/MAT/LAW26 (SESAM)
Block Format Keyword This ALE material law describes a SESAME tabular EOS, used with a JohnsonCook yield criterion.
SESAME EOS covers a wide range of phases including solids, fluids and high temperature/high density plasmas, and the wellknown transitions between these various phases. It requires SESAME tables, which were developed at Los Alamos National Laboratory in USA.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/MAT/LAW26/mat_ID or /MAT/SESAM/mat_ID  
mat_title  
${\rho}_{i}$  ${\rho}_{0}$  
E  $\upsilon $  
a  b  n  ${\epsilon}_{p}^{\text{max}}$  ${\sigma}_{\mathrm{max}}$  
E_{0}  
SESAM301  
c  ${\epsilon}_{0}$  m  T_{melt}  T_{max}_{} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

SESAM505  
K_{LOR}  $\lambda $  A  K_{max}  
SESAM502  
$\sigma $ 
Definition
Field  Contents  SI Unit Example 

mat_ID  Material identifier. (Integer, maximum 10 digits) 

mat_title  Material title. (Character, maximum 100 characters) 

${\rho}_{i}$  Initial density. (Real) 
$\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\right]$ 
${\rho}_{0}$  Reference density used in E.O.S (equation of
state). Default ${\rho}_{0}$ = ${\rho}_{i}$ (Real) 
$\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\right]$ 
E  Young's modulus. (Real) 
$\left[\text{Pa}\right]$ 
$\upsilon $  Poisson's ratio. (Real) 

a  Plasticity yield stress. (Real) 
$\left[\text{Pa}\right]$ 
b  Hardening hardening
parameter. (Real) 

n  Plasticity hardening exponent (must be ≤
1). Default = 1.0 (Real) 

${\epsilon}_{p}^{\text{max}}$  Failure plastic strain. (Real) 

${\sigma}_{\mathrm{max}}$  Maximum stress. (Real) 
$\left[\text{Pa}\right]$ 
E_{0}  Initial energy per unit
volume. (Real) 
$\left[\text{Pa}\right]$ 
SESAM301  File name of the SESAME EOS
table (301). (Character, maximum 100 characters) 

c  Strain rate coefficient.
Default = 0.00 (Real) 

${\epsilon}_{0}$  Reference strain rate. Default = 10^{06} (Real) 
$\left[\frac{\text{1}}{\text{s}}\right]$ 
m  Temperature exponent. Default = 1.00 (Real) 

T_{melt}  Melting temperature.
Default = 10^{30} (Real) 
$\left[\text{K}\right]$ 
T_{max}  Maximum temperature. for T > T_{max}: m = 1 is used. (Real) 
$\left[\text{K}\right]$ 
SESAM505  File name of the SESAME table
(504). (Character, maximum 100 characters) 

K_{LOR}  Lorentz conductivity. Default = 1.6833x10^{9} (Real) 
$\left[\frac{\text{J}}{\text{m}\cdot \text{s}\cdot {\text{K}}^{\raisebox{1ex}{$7$}\!\left/ \!\raisebox{1ex}{$2$}\right.}}\right]$ 
$\lambda $  Lamda. Default = 8.3x10^{6} (Real) 
$\left[{\left(\frac{\text{m}}{\text{K}}\right)}^{\text{3}/\text{2}}\right]$ 
A  Atomic weight. (Real) 
$\left[\frac{\text{kg}}{\text{mole}}\right]$ 
K_{max}  Maximum conductivity. (Real) 
$\left[\frac{\text{J}}{\text{m}\cdot \text{s}\cdot \text{K}}\right]$ 
SESAM502  File name of the SESAME table
(502). (Character, maximum 100 characters) 

$\sigma $  StefanBoltzman constant (equal to
5.6697x10^{8}). (Real) 
$\left[\frac{\text{W}}{{\text{m}}^{2}\cdot {\text{K}}^{4}}\right]$ 
Example (Water)
#RADIOSS STARTER
#12345678910
# 2. MATERIALS:
#12345678910
/MAT/LAW26/1
WATER  560 K  130 bars  Initially Liquid  Without Plastic Behavior (Unit: kgmmms)
# RHO_I RHO_0
.00074 0
# Young Poisson
1.0E20 0.0
# A B N EPSP_MAX SIG_MAX
1.0E+20 0.0 0.0 0.0 0.0
# E0
740.0
# SESAM301 TABLE
sesamwater_301.dat
# C EPS_DOT_0 M T_MELT T_MAX
0.0 0.0 0.0 0.0 0.0
# SESAM505 TABLE
sesamwater_505.dat
# XKL XLAMB ATOM XKMAX
0.0 0.0 0.0 0.0
# SESAM502 TABLE
sesamwater_502.dat
# SIG
0.0
#12345678910
#ENDDATA
/END
#12345678910
Comments
 The thermal conductivity flux
is:
(1) $${F}_{e}={K}_{e}\nabla {T}_{e}$$Where, K_{e}
 Thermal conductivity
 K_{L}
 Conductivity for a Lorentz gas
(2) $${K}_{e}=0.4{\delta}_{T}{K}_{L}$$With:(3) $${K}_{L}={K}_{LOR}\cdot \frac{{T}_{e}^{5/2}}{Z\mathrm{ln}\left(\Lambda \right)}$$and(4) $${\delta}_{T}=\frac{1}{1+\left(3.44\times 0.26\frac{\text{ln}\left(Z\right)}{Z}\right)}$$K_{LOR} (Lorentz conductivity) is:(5) $${K}_{LOR}=1.6833\times {10}^{9}\left[\frac{J}{m\cdot s\cdot {K}^{7/2}}\right]$$LAMBDA depends of the electronic temperature (T_{e}), the electronic density (n_{e}) and the coefficient $\lambda $ :(6) $$\mathrm{\Lambda}=\lambda \cdot \frac{{T}_{e}^{3/2}}{{n}_{e}^{1/2}}$$(7) $${n}_{e}=\frac{\rho \cdot {N}_{A}\cdot Z}{A}$$Where, A
 Atomic weight
 N_{A}
 Avogadro number N_{A} = 6.0225 x 10^{23}
 Z
 Atomic number obtained from the SESAME EOS table 504
 $\rho $
 Density
 T_{e}
 Electronic temperature obtained from the SESAME table
 The thermal radiation flux
is:
(8) $${F}_{r}={K}_{r}\nabla {T}_{r}$$With:(9) $${K}_{r}=\frac{\frac{16}{3}\cdot \sigma \cdot {L}_{R}\cdot {T}^{3}\cdot \frac{\partial T}{\partial x}}{1+\frac{16}{3}\cdot \frac{{L}_{R}}{T}\cdot \left\frac{\partial T}{\partial x}\right}$$Where, $\sigma $
 StefanBoltzmann constant
 L_{R}
 Rosseland mean length obtained from the SESAME tables.
 ${T}_{r}$ (equivalent to T)
 Radiation temperature is obtained from the SESAME tables
 Files SESAM301, SESAM505, and SESAM502 are tabulated equations from analytical model selected to describe material state in different states. Most of SESAME tables are double entry tables (two variable functions). These tabulated EOS provide pressure and energy in function of density and temperature. Tables are interpolated in both directions. With Radioss the two variables are density and specific energy.
 /EOS/SESAM is able to handle SESAME tabulated EOS. This present material law also take into account JohnsonCook yield criteria and conductive/radiative transports in potential plasma.