/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 β m
Optional line
(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)

β Damage parameter. 1 3

(Real)

m Damage parameter relative to deformation. 1 3

(Real)

[ J ]

Example

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for material and failure
                  Mg                  mm                   s
/MAT/LAW100/1/1 
Neo Hookean material
#
 1.000000000000E-09
#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
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

  1. This failure model can only be used with materials /MAT/LAW92, /MAT/LAW95, and /MAT/LAW100.
  2. 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)
    σ = η d e v ( σ ) p Ι MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaeq4WdmNaeyypa0Jaeq4TdGMaamizaiaadwgacaWG2bWaaeWaa8aa baWdbiabeo8aZbGaayjkaiaawMcaaiabgkHiTiaadchacaqGzoaaaa@43BB@
    Where,
    d e v ( σ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamizaiaadwgacaWG2bWaaeWaa8aabaWdbiabeo8aZbGaayjkaiaa wMcaaaaa@3C45@
    The deviatoric part of the stress.
    p MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamiCaaaa@3701@
    Hydrostatic pressure.
    η
    Damage factor that is a function of the strain energy of the hyperelastic model which respects:
    (2)
    η = { = 1   if   W = W m a x < 1 , if   W < W m a x MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaeq4TdGMaeyypa0Zaaiqaa8aabaqbaeqabiqaaaqaa8qacqGH9aqp caaIXaGaaeilaiaabccacaGGGcGaaeyAaiaabAgacaGGGcGaam4vai abg2da9iaadEfapaWaaSbaaSqaa8qacaWGTbGaamyyaiaadIhaa8aa beaaaOqaa8qacqGH8aapcaaIXaGaaeilaiaabckacaqGPbGaaeOzai aacckacaWGxbGaeyipaWJaam4va8aadaWgaaWcbaWdbiaad2gacaWG HbGaamiEaaWdaeqaaaaaaOWdbiaawUhaaaaa@53CA@
    Where, W m a x MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4va8aadaWgaaWcbaWdbiaad2gacaWGHbGaamiEaaWdaeqaaaaa @3A17@ is the maximum strain energy that the material has been subjected to during its loading history:(3)
    η = 1 1 R e r f ( W m a x W m + β W m a x ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaeq4TdGMaeyypa0JaaGymaiabgkHiTmaalaaapaqaa8qacaaIXaaa paqaa8qacaWGsbaaaiaadwgacaWGYbGaamOzamaabmaapaqaa8qada WcaaWdaeaapeGaam4va8aadaWgaaWcbaWdbiaad2gacaWGHbGaamiE aaWdaeqaaOWdbiabgkHiTiaadEfaa8aabaWdbiaad2gacqGHRaWkcq aHYoGycaWGxbWdamaaBaaaleaapeGaamyBaiaadggacaWG4baapaqa baaaaaGcpeGaayjkaiaawMcaaaaa@4E90@

    Where, e r f MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamyzaiaadkhacaWGMbaaaa@38D8@ is the Gauss error function.

  3. The larger the parameter R MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamiCaaaa@3701@ , the less η 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 β result in increased damage.
  4. There is no failure or element deletion with this failure model.
1 Ogden, R. W., and D. G. Roxburgh, “A Pseudo-Elastic Model for the Mullins Effect in Filled Rubber,” Proceedings of the Royal Society of London, Series A, vol. 455, pp. 2861–2877, 1999