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LILYCQ
Description
Ilyushin's type constitutive law for 3d shell (COQJ4) element. Use the resultant stresses directly.
The model
This law is only used for mechanical analysis of elasto-anisotropic plastic with linear anisotropic or non-linear isotropic hardening. The resultants stresses are used directly.
Files
Prepro: LILYCQ.F
Lagamine: CQ4ILY.F
Input file
Parameters defining the type of constitutive law
| Line 1 (2I5, 60A1) | |
|---|---|
| IL | Law number |
| ITYPE | = 34 |
| COMMENT | Any comment (up to 60 characters) that will be reproduced on the output listing |
Integer parameters
| Line 1 (3I5) | |
|---|---|
| IND | Index of the thickness variable |
| = 0 the thickness is variable during deformation | |
| = 1 it is constant during deformation. | |
| NPO | Number of points to define the uniaxial constitutive law ($\geq$ 0) |
| NINTV | Number of sub-interval step for integrating the constitutive law ($\geq$ 0) |
Real parameters
Global Data
| Line 1 (3G10.0) | |
|---|---|
| E | Young Modulus |
| ANU | Poisson's coefficient |
| $D_{NM}$ | the parameter for the couple of normal effort and moment. |
| = 0, it is decoupled | |
| = 1, it is coupled | |
\[
f = \frac{1}{h^2}Q_{NN} + D_{NM} \frac{4}{\sqrt{3}h^3}Q_{NM} + \frac{16}{h^4}Q_{MM} - \sigma_y^2
\]
Where
\[
Q_NN = \alpha_{11}N_x^2 + \alpha_{22}N_y^2 + \alpha_{33}N_{xy}^2 - 2 \alpha_{12}N_xN_y
\]
\[
Q_MM = \alpha_{11}M_x^2 + \alpha_{22}M_y^2 + \alpha_{33}M_{xy}^2 - 2 \alpha_{12}M_xM_y
\]
\[
Q_NM = \alpha_{11}N_xM_x + \alpha_{22}N_yM_y + \alpha_{33}N_{xy}M_{xy} - \alpha_{12}N_xM_y + N_yM_x
\]
Uniaxial Constitutive Law
For NPO = 0
| Line 1 (2G10.0) | |
|---|---|
| SY11 | Initial yield stress of tension or compression in 1 – direction. |
| ET11 | The tangent modulus in this direction |
| Line 2 (2G10.0) | |
| SY22 | Initial yield stress in tension or compression in 2 – direction |
| ET22 | The tangent modulus in this direction |
| Line 3 (2G10.0) | |
| SY33 | Initial yield stress in tension or compression in 3 – direction |
| ET33 | The tangent modulus in this direction |
| Line 4 (2G10.0) | |
| SY12 | Initial yield shear stress in 1 - 2 plan |
| ET12 | The tangent modulus in this plan |
REMARK:
It is possible to use the linear anisotropic or nonlinear isotropic hardening law for the model. For linear anisotropic hardening, it is only valuable for the case: NPO = 0
For NPO > 0
| Line 1 (4G10.0) | |
|---|---|
| SY11 | |
| SY22 | |
| SY33 | |
| SY12 | |
| Line 2 - repeated N times (2G10.0) | |
| $\sigma_i$ | the value of stree for the referent directional considered point |
| $\varepsilon_i$ | the value of strain for this direction at the considered point |
Results
Stresses
| SIG(1) | $N_x$, normal effort in the local X‑direction |
| SIG(2) | $N_y$, normal effort in the local Y‑direction |
| SIG(3) | $N_{xy}$, normal effort in the local X-Y plan |
| SIG(4) | $M_x$, moment associated to the local X‑direction |
| SIG(5) | $M_y$, moment associated to the local Y‑direction |
| SIG(6) | $M_{xy}$, moment associated to the local X-Y plan |
State variables
| Q(1) | thick, the actual thickness for this IP. |
| Q(2) | $\sigma_n^e$, the equivalent VM type stress of the membrane part for this IP. |
| Q(3) | $\sigma_m^e$, the equivalent VM type stress of the flexion part for this IP. |
| Q(4) | $\varepsilon_{ep}^p$, equivalent plastic strain at this IP. |
| Q(5) | $\sigma_y$, the current yield stress for this IP. |
| Q(6) | $\alpha_{11}$, the anisotropic parameter for this IP. |
| Q(7) | $\alpha_{12}$, idem. |
| Q(8) | $\alpha_{22}$, idem. |
| Q(9) | $\alpha_{33}$, idem. |
