/FAIL/MULLINS_OR
Block Format Keyword Describes the stress softening mullins effect that is observed during a cyclic loading unloading based on the criterion proposed by Ogden and Roxburgh.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/FAIL/MULLINS_OR/mat_ID/unit_ID  
R  $\beta $  m 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

fail_ID 
Definitions
Field  Contents  SI Unit Example 

mat_ID  Material identifier. (Integer, maximum 10 digits) 

unit_ID  Optional unit identifier. (Integer, maximum 10 digits) 

R  Damage parameter relative to undeformed material. 1
3 Default = 1.0 (Real) 

$\beta $  Damage parameter. 1
3 (Real) 

m  Damage parameter relative to deformation. 1
3 (Real) 
$\left[\text{J}\right]$ 
Example
#RADIOSS STARTER
#12345678910
/UNIT/1
unit for material and failure
Mg mm s
/MAT/LAW100/1/1
Neo Hookean material
#
1.000000000000E09
#N_NETWORK FLAG_HE FLAG_CR
0 3
# C10 D1
0.5000
/FAIL/MULLINS_OR/1/1
# R BETA m
2.0 0.02 0.2
#12345678910
#ENDDATA
#12345678910
Comments
 This failure model can only be used with materials /MAT/LAW92, /MAT/LAW95, and /MAT/LAW100.
 The stress during the
first loading process is equal to the undamaged stress. Upon unloading and
reloading the stress is multiplied by a positive softening factor
function:
(1) $$\sigma =\eta dev\left(\sigma \right)p\text{\Iota}$$Where, $dev\left(\sigma \right)$
 The deviatoric part of the stress.
 $p$
 Hydrostatic pressure.
 $\eta $
 Damage factor that is a function of the strain energy of the hyperelastic model which respects:
(2) $$\eta =\{\begin{array}{c}=1\text{,}\text{if}W={W}_{max}\\ 1\text{,if}W{W}_{max}\end{array}$$Where, ${W}_{max}$ is the maximum strain energy that the material has been subjected to during its loading history:(3) $$\eta =1\frac{1}{R}erf\left(\frac{{W}_{max}W}{m+\beta {W}_{max}}\right)$$Where, $erf$ is the Gauss error function.
 The larger the parameter $R$ , the less $\eta $ can depart from unity and hence less damage can occur. For small values of m, there is more damage at smaller strains. For higher values of m, there is less damage in the small strain region during the initial loading, but during reloading there is will be more damage at smaller strains. Smaller values of $\beta $ result in increased damage.
 There is no failure or element deletion with this failure model.