/MAT/LAW16 (GRAY)

Block Format Keyword This material law is based on Gray EOS and Johnson-Cook yield criteria.

Format

(1)	(3)	(5)	(7)	(9)
/MAT/LAW16/`mat_ID` or /MAT/GRAY/`mat_ID`
`mat_title`
$ρ_{i}$	$ρ_{0}$
`E`	`ν`
`a`	`b`	`n`	$ε_{\max}$	$σ_{\max}$
`P`₀	`C`	`S`	$γ$ ₀	α_e
`AW`	`P`_min	`E`₀
`c`	${\dot{ε}}_{0}$	`m`	`T`_melt	`T`_max
$γ$ _0m	α_m	$γ$ _e	`g`_e	$Δ S$
`T`_m0	`V`_j	`V`_b
	`E`_oh	`A`_y	$θ$

Definition

Field	Contents	SI Unit Example
`mat_ID`	Material identifier. (Integer, maximum 10 digits)
`mat_title`	Material title. (Character, maximum 100 characters)
$ρ_{i}$	Initial density. (Real)	$[\frac{kg}{m^{3}}]$
$ρ_{0}$	Reference density used in E.O.S (equation of state). Default = $ρ_{0}$ = $ρ_{i}$ (Real)	$[\frac{kg}{m^{3}}]$
`E`	Young's modulus. (Real)	$[Pa]$
`ν`	Poisson's ratio. (Real)
`a`	Plasticity yield stress. (Real)	$[Pa]$
`b`	Plasticity hardening parameter. (Real)	$[Pa]$
`n`	Plasticity hardening exponent. Default = 1.0001 (Real)
$ε_{\max}$	Failure plastic strain. Default = 10³⁰ (Real)
$σ_{\max}$	Plasticity maximum stress. Default = 10³⁰ (Real)	$[Pa]$
`P`₀	Initial pressure. (Real)	$[Pa]$
`C`	Hugoniot parameters. (Real)	$[\frac{m}{s}]$
`S`	$U_{s} = C + S U_{p}$ (Real)
$γ$ ₀	Lattice gamma. (Real)
$σ$ _e	$γ = γ_{0} - a x$ (Real)
`AW`	Atomic weight. (Real)	$[\frac{k g}{m o l e}]$
`P`_min	Pressure cutoff. Default = -10³⁰ (Real)	$[Pa]$
`E`₀	Initial energy per unit volume. (Real)	$[\frac{J}{m^{3}}]$
`c`	Strain rate coefficient. = 0 (Default) No strain rate effect. (Real)
${\dot{ε}}_{0}$	Reference strain rate (time unit)^-1. (Real)	$[\frac{1}{s}]$
`m`	Temperature exponent. Default = 1.0 (Real)
`T`_melt	Melting temperature. Default = 10³⁰ (Real)	$[K]$
`T`_max	For `T` > `T`_max: `m` =1 is used. Default = 10³⁰ (Real)	$[K]$
$γ$ _0m	Melting gamma. Default = $γ$ ₀ (Real)
$σ$ _m	$γ_{m} = γ_{0 m} - a_{m} x$ Default = `a` (Real)
$γ$ _e	Electronic gamma. Default = 2/3 (Real)
`g`_e	Electronic energy coefficient. Default = 0.0 (Real)	$[\frac{J}{m o l e \cdot K^{2}}]$
$Δ S$	Entropy of melting. Default = 9.637e+3 $[\frac{J}{kg \cdot K}]$ (Real) If blank or 0, default entropy of melting value is automatically translated to the working units.	$[\frac{J}{kg \cdot K}]$
`T`_m0	Melting temperature parameter. Default = 1.3 `T`_melt (Real)	$[K]$
`V`_j	Volume where EOS are joined. (Real)	$[\frac{m^{3}}{k g}]$
`V`_b	Excluded volume for vapor phase. Default = 0.5/`r`₀ (Real)	$[\frac{m^{3}}{k g}]$
`E`_oh	Energy at `V`=`V`₀, `T`=300K, `P`=0. Default = 0.0 (Real)	$[J]$
`A`_y	Coefficient of attractive potential. (Real)	$[\frac{J m^{3}}{{mole}^{2}}]$
$θ$	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 model units must be defined in the /BEGIN card because the default value of $Δ S$ entropy of melting is calculated based on the unit system.
(1)
$\begin{matrix} σ = (a + b {ε_{p}}^{n}) (1 + c ln \frac{\dot{ε}}{{\dot{ε}}_{0}}) (1 - {(T^{*})}^{m}) & T^{*} = \frac{T - T_{0}}{T_{melt} - T_{0}} \end{matrix}$

¹ E. B. Royce, GRAY, a three-phase equation of state, UCRL-51121, Lawrence Livermore Laboratory, 1971