laws:sgcp
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laws:sgcp [2019/04/04 11:08] sibo [List of state variables] |
laws:sgcp [2021/06/30 11:03] (current) sibo [Description] |
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| ====== SGCP ====== | ====== SGCP ====== | ||
| ===== Description ===== | ===== Description ===== | ||
| - | STRAIN GRADIENT CRYSTAL PLASTICITY CONSTITUTIVE \\ | + | STRAIN GRADIENT CRYSTAL PLASTICITY CONSTITUTIVE LAW \\ |
| - | Implemented by S. Yuan 2017 | + | Implemented by S. Yuan, L. Duchêne, 2017 |
| ==== The model ==== | ==== The model ==== | ||
| Mechanical analysis of strain gradient crystal plasticity problem \\ | Mechanical analysis of strain gradient crystal plasticity problem \\ | ||
| - | Keller, C., Habraken, A.M., Duchene, L., 2012a. Finite element investigation of size effects on the mechanical behavior of nickel single crystals. Mater. Sci. Eng. A 550, 342–349. https://doi.org/10.1016/j.msea.2012.04.085 \\ | + | Evers, L.P., Brekelmans, W.A.M., Geers, M.G.D., 2004, J. Mech. Phys. Solids. 52, 2379-2401. doi: 10.1016/j.jmps.2004.03.007 \\ |
| - | Keller, C., Hug, E., Habraken, A.M., Duchene, L., 2012b. Finite element analysis of the free surface effects on the mechanical behavior of thin nickel polycrystals. Int. J. Plast. 29, 155–172. https://doi.org/10.1016/j.ijplas.2011.08.007 \\ | + | Evers, L.P., Brekelmans, W.A.M., Geers, M.G.D., 2004, Int. J. Solids Struct. 41, 5209-5230. doi: 10.1016/j.ijsolstr.2004.04.021 \\ |
| - | Bayley, C.J., Brekelmans, W.A.M., Geers, M.G.D., 2006. A comparison of dislocation induced back stress formulations in strain gradient crystal plasticity. Int. J. Solids Struct. 43, 7268–7286. https://doi.org/10.1016/j.ijsolstr.2006.05.011 | + | Bayley, C.J., Brekelmans, W.A.M., Geers, M.G.D., 2006, Int. J. Solids Struct. 43, 7268–7286. doi: 10.1016/j.ijsolstr.2006.05.011 \\ |
| ==== Files ==== | ==== Files ==== | ||
| Prepro: T151_V3.F \\ | Prepro: T151_V3.F \\ | ||
| Line 25: | Line 25: | ||
| |ITYPE| 973| | |ITYPE| 973| | ||
| |COMMENT| Any comment (up to 60 characters) | | |COMMENT| Any comment (up to 60 characters) | | ||
| + | ^ Line 2 (2I5, 8G10.0)^^ | ||
| + | |INRM|iterative method (0, 1, 2)| | ||
| + | |MAXIT| | | ||
| + | |PREC| | | ||
| + | |damp1| | | ||
| + | |damp2| | | ||
| + | if (INRM .eq. 0) AMOR=damp1=1; | ||
| + | if (INRM .eq. 1) $h_k$=damp1 & $\nu(NS)$=damp2; | ||
| + | if (INRM .eq. 2) damping is computed automatically | ||
| + | |||
| ==== Real parameters ==== | ==== Real parameters ==== | ||
| ^ Line 1 (3G10.0) ^^ | ^ Line 1 (3G10.0) ^^ | ||
| Line 90: | Line 100: | ||
| ===== State variables ===== | ===== State variables ===== | ||
| ==== Number of state variables ==== | ==== Number of state variables ==== | ||
| - | 1813 | + | 1839 × 8 (integration points) |
| ==== List of state variables ==== | ==== List of state variables ==== | ||
| |Q(1:9)|${(F^{B}_{P})}^{-1}$| | |Q(1:9)|${(F^{B}_{P})}^{-1}$| | ||
| Line 98: | Line 108: | ||
| |Q(46:54)|$1^{th}$ Piola-Kirchhoff stress $P_{11} P_{22} P_{33} P_{12} P_{13} P_{23} P_{21} P_{31} P_{32}$| | |Q(46:54)|$1^{th}$ Piola-Kirchhoff stress $P_{11} P_{22} P_{33} P_{12} P_{13} P_{23} P_{21} P_{31} P_{32}$| | ||
| |Q(55:72)|reserved for $\rho^{\xi}_{GND}$| | |Q(55:72)|reserved for $\rho^{\xi}_{GND}$| | ||
| - | |Q(73:126)|reserved for $\r^{\xi}_{i}$| | + | |Q(73:126)|reserved for $r^{\xi}_{i}$| |
| - | |Q(127:135)|reserved for $\F_{ij}$| | + | |Q(127:135)|reserved for $F_{ij}$| |
| |Q(136:297)|$(\frac{d\sigma_{ij}}{d\rho^{\xi}_{GND}})_{ij\xi}$| | |Q(136:297)|$(\frac{d\sigma_{ij}}{d\rho^{\xi}_{GND}})_{ij\xi}$| | ||
| - | |Q(298:783)|$(\frac{d\sigma_{ij}}{d\rho^{\xi}_{GND}})_{ij\xi}$| | + | |Q(298:783)|$(\frac{d\sigma_{ij}}{dr^{\xi}_{k}})_{ijk\xi}$| |
| + | |Q(784:981)|$(\frac{d\gamma^{\alpha}}{dF_{kl}})_{\alpha kl}$| | ||
| + | |Q(982:1107)|$(\frac{d\gamma^{\alpha}}{d\rho_{GND}^{\xi}})_{\alpha \xi}$| | ||
| + | |Q(1108:1755)|$(\frac{d\gamma^{\alpha}}{dr_{k}^{\xi}})_{\alpha k \xi}$| | ||
| + | |Q(1756:1764)|$2^{nd}$ Piola-Kirchhoff stress $S_{11} S_{22} S_{33} S_{12} S_{13} S_{23} S_{21} S_{31} S_{32}$| | ||
| + | |Q(1765:1770)|$\epsilon^{u}$ nature strain $e_{11} e_{12} e_{13} e_{22} e_{23} e_{33} $| | ||
| + | |Q(1771:1773)|$\gamma^{norm} \rho_{SSD}^{norm} \rho_{GND}^{norm}$| | ||
| + | |Q(1774:1776)|Blank| | ||
| + | |Q(1777)|Blank but resreved for $\epsilon_{eq}^{p}$| | ||
| + | |Q(1778:1813)|reserved for ${(F^{B}_{e})}$ ${(F^{B}_{e})}^{-1}$ ${(F^{B})}^{-1}$ ${(F^{B}_{P})}$| | ||
| + | |Q(1814:1825)|Schmid stress ($\alpha=1..12$)| | ||
| + | |Q(1826)|Schmid stress (square root norm)| | ||
| + | |Q(1827:1838)|back-stress ($\alpha=1..12$)| | ||
| + | |Q(1839)|back-stress (square root norm)| | ||
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laws/sgcp.1554368938.txt.gz · Last modified: 2020/08/25 15:35 (external edit)
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