laws:cazacutn
Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision | ||
|
laws:cazacutn [2022/03/15 14:37] carlos |
laws:cazacutn [2022/10/14 15:52] (current) carlos |
||
|---|---|---|---|
| Line 4: | Line 4: | ||
| ==== The model ==== | ==== The model ==== | ||
| - | The mathematical model was developed by [[https://www.sciencedirect.com/science/article/pii/S002076831000363X|(J. Stewart & O. Cazacu, 2011)]], where the [[https://www.sciencedirect.com/science/article/pii/S0749641905001257|CPB06 yield criterion]] is coupled with a phenomenological damage definition following a Gurson-type approach. The damage is modeled in the form of porosity ratio, and its evolution is ruled by phenomenological models of growth, nucleation and coalescence of voids. This constitutive law also integrates an automatic definition of coalescence onset, throughout the implementation of a [[https://www.sciencedirect.com/science/article/pii/S0013794400000552|Thomason-Zhang]] coalescence extension. | + | The mathematical model was developed by [[https://www.sciencedirect.com/science/article/pii/S002076831000363X|(J. Stewart & O. Cazacu, 2011)]],following a Gurson-type approach where the material yield stress is determined by the [[https://www.sciencedirect.com/science/article/pii/S0749641905001257|CPB06 yield criterion]]. The damage is modeled in the form of porosity ratio, and its evolution is ruled by phenomenological models of growth, nucleation and coalescence of voids. This constitutive law also integrates an automatic definition of coalescence onset, throughout the implementation of the [[https://www.sciencedirect.com/science/article/pii/S0013794400000552|Thomason-Zhang]] coalescence extension. |
| The inverse of the orthotropic elastic matrix is defined: | The inverse of the orthotropic elastic matrix is defined: | ||
| Line 24: | Line 24: | ||
| \sigma_{23}\\ | \sigma_{23}\\ | ||
| \end{pmatrix}\] | \end{pmatrix}\] | ||
| + | |||
| + | The yield locus of this damage law is defined as:\\ | ||
| + | |||
| + | \[\Phi= \bar{\Sigma}_{CPB06} - \sigma_{y}\cdot{STF} = 0 \] | ||
| + | |||
| + | Where: | ||
| + | * $\bar{\Sigma}_{CPB06}$ is the CPB06 yield stress: | ||
| + | \[\bar{\Sigma}_{CPB06}=\tilde{m}\Big[ \overset{3}{\underset{i=1}{\Sigma}} \big(|\Sigma_{i}| - k\Sigma_{i}\big)^a \Big] ^{\frac{1}{a}}\] | ||
| + | * $\sigma_{y}$ 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: | ||
| + | \[STF= 1 - 2fq_{1}cosh\Big[\frac{3q_{2}\big(\sigma_{m} - X_{m}\big)}{h\sigma_{y}}\Big] - q_{3}f^{2}\] | ||
| + | |||
| + | |||
| + | 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: | ||
| + | |||
| + | \[dX = S_{x}[C_{x}d{\epsilon^p}-Xd\bar{\epsilon}^p]\] | ||
| ==== Files ==== | ==== Files ==== | ||
| Prepro: LCAZACUTN.F \\ | Prepro: LCAZACUTN.F \\ | ||
| Lagamine: CAZACUTN.F \\ | Lagamine: CAZACUTN.F \\ | ||
| - | Thomason-Zhang coalescence onset criterion: THZCOAL.F | + | Coalescence onset criterion: COALCITERIA.F |
| ==== Subroutines ==== | ==== Subroutines ==== | ||
| - | ^ Files ^ Contained subroutines ^ Description ^ | + | ^ Files ^ Contained subroutines ^ Description ^ |
| - | | LCAZACUTN.F | LCAZACUTN |Main Prepro LCAZACUTN subroutine | | + | | LCAZACUTN.F | LCAZACUTN |Main Prepro LCAZACUTN subroutine | |
| - | | CAZACUTN.F | CAZACUTN |Main Lagamine CAZACUTN subroutine | | + | | CAZACUTN.F | CAZACUTN |Main Lagamine CAZACUTN subroutine | |
| - | | ::: | CAZACUTNFUN |Calculation of CAZACUTN yield locus | | + | | ::: | CAZACUTNFUN |Calculation of CAZACUTN yield locus | |
| - | | THZCOAL.F | THOMASON_ZHANG |Calculation of coalescence criterion| | + | | COALCRITERIA.F | THOMASON_ZHANG |Calculation of [[https://www.sciencedirect.com/science/article/pii/S0013794400000552|ThZ coalescence criterion]]| |
| + | | ::: | LSP_2006 |Calculation of [[https://www.sciencedirect.com/science/article/pii/S0013794405003048|LSP06 coalescence criterion]]| | ||
| ===== Availability ===== | ===== Availability ===== | ||
| Line 48: | Line 72: | ||
| ^ Line 1 (2I5, 60A1)^^ | ^ Line 1 (2I5, 60A1)^^ | ||
| |IL |Law number| | |IL |Law number| | ||
| - | |ITYPE|336 | | + | |ITYPE|337 | |
| |COMMENT| Any comment (up to 60 characters) that will be reproduced on the output listing| | |COMMENT| Any comment (up to 60 characters) that will be reproduced on the output listing| | ||
| ==== Integer parameters ==== | ==== Integer parameters ==== | ||
| - | ^ Line 1 (1I5) ^^ | + | ^ Line 1 (3I5) ^^ |
| - | |MAXIT|Maximal number of iterations during stress integration| | + | |MAXIT |Maximal number of iterations during stress integration | |
| + | |IDAMAGE|Active damage mechanism(s) identifier, //param(35, ilaw)// | | ||
| + | |IDELEM |DELEM section identifier, | | ||
| ==== Real parameters ==== | ==== Real parameters ==== | ||
| ^ Line 1 (6G10.0) ^^ | ^ Line 1 (6G10.0) ^^ | ||
| Line 58: | Line 84: | ||
| |$E_{2}$|:::| | |$E_{2}$|:::| | ||
| |$E_{3}$|:::| | |$E_{3}$|:::| | ||
| - | |$\mbox{ANU}_{12}$|Orthotropic POISSON's ratios| | + | |$\nu_{12}$|Orthotropic POISSON's ratios| |
| - | |$\mbox{ANU}_{13}$|:::| | + | |$\nu_{13}$|:::| |
| - | |$\mbox{ANU}_{23}$|:::| | + | |$\nu_{23}$|:::| |
| - | ^Line 2 (1G10.0)^^ | + | ^Line 2 (1G10.0) ^^ |
| - | |A|degree of homogeneity, //param(16, ilaw) //| | + | |$a$ |degree of homogeneity, //param(16, ilaw) // | |
| - | ^Line 3 (1G10.0)^^ | + | ^Line 3 (1G10.0) ^^ |
| - | |k| Asymmetry parameter, //param(17, ilaw) //| | + | |k | Asymmetry parameter, //param(17, ilaw) // | |
| - | ^Line 4 (3G10.0) Components of orthotropic constants tensor^^ | + | ^Line 4 (3G10.0) Components of orthotropic constants tensor ^^ |
| - | |$C_{11}$| // param(18,ilaw) //| | + | |$C_{11}$| // param(18,ilaw) // | |
| - | |$C_{12}$| // param(19,ilaw) //| | + | |$C_{12}$| // param(19,ilaw) // | |
| - | |$C_{13}$| // param(20,ilaw) //| | + | |$C_{13}$| // param(20,ilaw) // | |
| - | ^Line 5 (3G10.0) Components of orthotropic constants tensor^^ | + | ^Line 5 (3G10.0) Components of orthotropic constants tensor ^^ |
| - | |$C_{22}$| // param(21,ilaw) //| | + | |$C_{22}$| // param(21,ilaw) // | |
| - | |$C_{23}$| // param(22,ilaw) //| | + | |$C_{23}$| // param(22,ilaw) // | |
| - | |$C_{33}$| // param(23,ilaw) //| | + | |$C_{33}$| // param(23,ilaw) // | |
| - | ^Line 6 (3G10.0) Components of orthotropic constants tensor^^ | + | ^Line 6 (3G10.0) Components of orthotropic constants tensor ^^ |
| - | |$C_{44}$| // param(24,ilaw) //| | + | |$C_{44}$| // param(24,ilaw) // | |
| - | |$C_{55}$| // param(25,ilaw) //| | + | |$C_{55}$| // param(25,ilaw) // | |
| - | |$C_{66}$| // param(26,ilaw) //| | + | |$C_{66}$| // param(26,ilaw) // | |
| - | ^Line 7 (4G10.0, 1I5) Damage control parameters^^ | + | ^Line 7 (3G10.0) Isotropic hardening law parameters ^^ |
| - | |$f_{0}$| Initial porosity ratio, // VARIN(21,ilaw) //| | + | |$\sigma_{0}$ | Initial Yield stress [MPa], //param(27, ilaw)// | |
| - | |$q_{1}$| Tvergaard&Needleman parameter, // param(27,ilaw) //| | + | |$S_{R}$ | Saturation rate [MPa], //param(28, ilaw)// | |
| - | |$q_{2}$| Tvergaard&Needleman parameter, // param(28,ilaw) //| | + | |$C_{R}$ | Saturation value [-], //param(29, ilaw)// | |
| - | |$q_{3}$| Tvergaard&Needleman parameter, // param(29,ilaw) //| | + | ^Line 8 (2G10.0) Kinematic hardening parameters ^^ |
| - | |IDAMAGE| Active damage mechanism ID, // param(39,ilaw) //| | + | |$S_{X}$ | Saturation rate [-], //param(30, ilaw)// | |
| + | |$C_{X}$ | Saturation value [MPa], //param(31, ilaw)// | | ||
| + | ^Line 9 (4G10.0) Standard initial damage control parameters ^^ | ||
| + | |$f_{0}$| Initial porosity ratio, // VARIN(5,ilaw) // | | ||
| + | |$q_{1}$| Tvergaard&Needleman parameter, // param(32,ilaw) // | | ||
| + | |$q_{2}$| Tvergaard&Needleman parameter, // param(33,ilaw) // | | ||
| + | |$q_{3}$| Tvergaard&Needleman parameter, // param(34,ilaw) // | | ||
| |**SELECT CASE (IDAMAGE)** |||| | |**SELECT CASE (IDAMAGE)** |||| | ||
| ^ |**CASE (0)**: //No damage increment is calculated// ||| | ^ |**CASE (0)**: //No damage increment is calculated// ||| | ||
| - | | |^Line 8 (3G10.0) Isotropic hardening law parameters ^^ | ||
| - | | ||$\sigma_{0}$ | Initial Yield stress [MPa], //param(30, ilaw)// | | ||
| - | | ||$S_{R}$ | Saturation rate [MPa], //param(31, ilaw)// | | ||
| - | | ||$C_{R}$ | Saturation value [-], //param(32, ilaw)// | | ||
| - | | |^Line 9 (2G10.0) Kinematic hardening parameters ^^ | ||
| - | | ||$S_{X}$ | Saturation rate [-], //param(33, ilaw)// | | ||
| - | | ||$C_{X}$ | Saturation value [MPa], //param(34, ilaw)// | | ||
| | |||| | | |||| | ||
| ^ |**CASE (1)**: //Growth is the only active damage mechanism// ||| | ^ |**CASE (1)**: //Growth is the only active damage mechanism// ||| | ||
| - | | |^Line 8 (3G10.0) Isotropic hardening law parameters ^^ | ||
| - | | ||$\sigma_{0}$ | Initial Yield stress [MPa], //param(30, ilaw)// | | ||
| - | | ||$S_{R}$ | Saturation rate [MPa], //param(31, ilaw)// | | ||
| - | | ||$C_{R}$ | Saturation value [-], //param(32, ilaw)// | | ||
| - | | |^Line 9 (2G10.0) Kinematic hardening parameters ^^ | ||
| - | | ||$S_{X}$ | Saturation rate [-], //param(33, ilaw)// | | ||
| - | | ||$C_{X}$ | Saturation value [MPa], //param(34, ilaw)// | | ||
| | |||| | | |||| | ||
| - | ^ |**CASE (2)**: //Growth and nucleation of voids are considered// ||| | + | ^ |**CASE (2)**: //Growth and nucleation of voids are active// ||| |
| - | | |^Line 8 (3G10.0) Nucleation model parameters ^^ | + | | |^Line 10 (3G10.0) Nucleation model parameters ^^ |
| - | | ||$F_{N}$ | Total nucleated porosity ratio, //param(40, ilaw)// | | + | |::: ||$F_{N}$ | Total nucleated porosity ratio, //param(36, ilaw)// | |
| - | | ||$S_{N}$ | Standard deviation, //param(40, ilaw)// | | + | |::: ||$S_{N}$ | Standard deviation, //param(37, ilaw)// | |
| - | | ||$\epsilon_{N}$ | Standard mean, //param(40, ilaw)// | | + | |::: ||$\epsilon_{N}$ | Standard mean, //param(38, ilaw)// | |
| - | | |^Line 9 (3G10.0) Isotropic hardening law parameters ^^ | + | |
| - | | ||$\sigma_{0}$ | Initial Yield stress [MPa], //param(30, ilaw)// | | + | |
| - | | ||$S_{R}$ | Saturation rate [MPa], //param(31, ilaw)// | | + | |
| - | | ||$C_{R}$ | Saturation value [-], //param(32, ilaw)// | | + | |
| - | | |^Line 10 (2G10.0) Kinematic hardening parameters ^^ | + | |
| - | | ||$S_{X}$ | Saturation rate [-], //param(33, ilaw)// | | + | |
| - | | ||$C_{X}$ | Saturation value [MPa], //param(34, ilaw)// | | + | |
| | |||| | | |||| | ||
| ^ |**CASE (3)**: //Growth, nucleation and coalescence are active// ||| | ^ |**CASE (3)**: //Growth, nucleation and coalescence are active// ||| | ||
| - | | |^Line 8 (3G10.0) Nucleation model parameters ^^ | + | | |^Line 10 (3G10.0) Nucleation model parameters ^^ |
| - | | ||$F_{N}$ | Total nucleated porosity ratio, //param(40, ilaw)// | | + | |::: ||$F_{N}$ | Total nucleated porosity ratio, //param(36, ilaw)// | |
| - | | ||$S_{N}$ | Standard deviation, //param(41, ilaw)// | | + | |::: ||$S_{N}$ | Standard deviation, //param(37, ilaw)// | |
| - | | ||$\epsilon_{N}$ | Standard mean, //param(42, ilaw)// | | + | |::: ||$\epsilon_{N}$ | Standard mean, //param(38, ilaw)// | |
| - | | |^Line 9 (3G10.0) Coalescence model parameters ^^ | + | |::: |^Line 11 (3G10.0) Coalescence model parameters ^^ |
| - | | ||$f_{U}$ | Ultimate porosity ratio, //param(43, ilaw)// | | + | |::: ||$f_{U}$ | Ultimate porosity ratio, //param(39, ilaw)// | |
| - | | ||$f_{F}$ | Fracture porosity ratio, //param(44, ilaw)// | | + | |::: ||$f_{F}$ | Fracture porosity ratio, //param(40, ilaw)// | |
| - | | ||$f_{cr}$ | Critical porosity ratio for onset of coalescence, //param(45, ilaw)// | | + | |::: ||$f_{cr}$ | Critical porosity ratio for coalescence onset, //VARIN(19,ilaw) [If 0, Thomason criterion is applied]// | |
| - | | |^Line 10 (3G10.0) Isotropic hardening law parameters ^^ | + | |
| - | | ||$\sigma_{0}$ | Initial Yield stress [MPa], //param(30, ilaw)// | | + | |
| - | | ||$S_{R}$ | Saturation rate [MPa], //param(31, ilaw)// | | + | |
| - | | ||$C_{R}$ | Saturation value [-], //param(32, ilaw)// | | + | |
| - | | |^Line 11 (2G10.0) Kinematic hardening parameters ^^ | + | |
| - | | ||$C_{X}$ | Saturation rate [-], //param(33, ilaw)// | | + | |
| - | | ||$S_{X}$ | Saturation value [MPa], //param(34, ilaw)// | | + | |
| - | | |||| | + | |
| + | ... If the previous was the $n^{th}$ line... | ||
| + | ^ |IF **IDELEM = 1** THEN ||| | ||
| + | | |^Line $(n+1)^{th}$ (2G10.0) DELEM control parameters ^^ | ||
| + | | ||FDELEM | Porosity ratio at which element starts being deleted, //param(42, ilaw)// | | ||
| + | |::: ||TDELEM | Time for deleting the element (linear interpolation), //param(43, ilaw)// | | ||
laws/cazacutn.1647351458.txt.gz · Last modified: 2022/03/15 14:37 by carlos
Page Tools
