/MAT/LAW63 (HANSEL)

Block Format Keyword This law describes the trip steel plastic material. This material law can be used only with shell elements.

Format

(1)	(3)	(5)	(7)	(9)
/MAT/LAW63/`mat_ID`/`unit_ID` or /MAT/HANSEL/`mat_ID`/`unit_ID`
`mat_title`
$ρ_{i}$
`E`	$ν$	`C`_p
`A`	`B`	`Q`	`C`	`D`
`P`	`A`_HS	`B`_HS	`m`	`n`
`K`₁	`K`₂	$Δ H$	`V`_m0	${\dot{ε}}_{0}$
`T`₀	`H`_l	$η$

Definitions

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)	$[\frac{kg}{m^{3}}]$
`E`	Initial Young's modulus. (Real)	$[Pa]$
`v`	Poisson's ratio. (Real)
`C`_p	Specific heat capacity. Default = 10³⁰ (Real)	$[\frac{J}{k g K}]$
`A`	Material parameter 1. (Real)
`B`	Material parameter 2. 5 Default = -1.0 (Real)
`Q`	Material parameter 3. (Real)	$[K]$
`C`	Material parameter 4. (Real)
`D`	Material parameter 5. (Real)	$[\frac{1}{K}]$
`P`	Material parameter 6. (Real)
`A`_HS	Material parameter 7. (Real)
`B`_HS	Material parameter 8. (Real)	$[Pa]$
`m`	Material parameter 9. (Real)	$[Pa]$
`n`	Material parameter 10. (Real)
`K`₁	Material parameter 11. (Real)
`K`₂	Material parameter 12. (Real	$[\frac{1}{K}]$
$Δ H$	Material parameter 13. (Real	$[Pa]$
`V`_m0	Initial martensite fraction. Default = 10^-20 (Real)
${\dot{ε}}_{0}$	Initial plastic strain. (Real)
`T`₀	Initial temperature. (Real)	$[K]$
`H`_l	Latent heat of martensite. (Real)	$[J]$
$η$	Taylor-Quinney coefficient. Default = 1.0 (Real)

Example (Steel)

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
                  Mg                  mm                   s
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  2. MATERIALS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW63/1/1
Steel
#              RHO_I
              7.8E-9                   
#                  E                  Nu                  Cp
              210000                  .3           460000000
#                  A                   B                   Q                   C                   D
                 .32                .226              1379.4              -2.173               .0084
#                  P                 AHS                 BHS                   m                   n
                6.25               318.2                2170                2.94                1.39
#                 K1                  K2                  DH                VM_0                EPS0
                   1                   0               414.7                1E-4                .002
#                 T0                  Hl                 eta
                 273                 150                 0.9
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

Martensite fraction rate:(1)
$\frac{\partial V_{m}}{\partial ε_{p}} = \frac{B}{A} \exp (\frac{Q}{T}) {(\frac{1 - V_{m}}{V_{m}})}^{\frac{(1 + B)}{B}} V_{m}^{P} \frac{1}{2} [1 - \tanh (C + D \cdot T)]$
Martensite fraction:(2)
$V_{m} = \int_{0}^{ε_{p}} \frac{\partial V_{m}}{\partial ε_{p}} \partial ε_{p}$
Mechanical behavior:(3)
$σ_{y} = (B_{HS} - (B_{HS} - A_{HS}) exp (- m {(ε_{p} + ε_{0})}^{n})) (K_{1} + K_{2} T) + Δ H_{γ \to α}, V_{m}$
The temperature is computed assuming the adiabatic condition (by default the condition is isothermal with C_p = 10³⁰):(4)
$T = T_{0} + \frac{η E_{i n t} + V_{m} H_{l}}{ρ C_{p} (V o l u m e)}$

Where, E_int is the internal energy of the element.
B must satisfy this condition:(5)
$\frac{1 + B}{B} < p$
The Taylor-Quinney coefficient must satisfy this condition:(6)
$0 \leq η \leq 1$