/MAT/LAW49 (STEINB)

Block Format Keyword Defines an elastic plastic material with thermal softening.

Format


(1)	(3)	(5)	(7)	(9)
/MAT/LAW49/`mat_ID`/`unit_ID` or /MAT/STEINB/`mat_ID`/`unit_ID`
`mat_title`
$ρ_{i}$	$ρ_{0}$
`E`₀	$ν$
$σ_{0}$	$β$	`n`	$ε_{p}^{m a x}$	$σ_{\max}$
`T`₀	`T`_m	$ρ C_{p}$	`P`_min
`b`₁	`b`₂	`h`	`f`

Definition


Field	Contents	SI Unit Example
`mat_ID`	Material identifier. (Integer, maximum 10 digits)
`unit_ID`	Unit 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`₀	Initial Young's modulus. (Real)	$[Pa]$
$ν$	Poisson's ratio. (Real)
$σ_{0}$	Plasticity initial yield stress. No default (Real)	$[Pa]$
$β$	Plasticity hardening parameter. No default (Real)
`n`	Plasticity hardening exponent. No default (Real)
$ε_{p}^{m a x}$	Maximum plastic strain. Default = 10³⁰ (Real)
$σ_{\max}$	Plasticity maximum stress. Default = 10³⁰ (Real)	$[Pa]$
`T`₀	Initial temperature. Default = 300 (Real)	$[K]$
`T`_m	Melting temperature. (Real)	$[K]$
$ρ C_{p}$	Specific heat. (Real)	$[\frac{k g}{s^{2} \cdot m \cdot K}]$
`P`_min	Pressure cutoff. Default = 0.0 (Real)	$[Pa]$
`b`₁	Law coefficient. No default (Real)
`b`₂	Law coefficient. No default (Real)
`h`	Law coefficient. No default (Real)
`f`	Law coefficient. No default (Real)

Example (Aluminum)

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
                  g                  cm                 mus
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  2. MATERIALS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW49/1/1
Aluminum
#              RHO_I               RHO_0
                2.73                   0
#                 E0                  nu
                .734                 .33
#            sigma_0                beta                   n             EPS_max           SIGMA_max
               .0029                 125                  .1                   9               .0068
#                T_0               Tmelt              rhoC_p                Pmin
                 300                1220             2.59E-5               -.005
#                 b1                  b2                   h                   f
                 6.5                 6.5              6.2E-4                   0
/EOS/GRUNEISEN/1/1
Aluminum
#                  C                  S1                  S2                  S3
                .524                 1.5                   0                   0
#             GAMMA0               ALPHA                  E0               RHO_0
                1.97                   0                   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

When material approaches melting point, the yield strength and shear modulus diminish to zero. Melting energy is defined as:
$E_{m} = E_{c} + ρ_{0} C_{p} T_{m}$
Where,

$E_{c}$

Cold compression energy

$T_{m}$

Melting temperature supposed to be constant

If the internal energy $E$ is less than $E_{m}$ , the shear modulus and the yield strength are defined as:
$G = G_{0} [1 + b_{1} p V^{\frac{1}{3}} - h (T - T_{0})] e^{- \frac{f E}{E - E_{m}}}$
With
$G_{0} = \frac{E_{0}}{2 (1 + ν)}$
$σ_{y} = {σ^{'}}_{0} [1 + b_{2} p V^{\frac{1}{3}} - h (T - T_{0})] e^{- \frac{f E}{E - E_{m}}}$
Where, ${σ^{'}}_{0}$ is given by a hardening rule:
${σ^{'}}_{0} = σ_{0} {(1 + β ε_{p})}^{n}$
If $ε_{p} > ε_{p}^{\max}$ , then
${σ^{'}}_{0} = σ_{0} {[1 + β ε_{p}^{\max}]}^{n}$
The value of ${σ^{'}}_{0}$ is limited by:
$\min (σ_{0}) \leq {σ^{'}}_{0} \leq σ_{\max}$
If an Equation of State (/EOS) does not refer to this material, the pressure is computed as:
$p = \frac{E_{0}}{3 (1 - 2 ν)} μ$
with $μ = \frac{ρ}{ρ_{0}} - 1$
When $ε_{p}$ reaches $ε_{p}^{m a x}$ , in one integration point, the deviatoric stress of the corresponding integral point is permanently set to 0; however, the solid element is not deleted.