laws:chab
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laws:chab [2022/09/15 15:33] helene [List of state variables] |
laws:chab [2022/09/28 16:23] (current) helene |
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| |$k_4$|Safety coefficient applied to stress level on creep damage| | |$k_4$|Safety coefficient applied to stress level on creep damage| | ||
| ^If IARRH=1 - Line 3+i (i=1:nAF) (2G10)*i^^ | ^If IARRH=1 - Line 3+i (i=1:nAF) (2G10)*i^^ | ||
| - | |$A_i$| coefficient for expression of bi using Arrhenius equation| | + | |$A_i$| coefficient for expression of $b_i$ using Arrhenius equation: $b_i=A_i \exp(-B_i/T)$| |
| - | |$B_i$| coefficient for expression of bi using Arrhenius equation| | + | |$B_i$| coefficient for expression of $b_i$ using Arrhenius equation: $b_i=A_i \exp(-B_i/T)$| |
| === Temperature-dependent parameters - Case where iarrh=0 or iarrh=1 === | === Temperature-dependent parameters - Case where iarrh=0 or iarrh=1 === | ||
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| ===== State variables ===== | ===== State variables ===== | ||
| ==== Number of state variables ==== | ==== Number of state variables ==== | ||
| - | 24+6*nAF+6*nAFY+H(UIDAM)*(2+2*ddim+6)+2*H(DIDAM)+8*ILCF \\ | + | $24+6n_{AF}+6n_{AF_Y}+(8+2ddim)\mathscr{H}(u_{i_{dam}})+2\mathscr{H}(d_{i_{dam}})+8i_{LCF}$ |
| - | Where: UIDAM=IDAM mod 10 and DIDAM=IDAM-UIDAM \\ | + | \\ |
| - | H() is the Heaviside step function. | + | Where: $u_{i_{dam}}\equiv i_{dam} \mod 10$ \\ and $d_{i_{dam}}=i_{dam}-u_{i_{dam}}$. \\ |
| + | $\mathscr{H}(x)$ is the Heaviside step function: $\mathscr{H}(x)=1$ if and only if $x>0$, otherwise, $\mathscr{H}(x)=0$. | ||
| ==== List of state variables ==== | ==== List of state variables ==== | ||
| |Q(1)|plastic strain norm $p$| | |Q(1)|plastic strain norm $p$| | ||
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| |Q(18+6nAF+6i:23+6nAF+6i)|Modification tensor $\underline{Y}_i$ (6 components) for i=1:nAFY| | |Q(18+6nAF+6i:23+6nAF+6i)|Modification tensor $\underline{Y}_i$ (6 components) for i=1:nAFY| | ||
| |Q(24+6nAF+6nAFY)|Maximum temperature in the loading history| | |Q(24+6nAF+6nAFY)|Maximum temperature in the loading history| | ||
| - | ===Only if 10>IDAM>0=== | + | ===Only if $u_{i_{dam}}>0$=== |
| - | In the following table, ddim=1 for isotropic damage (scalar damage variable D) and ddim=6 for anisotropic damage (not implemented). | + | In the following table, ddim=1 for isotropic damage (scalar damage variable $D$) and ddim=6 for anisotropic damage (not implemented). |
| |Q(25+6NAF+6NAFY)| Stored energy $w_s$| | |Q(25+6NAF+6NAFY)| Stored energy $w_s$| | ||
| |Q(26+6NAF+6NAFY)| Visco-plastic multiplicator with damage $r$| | |Q(26+6NAF+6NAFY)| Visco-plastic multiplicator with damage $r$| | ||
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| | Q(27+ddim+6NAF+6NAFY) \\ Q(26+2ddim+6nAF+6nAFY)|Creep damage variable $D_c$ (isotropic) or tensor $\underline{D}_c$ (anisotropic - not implemented)| | | Q(27+ddim+6NAF+6NAFY) \\ Q(26+2ddim+6nAF+6nAFY)|Creep damage variable $D_c$ (isotropic) or tensor $\underline{D}_c$ (anisotropic - not implemented)| | ||
| | Q(27+2ddim+6NAF+6NAFY) \\ … \\ Q(32+2ddim+6nAF+6nAFY)|Delayed stress tensor $\sigma^d$| | | Q(27+2ddim+6NAF+6NAFY) \\ … \\ Q(32+2ddim+6nAF+6nAFY)|Delayed stress tensor $\sigma^d$| | ||
| - | ===Only if IDAM≥10=== | + | ===Only if $i_{dam}$≥10=== |
| - | NQDU=25+6nAF+6nAFY+(8+2ddim)<UIDAM> | + | $N_{Q,D_u}=25+6n_{AF}+6n_{AF_Y}+(8+2ddim)*\mathscr{H}(u_{i_{dam}})$ |
| + | \\ with $\mathscr{H}(u_{i_{dam}})=1$ if and only if $u_{i_{dam}}>0$ | ||
| | Q(NQDU)| $D_u$ - Uniform corrosion damage| | | Q(NQDU)| $D_u$ - Uniform corrosion damage| | ||
| | Q(NQDU+1)| $L_E=\sqrt[3]{V_E}$ - Characteristic length of the element where $V_E$ is the volume of the element (:!: only works with BWD3T elements)| | | Q(NQDU+1)| $L_E=\sqrt[3]{V_E}$ - Characteristic length of the element where $V_E$ is the volume of the element (:!: only works with BWD3T elements)| | ||
| - | === Only if ILCF>0 === | + | === Only if $i_{LCF}>0$ === |
| - | NQLCF=25+6nAF+6nAFY+(8+2ddim)<UIDAM>+2DIDAM (where DIDAM=1 if IDAM≥10 and 0 otherwise) | + | $N_{Q,LCF}=25+6n_{AF}+6n_{AF_Y}+(8+2ddim)*\mathscr{H}(u_{i_{dam}})+2d_{i_{dam}}$ \\ where $d_{i_{dam}}=1$ if $i_{dam}$≥10 and 0 otherwise) |
| | Q(NQLCF)| t (time)| | | Q(NQLCF)| t (time)| | ||
| |Q(1+NQLCF) |N (cycle)| | |Q(1+NQLCF) |N (cycle)| | ||
laws/chab.1663248833.txt.gz · Last modified: 2022/09/15 15:33 by helene
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