/MAT/LAW26 (SESAM)

Block Format Keyword This ALE material law describes a SESAME tabular EOS, used with a Johnson-Cook yield criterion.

SESAME EOS covers a wide range of phases including solids, fluids and high temperature/high density plasmas, and the well-known 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
ρ i ρ 0
E υ
a b n ε p max σ max
E0
SESAM301
c ε 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aaS baaSqaaiaaicdaaeqaaaaa@3884@ m Tmelt Tmax
If thermal effects are taken into account (otherwise must keep the following blank):
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
SESAM505
KLOR λ A Kmax
SESAM502
σ

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)

[ kg m 3 ]
ρ 0 Reference density used in E.O.S (equation of state).

Default ρ 0 = ρ i (Real)

[ kg m 3 ]
E Young's modulus.

(Real)

[ Pa ]
υ Poisson's ratio.

(Real)

a Plasticity yield stress.

(Real)

[ Pa ]
b Hardening hardening parameter.

(Real)

n Plasticity hardening exponent (must be ≤ 1).

Default = 1.0 (Real)

ε p max Failure plastic strain.

(Real)

σ max Maximum stress.

(Real)

[ Pa ]
E0 Initial energy per unit volume.

(Real)

[ Pa ]
SESAM301 File name of the SESAME EOS table (301).

(Character, maximum 100 characters)

c Strain rate coefficient.
= 0
No strain rate effect.

Default = 0.00 (Real)

ε 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aaS baaSqaaiaaicdaaeqaaaaa@3884@ Reference strain rate.

Default = 10-06 (Real)

[ 1 s ]
m Temperature exponent.

Default = 1.00 (Real)

Tmelt Melting temperature.
= 0
No temperature affect.

Default = 1030 (Real)

[ K ]
Tmax Maximum temperature.

for T > Tmax: m = 1 is used.

(Real)

[ K ]
SESAM505 File name of the SESAME table (504).

(Character, maximum 100 characters)

KLOR Lorentz conductivity.

Default = 1.6833x10-9 (Real)

[ J ms K 7 2 ]
λ Lamda.

Default = 8.3x106 (Real)

[ ( m K ) 3/2 ]
A Atomic weight.

(Real)

[ kg mole ]
Kmax Maximum conductivity.

(Real)

[ J msK ]
SESAM502 File name of the SESAME table (502).

(Character, maximum 100 characters)

σ Stefan-Boltzman constant (equal to 5.6697x10-8).

(Real)

[ W m 2 K 4 ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada WcaaqaaiaadEfaaeaacaWGTbWaaWbaaSqabeaacaaIYaaaaOGaeyyX ICTaam4samaaCaaaleqabaGaaGinaaaaaaaakiaawUfacaGLDbaaaa a@3EC7@

Example (Water)

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  2. MATERIALS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW26/1
WATER - 560 K - 130 bars - Initially Liquid - Without Plastic Behavior (Unit: kg-mm-ms)
#              RHO_I               RHO_0
              .00074                   0
#              Young             Poisson
             1.0E-20                 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
sesam--water_301.dat   
#                  C           EPS_DOT_0                  M               T_MELT               T_MAX
                 0.0                 0.0                0.0                  0.0                 0.0
# SESAM505 TABLE
sesam--water_505.dat
#                XKL               XLAMB               ATOM                XKMAX
                 0.0                 0.0                0.0                  0.0    
# SESAM502 TABLE
sesam--water_502.dat 
#                SIG                                                                               
                 0.0   
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

  1. The thermal conductivity flux is:
    F e = K e T e MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCOramaaBa aaleaacaWGLbaabeaakiabg2da9iabgkHiTiaadUeadaWgaaWcbaGa amyzaaqabaGccqGHhis0caWHubWaaSbaaSqaaiaadwgaaeqaaaaa@3F42@
    Where,
    Ke
    Thermal conductivity
    KL
    Conductivity for a Lorentz gas
    K e = 0.4 δ T K L

    With:

    K L = K L O R T e 5 / 2 Z ln ( Λ )

    and

    δ T = 1 1 + ( 3.44 × 0.26 ln ( Z ) Z )

    KLOR (Lorentz conductivity) is:

    K L O R = 1.6833 × 10 9 [ J m s K 7 / 2 ]

    LAMBDA depends of the electronic temperature (Te), the electronic density (ne) and the coefficient λ :

    Λ = λ T e 3 / 2 n e 1 / 2
    n e = ρ N A Z A

    Where,
    A MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqaaaa@36B9@
    Atomic weight
    NA
    Avogadro number NA = 6.0225 x 1023
    Z
    Atomic number obtained from the SESAME EOS table 504
    ρ
    Density
    Te
    Electronic temperature obtained from the SESAME table
  2. The thermal radiation flux is:
    F r = K r T r MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCOramaaBa aaleaacaWGYbaabeaakiabg2da9iabgkHiTiaadUeadaWgaaWcbaGa amOCaaqabaGccqGHhis0caWHubWaaSbaaSqaaiaadkhaaeqaaaaa@3F69@

    With:

    K r = 16 3 σ L R T 3 T x 1+ 16 3 L R T | T x | MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4samaaBa aaleaacaWGYbaabeaakiabg2da9maalaaabaWaaSaaaeaacaaIXaGa aGOnaaqaaiaaiodaaaGaeyyXICTaeq4WdmNaeyyXICTaamitamaaBa aaleaacaWGsbaabeaakiabgwSixlaadsfadaahaaWcbeqaaiaaioda aaGccqGHflY1daWcaaqaaiabgkGi2kaahsfaaeaacqGHciITcaWG4b aaaaqaaiaaigdacqGHRaWkdaWcaaqaaiaaigdacaaI2aaabaGaaG4m aaaacqGHflY1daWcaaqaaiaadYeadaWgaaWcbaGaamOuaaqabaaake aacaWGubaaaiabgwSixpaaemaabaWaaSaaaeaacqGHciITcaWHubaa baGaeyOaIyRaamiEaaaaaiaawEa7caGLiWoaaaaaaa@61B6@

    Where,
    σ
    Stefan-Boltzmann constant
    LR
    Rosseland mean length obtained from the SESAME tables.
    T r MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCivamaaBa aaleaacaWGYbaabeaaaaa@37F7@ (equivalent to T)
    Radiation temperature is obtained from the SESAME tables
  3. 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.
  4. /EOS/SESAM is able to handle SESAME tabulated EOS. This present material law also take into account Johnson-Cook yield criteria and conductive/radiative transports in potential plasma.