/MAT/LAW22 (DAMA)

Block Format Keyword This law is identical to Johnson-Cook material (/MAT/LAW2), except that the material undergoes damage if plastic strains reach a user-defined value ( $ε_{d a m}$ $ε_{d a m}$ ). This law can be applied to both shell and solid elements.

Format

(1)	(3)	(5)	(7)	(9)
/MAT/LAW22/`mat_ID`/`unit_ID` or /MAT/DAMA/`mat_ID`/`unit_ID`
`mat_title`
$ρ_{i}$ $ρ_{i}$
`E`	$ν$ $ν$
`a`	`b`	`n`	$ε_{p}^{m a x}$ $ε_{p}^{m a x}$	$σ_{\max 0}$ $σ_{\max 0}$
`c`	${\dot{ε}}_{0}$ ${\dot{ε}}_{0}$	`ICC`
$ε_{d a m}$ $ε_{d a m}$	`E`_t

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

▸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/DAMA/1/1
Alu
#              RHO_I
               .0027                   
#                  E                  Nu
               70000                  .3
#                  a                   b                   n             Eps_max          SIGMA_max0
                 100                   0                   1                  .2                 100
#                  c           Eps_dot_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

Damage is isotropic, its effect are the same in tension and compression.
(1)
$σ = (a + b ε_{p}^{n}) (1 + c \ln \frac{\dot{ε}}{{\dot{ε}}_{0}})$ $σ = (a + b ε_{p}^{n}) (1 + c \ln \frac{\dot{ε}}{{\dot{ε}}_{0}})$

Where,

$ε_{p}$ $ε_{p}$

Plastic strain

$\dot{ε}$ $\dot{ε}$

Strain rate

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

σ_{\max}

$σ_{\max}$ .

The damage appears in the material when the strain is larger than a maximum value $ε_{d a m}$ $ε_{d a m}$ :(2)
$0 \leq δ \leq 1$ $0 \leq δ \leq 1$

If $ε < ε_{d a m} \Rightarrow δ = 0$ $ε < ε_{d a m} \Rightarrow δ = 0$ , Law 22 is identical to law /MAT/LAW2.

If $ε \geq ε_{d a m} \Rightarrow E_{d a m} = (1 - δ) E$ $ε \geq ε_{d a m} \Rightarrow E_{d a m} = (1 - δ) E$ and $ν_{d a m} = \frac{1}{2} δ + (1 - δ) ν$ $ν_{d a m} = \frac{1}{2} δ + (1 - δ) ν$

Figure 2.
For solid elements, the damage law can only be applied to the deviatoric stress tensor s_ij and $G_{d a m} = \frac{E_{d a m}}{2 (1 + ν_{d a m})}$ $G_{d a m} = \frac{E_{d a m}}{2 (1 + ν_{d a m})}$ .
When $ε_{p}$ $ε_{p}$ reaches $ε_{p}^{m a x}$ $ε_{p}^{m a x}$ in one integration point, then based on the element type:
- Shell elements: The corresponding shell element is deleted.
- Solid elements: The deviatoric stress of the corresponding integral point is permanently set to 0, however, the solid element is not deleted.

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