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laws:endc
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ENDC
Description
Endochronic (internal time) model coupled with damage for elasto-plastic cyclic loading analysis in plane state at constant temperature.
The model
This law is used for mechanical analysis of 2-D continuum element undergone large deformation by using endochronic (internal time) theory coupled with damage model for elasto-plastic cyclic loading.
Files
Prepro: LENDC.F
Lagamine: ENDC2D.F
Availability
| Plane stress state | NO |
| Plane strain state | YES |
| Axisymmetric state | YES |
| 3D state | NO |
| Generalized plane state | NO |
Input file
Parameters defining the type of constitutive law
| Line 1 (2I5, 60A1) | |
|---|---|
| IL | Law number |
| ITYPE | 85 |
| COMMENT | Any comment (up to 60 characters) that will be reproduced on the output listing |
Integer parameters
| Line 1 (2I5) | |
|---|---|
| NINTV | Number of sub-steps used to integrate numerically the constitutive equation in a time step |
| NPOINT | The function form |
| = 1 : Linear expansion (for 2-terms kernal function) | |
| = 2 : Saturated expansion (for 2-terms kernal function) | |
| \[\rho(\zeta)=\rho_0+\rho_1(\zeta)\]\[\rho_1(\zeta)=\frac{E_1}{E}\;e^{-\alpha_1.\zeta}+\frac{E_2}{E}\] | |
| = 3 : Linear expansion (for 3-terms kernal function) | |
| = 4 : Saturated expansion (for 3-terms kernal function) | |
| \[\rho(\zeta)=\rho_0+\rho_1(\zeta)\]\[\rho_1(\zeta)=\frac{E_1}{E}\;e^{-\alpha_1.\zeta}+\frac{E_2}{E}+\frac{E_3}{E}\;e^{-\alpha_3.\zeta}\] | |
Real parameters
| Line 1 (7G10.0) | |
|---|---|
| E | YOUNG's elastic modulus |
| $\nu$ | POISSON's ratio |
| $\sigma_o$ | Initial yield limit |
| $\sigma_f$ | Yield limit at finite strain |
| $E_{to}$ | Initial tangent modulus |
| $E_{tf}$ | Tangent modulus at finite strain |
| Thickness = 1.0 (by default) | |
| $\varepsilon_f$ | Equivalent plastic strain at the unloading point |
| Line 2 (7G10.0) | |
| $2\sigma_y$ | Stress drop during the elastic unloading |
| = 2$\sigma_0$ at initial yielding point | |
| $A_o$ | Ratio of saturated and initial stress |
| Only for the choice of saturated expansion form, meaning NPOINT = 2 or 4) | |
| $\sigma_{po}$ | Yield limit for three-terms kernal function |
| $E_{tpo}$ | Yield limit for three-terms kernal function |
| Dam | Parameter of damage model |
| Edam | Parameter of damage model |
| Rdam | Parameter of damage model \[D(\zeta)=Dam\;e^{-Edam\;.\;\zeta\;.\;Rdam}\] |
Stresses
Number of stresses
4 for plane state
Meaning
The stresses are the components of CAUCHY stress tensor in global (X,Y,Z) coordinates.
| SIG(1) | $\sigma_{xx}$ |
| SIG(2) | $\sigma_{yy}$ |
| SIG(3) | $\sigma_{xy}$ |
| SIG(4) | $\sigma_{zz}$ |
State variables
Number of state variables
21
List of state variables
| Q(1) | = 1 : Plane strain |
| Circumferential strain rate ($\dot{\varepsilon}_{\theta}$) in axisymmetrical state | |
| Q(2) | Current yield limit in tension |
| Q(3) | = 0 : Current stress state is elastic |
| = 1 : Current stress state is plastic | |
| Q(4) | = 0 : Loading occurs |
| = 1 : Neutral loading occurs | |
| Q(5) | Equivalent plastic strain ($\bar{\varepsilon}^p$) |
| Q(6) | Internal time $\zeta$ |
| Q(7) | Current kernal function's value $f_n$ |
| Q(8) | Current derived kernal function's value $df_n$ |
| Q(9)$\rightarrow$Q(20) | Current back stresses |
| Q(21) | Current damage coefficient |
laws/endc.txt · Last modified: 2020/08/25 15:46 (external edit)
