/MAT/LAW106 (JCOOK_ALM)
Block Format Keyword This law represents an isotropic elasto-plastic material using the Johnson-Cook material model. This model expresses material stress as a function of strain and temperature.
This law is not compatible with an EOS. The dependence between pressure and volumetric strain is linear. A built-in failure criterion, based on the maximum plastic strain is available. This material law is compatible with solid elements only.
Format
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) |
---|---|---|---|---|---|---|---|---|---|
/MAT/LAW106/mat_ID/unit_ID or /MAT/JCOOK_ALM/mat_ID/unit_ID | |||||||||
mat_title | |||||||||
E | fct_ID1 | fct_ID2 | fct_ID3 | ||||||
a | b | n | |||||||
Pmin | Nmax | Tol | |||||||
m | Tmelt | Tmax | |||||||
Tr |
Definition
Field | Contents | SI Unit Example |
---|---|---|
mat_ID | Material
identifier. (Integer, maximum 10 digits) |
|
unit_ID | Unit identifier (Integer, maximum 10 digits) |
|
mat_title | Material
title. (Character, maximum 100 characters) |
|
Initial
density. (Real) |
||
Reference density used in
EOS (equation of state). Default = (Real) |
||
E | If fct_ID1 = 0: Young's modulus. If fct_ID1 ≠ 0: Ordinate scale factor of fct_ID1 and fct_ID2. (Real) |
|
If fct_ID3 = 0: Poisson's ratio. If fct_ID3 ≠ 0: Ordinate scale factor of fct_ID3. (Real) |
||
fct_ID1 | Function identifier
defining Young’s modulus versus temperature when
heating. (Integer) |
|
fct_ID2 | Function identifier
defining Young’s modulus versus temperature when
cooling. (Integer) |
|
fct_ID3 | Function identifier
defining Poisson’s ratio versus temperature. (Integer) |
|
a | Yield
stress. (Real) |
|
b | Plastic hardening
parameter. (Real) |
|
n | Plastic hardening
exponent. Default = 1 (Real) |
|
Failure plastic
strain. Default = 1030 (Real) |
||
Maximum stress. Default = 1030 (Real) |
||
Pmin | Pressure cutoff (<
0). Default = -1030 (Real) |
|
Nmax | Maximum number of
iterations to compute plastic strains. Default = 1 (Integer) |
|
Tol | Tolerance. Default = 10-7 (Real) |
|
m | Temperature
exponent. Default = 1.0 (Real) |
|
Tmelt | Melting temperature.
Default = 1030 (Real) |
|
Tmax | For T > Tmax: m = 1 is used. Default = 1030 (Real) |
|
Specific heat per unit
volume. (Real) |
||
Tr | Reference
temperature. Default = 300K (Real) |
Example (Metal)
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
Mg mm s
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW106/1/1
Metal
# RHO_I
8E-9 0
# E Nu fct_ID1 fct_ID2 fct_ID3
200000 0.3 4 5 6
# a b n EPS_max SIG_max0
400 500 .5 0 0
# Pmin NMAX TOL
0 0 0
# m T_melt T_max
3 2500 3000
# RhoCP Tref
3.5 298
/HEAT/MAT/1
# T0 RHO0_CP AS BS IFORM
298 3.5 20 0 1
# T1 AL BL EFRAC
2500 20 0 .9
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/4
Young modulus factor versus temperature during heating
# X Y
0 1
300 1
1500 .1
2000 .1
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/5
Young modulus factor versus temperature during cooling
# X Y
0 1
300 1
1500 .1
2000 .1
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/6
Poisson's Ratio factor versus temperature
# X Y
0 1
300 1
1500 1.5
2000 1.5
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#enddata
Comments
- In this model, the
material behavior is elastic-plastic and the yield stress is calculated
as:
Where,
Where,- Equivalent plastic strain
- Temperature
- Reference temperature
- Melting temperature
The material behaves as a linear-elastic material when the equivalent stress is lower than the yield stress.
When /HEAT/MAT (with Iform =1) references this material model, the values of Tr and Tmelt defined in this card will be overwritten by the corresponding T0 and Tmelt defined in /HEAT/MAT.
When the temperature is not initialized using /HEAT/MAT or /INITEMP, the reference temperature (Tr) is also the initial temperature.
- The plastic yield stress should always be greater than zero. To model pure elastic behavior, the plastic yield stress, a can be set to 1030.
- When reaches the value of (for tension, compression or shear), in one integration point, then the deviatoric stress of the corresponding integration point is permanently set to 0; however, the solid element is not deleted.
- The plastic hardening exponent must be .
- The hydrostatic
pressure is linearly proportional to volumetric strain:Where,
- Bulk modulus
- Volumetric strain
- This material can be used with the material options /HEAT/MAT and /VISC.