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laws:levjet
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LEV-JET
Description
An elasto‑viscoplastic constitutive law for solid elements at constant temperature ‑ Levi model.
The model
This law is used for mechanical analysis of elastoplastic isotropic element undergone large deformation.
Files
Prepro: LJETV.F
Lagamine: JETLEV.F, JT3LEV.F
Availability
| Plane stress state | NO |
| Plane strain state | YES |
| Axisymmetric state | YES |
| 3D state | YES |
| Generalized plane state | NO |
Input file
Parameters defining the type of constitutive law
| Line 1 (2I5, 60A1) | |
|---|---|
| IL | Law number |
| ITYPE | 57 for JET2D; 59 for JET3D |
| COMMENT | Any comment (up to 60 characters) that will be reproduced on the output listing |
Integer parameters
| Line 1 (2I5) | |
|---|---|
| MLAW | = the method used to calculate the increments of stress |
| = 0 → Radial Return method | |
| = 1 → Implicit integration method | |
| = 2 → Modified implicit integration method | |
| MANA | See explanation below |
If MLAW = 0
| MANA | = 0 → The tangent matrix obtained by setting $\dot{\omega} = 0$ |
| = 1 → The tangent matrix obtained by setting $\dot{\sigma}_{eq} = \dot{\sigma}_{eq}^{Trial}$ | |
| = 2 → The tangent matrix obtained by setting $\dot{\sigma}_{eq} \Rightarrow \dot{\varepsilon}_{eq}$ |
Else
| MANA | = 0 → The tangent matrix obtained by setting $\dot{\lambda}_{vp} = 0$ |
| = 1 → The tangent matrix obtained by setting $\dot{\lambda}_{vp} \Rightarrow \dot{\sigma}_{eq}$ | |
| = 2 → The tangent matrix obtained by setting $\dot{\lambda}_{vp} \Rightarrow \dot{\varepsilon}_{eq}$ |
Real parameters
| Line 1 (4G10.0) | |
|---|---|
| E | YOUNG's elastic modulus |
| < | POISSON's ratio. |
| $A_c$ | parameter for $\sigma - \dot{\varepsilon}$ relation |
| $A_m$ | parameter for $\sigma - \dot{\varepsilon}$ relation |
\[ \hat{\sigma}_{eq} = A_c \hat{D}_{eq}^{A_m} \]
Stresses
Number of stresses
= 4 : for 2D analysis
= 6 : for 3D analysis
Meaning
The stresses are the components of CAUCHY stress tensor in global (X,Y) 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) | $\sigma_{yz}$ |
State variables
Number of state variables
= 24 for 2D analysis
= 15 for 3D analysis
List of state variables
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 |
| Q(25) | = 0 - if the current stress state is elastic |
| = 1 - if the current stress state is plastic. |
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 |
laws/levjet.txt · Last modified: 2020/08/25 15:46 (external edit)
