/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 | |||||||||
ρi | ρ0 | ||||||||
E | ν | fct_ID1 | fct_ID2 | fct_ID3 | |||||
a | b | n | εmaxp | σmax | |||||
Pmin | Nmax | Tol | |||||||
m | Tmelt | Tmax | |||||||
ρ0Cp | 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) |
|
ρi | Initial
density. (Real) |
[kgm3] |
ρ0 | Reference density used in
EOS (equation of state). Default = ρ0=ρi (Real) |
[kgm3] |
E | If fct_ID1 = 0: Young's modulus. If fct_ID1 ≠ 0: Ordinate scale factor of fct_ID1 and fct_ID2. (Real) |
[Pa] |
ν | 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) |
[Pa] |
b | Plastic hardening
parameter. (Real) |
[Pa] |
n | Plastic hardening
exponent. Default = 1 (Real) |
|
εmaxp | Failure plastic
strain. Default = 1030 (Real) |
|
σmax | Maximum stress. Default = 1030 (Real) |
[Pa] |
Pmin | Pressure cutoff (<
0). Default = -1030 (Real) |
[Pa] |
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) |
[K] |
Tmax | For T > Tmax: m = 1 is used. Default = 1030 (Real) |
[K] |
ρ0Cp | Specific heat per unit
volume. (Real) |
[Jm3⋅K] |
Tr | Reference
temperature. Default = 300K (Real) |
[K] |
▸Example (Metal)
Comments
- In this model, the
material behavior is elastic-plastic and the yield stress is calculated
as:
(1) σ=(a+bεpn)(1−(T∗)m)Where,(2) T∗=T−TrTmelt−TrWhere,- εp
- Equivalent plastic strain
- T
- Temperature
- Tr
- Reference temperature
- Tmelt
- 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 stres,s a can be set to 1030.
- When εp reaches the value of εmaxp (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 n≤1 .
- The hydrostatic
pressure is linearly proportional to volumetric strain:
(3) P=KμWhere,- K=E3(1−2v)
- Bulk modulus
- μ=ρρ0−1
- Volumetric strain
- This material can be used with the material options /HEAT/MAT and /VISC.