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--- laws:cazacutn [2022/03/17 10:49]
carlos
+++ laws:cazacutn [2022/10/14 15:52] (current)
carlos
@@ Line 31: / Line 31: @@
 Where:
   * $\bar{\Sigma}_{CPB06}$ is the CPB06 yield stress:
-\[\bar{\Sigma}_{CPB06}=\tilde{m}\Big[ \overset{3}{\underset{J=1}{\Sigma}} \big(|\Sigma_{J}| - k\Sigma_{J}\big)^a \Big] ^{\frac{1}{a}}\]
+\[\bar{\Sigma}_{CPB06}=\tilde{m}\Big[ \overset{3}{\underset{i=1}{\Sigma}} \big(|\Sigma_{i}| - k\Sigma_{i}\big)^a \Big] ^{\frac{1}{a}}\]
   * $\sigma_{y}$ is the current yield stress of the material:
 \[\sigma_{y} = \sigma_{0} + S_{R}\big[1-exp\big(-C_{R}\bar{\epsilon}^{p}\big)\big]\]
   * STF is the stress transformation function, containing all the damage-related variables:
-\[STF=2fq_{1}cosh\Big[\frac{3q_{2}\big(\sigma_{m} - X_{m}\big)}{h\sigma_{y}}\Big] - q_{3}f^{2} - 1\]
+\[STF= 1 - 2fq_{1}cosh\Big[\frac{3q_{2}\big(\sigma_{m} - X_{m}\big)}{h\sigma_{y}}\Big] - q_{3}f^{2}\]
+The corrected stress ($\hat{\sigma}$) and backstress ($\hat{X}$) are respectively calculated as:
+\[\hat{\sigma} = L_{ijmn}T_{mnkl}\sigma_{kl}\]
+\[\hat{X}= L_{ijmn}T_{mnkl}X_{kl}\]
+The backstress tensor is calculated using the Armstrong-Frederick model:
+\[dX = S_{x}[C_{x}d{\epsilon^p}-Xd\bar{\epsilon}^p]\]
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