  |          -         |
@@ Line 186: / 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 200: / 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.]]