Elasto-plastic constitutive law for solid elements at constant temperature
This law is used for mechanical analysis of elastoplastic isotropic element undergone large deformation. Isotropic hardening is assumed.
Prepro: LJET.F (2D), LJET3.F (3D)
Lagamine: JETVON.F (2D), JT3VM.F (3D)
| Plane stress state | NO |
| Plane strain state | YES |
| Axisymmetric state | YES |
| 3D state | YES |
| Generalized plane state | NO |
| Line 1 (2I5, 60A1) | |
|---|---|
| IL | Law number |
| ITYPE | 55 for 2D; 58 for 3D |
| COMMENT | Any comment (up to 60 characters) that will be reproduced on the output listing |
| Line 1 (2I5) | |
|---|---|
| NINTV | number of sub‑steps used to integrate numerically the constitutive equation in a time step (<0 automatic calculation of NINTV) |
| NPOINT | number of points to define the hardening law |
If NPOINT = 0
| Line 1 (4G10.0) | |
|---|---|
| E | Young's elastic modulus |
| $\nu$ | POISSON's ratio |
| RE | yield limit $(R_e)$ |
| ET | elasto‑plastic tangent modulus $(E_t)$ |
If NPOINT ≠ 0
| Line 1 (2G10.0) | |
|---|---|
| E | Young's elastic modulus |
| $\nu$ | POISSON's ratio |
| Line I = 2:NPOINT (2G10.0) | |
| EPS(I) | Points defining the hardening curve |
| SIG(I) | |
= 4 : for 2D analysis
= 6 : for 3D analysis
The stresses are the components of CAUCHY stress tensor in global (X,Y,Z) coordinates.
For the 2D analysis :
| SIG(1) | $\sigma_{xx}$ |
| SIG(2) | $\sigma_{yy}$ |
| SIG(3) | $\sigma_{xy}$ |
| SIG(4) | $\sigma_{zz}$ |
For 3D analysis :
| SIG(1) | $\sigma_{xx}$ |
| SIG(2) | $\sigma_{yy}$ |
| SIG(3) | $\sigma_{zz}$ |
| SIG(4) | $\sigma_{xy}$ |
| SIG(5) | $\sigma_{xz}$ |
| SIG(6) | $\sigma_{yz}$ |
= 27 : for 2D analysis
= 15 : for 3D analysis
For 2D analysis :
| Q(1) | current yield limit in tension; its initial value is $R_e$ |
| Q(2) | equivalent plastic strain $(\bar{\varepsilon}^p)$ |
| Q(3) | equivalent VM type stress in this element. |
| Q(4) | $\sigma_{xx}$ in local axes of the element |
| Q(5) | $\sigma_{yy}$ in local axes of the element |
| Q(6) | $\sigma_{zz}$ in local axes of the element |
| Q(7) | $\sigma_{xy}$ in local axes of the element |
| Q(8) | $\sigma_{1}$ anti‑hourglass stress |
| Q(9) | $\sigma_{2}$ anti‑hourglass stress |
| Q(10to13) | x nodal coordinates in local axes of the element |
| Q(14to17) | y nodal coordinates in local axes of the element |
| Q(18) | = 0 in plane strain state |
| = average radius (X coordinate) of the element in axisymmetric state | |
| Q(19) | area of the element in the XY plane |
| Q(20) | area of the no deformed element |
| Q(21) | X(4) ‑ X(2) in initial structure |
| Q(22) | X(3) ‑ X(1) in initial structure |
| Q(23) | Y(4) ‑ Y(2) in initial structure |
| Q(24) | Y(3) ‑ Y(1) in initial structure |
For 3D analysis :
| Q(1) | current yield limit tension |
| Q(2) | equivalent plastic strain $(\bar{\varepsilon}^p)$ |
| Q(3) | equivalent VM type stress for this element. |
| Q(4) | $\sigma_{11}$ anti‑hourglass stress |
| Q(5) | $\sigma_{12}$ anti‑hourglass stress |
| Q(6) | $\sigma_{13}$ anti‑hourglass stress |
| Q(7) | $\sigma_{21}$ anti‑hourglass stress |
| Q(8) | $\sigma_{22}$ anti‑hourglass stress |
| Q(9) | $\sigma_{23}$ anti‑hourglass stress |
| Q(10) | $\sigma_{31}$ anti‑hourglass stress |
| Q(11) | $\sigma_{32}$ anti‑hourglass stress |
| Q(12) | $\sigma_{33}$ anti‑hourglass stress |
| Q(13) | $\sigma_{41}$ anti‑hourglass stress |
| Q(14) | $\sigma_{42}$ anti‑hourglass stress |
| Q(15) | $\sigma_{43}$ anti‑hourglass stress |