/MAT/LAW65 (ELASTOMER)

Block Format Keyword This law describes nonlinear elastoplastic material with strain rate dependent loading and unloading behavior.

Format

(1)	(2)	(3)	(5)
/MAT/LAW65/`mat_ID`/`unit_ID` or /MAT/ELASTOMER/`mat_ID`/`unit_ID`
`mat_title`
$ρ_{i}$
`E`		$υ$	$ε_{p}^{m a x}$
`N`_rate	`F`_smooth	`F`_cut

N_rate times (Each loading/unloading function pair per line)

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
`fct_ID`_ld	`fct_ID`_ul	`Fscale`_stress		$\dot{ε}$

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)	$[\frac{kg}{m^{3}}]$
`E`	Young's modulus. (Real)	$[Pa]$
$υ$	Poisson's ratio. (Real)
$ε_{p}^{m a x}$	Failure plastic strain. (Real)
`N`_rate	Number of loading/unloading function pair. Default = 50 (Integer)
`F`_smooth	Smooth strain rate flag. = 0 (Default) No strain rate filtering. = 1 Strain rate filtering. (Integer)
`F`_cut	Cutoff frequency for strain rate filtering. Default = 10³⁰ (Real)	$[Hz]$
`fct_ID`_ld	True stress-true strain function identifier for loading. (Integer)
`fct_ID`_ul	True stress-true strain function identifier for unloading. (Integer)
`Fscale`_stress	Stress scale factor. Default = 1.0 (Real)	$[Pa]$
$\dot{ε}$	Strain rate. Default = 1.0 (Real)	$[\frac{1}{s}]$

Example (Nitinol)

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
                  kg                  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/LAW65/1/1
nitinol-like material
#              RHO_I
                6E-6                   
#                 E0                  NU             EPS_max
                  50                  .3                   0
#    Nrate   Fsmooth                Fcut
         1         1                   0
#FUNC_IDld FUNC_IDul       FSCALESTRESS             EPS_rate
         3         4                   1                   0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  3. FUNCTIONS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/3
Loading_stress_strain
#                  X                   Y
                   0                   0                                                            
               .0085                 .35                                                            
               .0575                 .55                                                            
                .077               1.262                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/4
Unloading_stress_strain
#                  X                   Y
                   0                   0                                                            
               .0055                .199                                                            
               .0502                 .25                                                            
                .077               1.245                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

The law is defined by pairs of true stress-true strain functions for loading and unloading at specified strain rates. Each of the curves should begin with point (0,0) and increase monotonically. Each unloading curve should lie below the loading curve for corresponding strain rate.
The loading/unloading curve with the higher strain rate ( ${\dot{ε}}_{2}$ ) should lie above the curve with lower strain rate ( ${\dot{ε}}_{1}$ ). The curves between ${\dot{ε}}_{2}$ and ${\dot{ε}}_{1}$ are interpolated linearly for intermediate strain rates. Curves are extrapolated for strain rates higher than maximum specified strain rate. It is advised to duplicate the last curves twice to avoid instability for high strain rates.
Yield stress is determined at the intersection point between loading and unloading curves.
If the load is removed prior to the intersection point between loading and unloading curves, the unloading follows the hyperelastic path with hysteresis (Fig. 1). This path is calculated based on the value of Young's modulus, E until it intersects with the unloading curve. Thereafter it follows the unloading curve back to its initial state (0,0).
If the load is removed after intersection point between loading and unloading curves, the unloading curve is shifted by the value of plastic strain (Fig. 2).
The Young's modulus must be greater than the maximum slope of all stress-strain curves. As mentioned before, Young's modulus is used to determine the unloading path between loading and unloading curves.
When $ε_{p}$ reaches $ε_{p}^{m a x}$ 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.
Figure 1. Loading and Unloading Function Sets for Constant Strain Rates - Hyperelastic Loading/Unloading

Figure 2. For Plastic Case the Unloading Curve is Shifted by the Value of the Actual Plastic Strain