/MAT/LAW23 (PLAS_DAMA)

Block Format Keyword This law models an isotropic elastic plastic material and combines Johnson-Cook material model with a generalized damage model. The law is applicable only for solid elements.

Format

(1)	(3)	(5)	(7)	(9)
/MAT/LAW23/`mat_ID`/`unit_ID` or /MAT/PLAS_DAMA/`mat_ID`/`unit_ID`
`mat_title`
$ρ_{i}$
`E`	$ν$
`a`	`b`	`n`	$ε_{p}^{m a x}$	$σ_{\max 0}$
`c`	${\dot{ε}}_{0}$	`ICC`
$ε_{d a m}$	`E`_t

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`	Young's modulus. (Real)	$[Pa]$
$ν$	Poisson's ratio. (Real)
`a`	Plasticity yield stress - should be strictly positive. (Real)	$[Pa]$
`b`	Plasticity hardening parameter. (Real)
`n`	Plasticity hardening exponent. 3 (Real)
$ε_{p}^{m a x}$	Failure plastic strain. Default = 10³⁰ (Real)
$σ_{\max 0}$	Plasticity maximum stress. Default = 10³⁰ (Real)	$[Pa]$
`c`	Strain rate coefficient. = 0 No strain rate effect. Default = 0.00 (Real)
${\dot{ε}}_{0}$	Reference strain rate. If $\dot{ε} \leq {\dot{ε}}_{0}$ , no strain rate effect. (Real)	$[\frac{1}{s}]$
`ICC`	Strain rate computation flag. 5 = 0 (Default) Set to 1. = 1 Strain rate effect on $σ_{\max}$ . = 2 No strain rate effect on $σ_{\max}$ . (Integer)
$ε_{d a m}$	Damage model starts at $ε_{d a m}$ . Default = 0.15 (Real)
`E`_t	Softening damage slope ( $- E < E_{t} \leq 0$ ). Default = 0.00 (Real)	$[Pa]$

Example (Aluminum)

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
                   g                  mm                  ms
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  2. MATERIALS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW23/1/1
Alu
#              RHO_I
               .0027                   
#                  E                  nu
               70000                  .3
#                  a                   b                   n             Eps_max            sig_max0
                 100                   0                   1                  .2                 100
#                  c               EPS_0       ICC
                   0                   0         0
#            EPS_dam                 E_t
                  .1               -2000
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

The damage law is applied to the stress tensor $σ_{i j}$ and damage occurs in tension, compression and shear.
The input is the same as material law (/MAT/LAW22 (DAMA)).
The plasticity hardening exponent n must be less than one.
When $ε_{p}$ reaches $ε_{p}^{m a x}$ , in one integration point, then the solid element is deleted.

ICC is a flag of the strain rate effect on material maximum stress

σ_{\max}

$σ = σ_{y} (1 + c \ln (\frac{\dot{ε}}{{\dot{ε}}_{o}}))$	$σ = σ_{y} (1 + c \ln (\frac{\dot{ε}}{{\dot{ε}}_{o}}))$
$σ_{\max} = σ_{\max 0} (1 + c \ln (\frac{\dot{ε}}{{\dot{ε}}_{o}}))$	$σ_{\max} = σ_{\max 0}$