/MAT/LAW16 (GRAY)
Block Format Keyword This material law is based on Gray EOS and Johnson-Cook yield criteria.
Format
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) |
---|---|---|---|---|---|---|---|---|---|
/MAT/LAW16/mat_ID or /MAT/GRAY/mat_ID | |||||||||
mat_title | |||||||||
ρiρi | ρ0ρ0 | ||||||||
E | ν | ||||||||
a | b | n | εmaxεmax | σmaxσmax | |||||
P0 | C | S | γγ 0 | αe | |||||
AW | Pmin | E0 | |||||||
c | ˙ε0˙ε0 | m | Tmelt | Tmax | |||||
γγ 0m | αm | γγ e | ge | ΔSΔS | |||||
Tm0 | Vj | Vb | |||||||
Eoh | Ay | θθ |
Definitions
Field | Contents | SI Unit Example |
---|---|---|
mat_ID | Material
identifier. (Integer, maximum 10 digits) |
|
mat_title | Material
title. (Character, maximum 100 characters) |
|
ρiρi | Initial
density. (Real) |
[kgm3][kgm3] |
ρ0ρ0 | Reference density used in
E.O.S (equation of state). Default = ρ0ρ0 = ρiρi (Real) |
[kgm3][kgm3] |
E | Young's
modulus. (Real) |
[Pa][Pa] |
ν | Poisson's
ratio. (Real) |
|
a | Plasticity yield
stress. (Real) |
[Pa][Pa] |
b | Plasticity hardening
parameter. (Real) |
[Pa][Pa] |
n | Plasticity hardening
exponent. Default = 1.0001 (Real) |
|
εmaxεmax | Failure plastic
strain. Default = 1030 (Real) |
|
σmaxσmax | Plasticity maximum
stress. Default = 1030 (Real) |
[Pa][Pa] |
P0 | Initial
pressure. (Real) |
[Pa][Pa] |
C | Hugoniot
parameters. (Real) |
[ms][ms] |
S |
Us=C+S UpUs=C+SUp
(Real) |
|
γγ 0 | Lattice
gamma. (Real) |
|
σσ e |
γ=γ0−a xγ=γ0−ax
(Real) |
|
AW | Atomic
weight. (Real) |
[kgmole][kgmole] |
Pmin | Pressure cutoff. Default = -1030 (Real) |
[Pa][Pa] |
E0 | Initial energy per unit
volume. (Real) |
[Jm3][Jm3] |
c | Strain rate coefficient.
(Real) |
|
˙ε0˙ε0 | Reference strain rate
(time unit)-1. (Real) |
[1s][1s] |
m | Temperature
exponent. Default = 1.0 (Real) |
|
Tmelt | Melting
temperature. Default = 1030 (Real) |
[K][K] |
Tmax | For T >
Tmax: m =1 is used. Default = 1030 (Real) |
[K][K] |
γγ 0m | Melting gamma. Default = γγ 0 (Real) |
|
σσ m |
γm=γ0m−am xγm=γ0m−amx
Default = a (Real) |
|
γγ e | Electronic
gamma. Default = 2/3 (Real) |
|
ge | Electronic energy
coefficient. Default = 0.0 (Real) |
[Jmole⋅K2][Jmole⋅K2] |
ΔSΔS | Entropy of
melting. Default = 9.637e+3 [Jkg⋅K][Jkg⋅K] (Real) If blank or 0, default entropy of melting value is automatically translated to the working units. |
[Jkg⋅K][Jkg⋅K] |
Tm0 | Melting temperature
parameter. Default = 1.3 Tmelt (Real) |
[K][K] |
Vj | Volume where EOS are
joined. (Real) |
[m3kg][m3kg] |
Vb | Excluded volume for vapor
phase. Default = 0.5/r0 (Real) |
[m3kg][m3kg] |
Eoh | Energy at
V=V0,
T=300K,
P=0. Default = 0.0 (Real) |
[J][J] |
Ay | Coefficient of attractive
potential. (Real) |
[Jm3mole2][Jm3mole2] |
θθ | Join parameter. Default = 1.0 (Real) |
Example (Aluminum)
#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW16/1
Aluminium - GRAY EOS (unit g_cm_mus)
# RHO_I RHO_0
2.7 0
# E Nu
0.71 .33
# a b n Eps_max sigmax
0.002 0.00144 0.62 0 0
# P0 C S Gamma_0 a_e
0 0.533 1.338 2.18 1.7
# AW P_min E0
26.98 -5e-3
# c eps_dot_0 m T_melt T_max
1 1E30
# Gamma_0m a_m Gamma_e g_e delta_S
2.18 1.7 0.6667 8.7e-9 9.637E5
# T_m0 V_j V_b
1220 0.47388 0.19025
# E_0h a_y Theta
0 47 1
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
Comment
- The correct moel units must
be defined in the /BEGIN card because the default value of
ΔSΔS
entropy of melting is calculated based on the unit system.
(1) σ=(a+bεpn)(1+c ln˙ε˙ε0)(1−(T*)m)T*=T−T0Tmelt−T0