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/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
ρi ρ0            
E υ            
a b n εmaxp σmax
E0                
SESAM301
c ε0 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)

 
ρi Initial density.

(Real)

[kgm3]
ρ0 Reference density used in E.O.S (equation of state).

Default ρ0 = ρi (Real)

[kgm3]
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)

 
εmaxp Failure plastic strain.

(Real)

 
σmax 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)

 
ε0 Reference strain rate.

Default = 10-06 (Real)

[1s]
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)

[JmsK72]
λ Lamda.

Default = 8.3x106 (Real)

[(mK)3/2]
A Atomic weight.

(Real)

[kgmole]
Kmax Maximum conductivity.

(Real)

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

(Character, maximum 100 characters)

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

(Real)

[Wm2K4]

Example (Water)

Comments

  1. The thermal conductivity flux is:(1)
    Fe=KeTe
    Where,
    Ke
    Thermal conductivity
    KL
    Conductivity for a Lorentz gas
    (2)
    Ke=0.4δTKL
    With:(3)
    KL=KLORT5/2eZln(Λ)
    and(4)
    δT=11+(3.44×0.26ln(Z)Z)
    KLOR (Lorentz conductivity) is:(5)
    KLOR=1.6833×109[JmsK7/2]
    LAMBDA depends of the electronic temperature (Te), the electronic density (ne) and the coefficient λ :(6)
    Λ=λT3/2en1/2e
    (7)
    ne=ρNAZA
    Where,
    A
    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:(8)
    Fr=KrTr
    With:(9)
    Kr=163σLRT3Tx1+163LRT|Tx|
    Where,
    σ
    Stefan-Boltzmann constant
    LR
    Rosseland mean length obtained from the SESAME tables.
    Tr (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.