Additional Information
For a description of the material constants required for this option, see Bergstrom-Boyce Material in
the Material Reference. For more detailed information about this material model, see the documentation
for the TB,BB command, and Bergstrom-Boyce in the Mechanical APDL Theory Reference.
8.4.1.4. Mullins Effect Material Model
Use the Mullins effect option (TB,CDM) for modeling load-induced changes to constitutive response
exhibited by some hyperelastic materials. Typical of filled polymers, the effect is most evident during
cyclic loading where the unloading response is more compliant than the loading behavior. The condition
causes a hysteresis in the stress-strain response and is a result of irreversible changes in the material.
The Mullins effect option is used with any of the nearly- and fully-incompressible isotropic hyperelastic
constitutive models (all TB,HYPER options with the exception of TBOPT = BLATZ or TBOPT = FOAM)
and modifies the behavior of those models. The Mullins effect model is based on maximum previous
load, where the load is the strain energy of the virgin hyperelastic material. As the maximum previous
load increases, changes to the virgin hyperelastic constitutive model due to the Mullins effect also in-
crease. Below the maximum previous load, the Mullins effect changes are not evolving; however, the
Mullins effect still modifies the hyperelastic constitutive response based on the maximum previous load.
To select the modified Ogden-Roxburgh pseudo-elastic Mullins effect model, use the TB command to
set TBOPT = PSE2.The pseudo-elastic model results in a scaled stress given by
ij= η ij0where η is a damage variable.
The functional form of the modified Ogden-Roxburgh damage variable is
η
β= −−
+m
m , (TBOPT = PSE2)where Wm is the maximum previous strain energy and W 0 is the strain energy for the virgin hyperelastic
material. The modified Ogden-Roxburgh damage function requires and enforces NPTS = 3 with the
three material constants r, m, and β.
Select the material constants to ensure η ∈ over the range of application. This condition is guar-
anteed for r > 0, m > 0, and β ≥ 0; however, it is also guaranteed by the less stringent bounds r > 0,
m > 0, and (m + βWm) > 0. The latter bounds are solution-dependent, so you must ensure that the
limits for η are not violated if β < 0.
Following is an example input fragment for the modified Ogden-Roxburgh pseudo-elastic Mullins effect
model:
TB,CDM,1,,3,PSE2 !Modified Ogden Roxburgh pseudo-elastic
TBDATA,1,1.5,1.0E6,0.2 !Define r, m, and βAdditional Information
For a description of the material constants required for this option, see Mullins Effect in the Material
Reference. For more detailed information about this material model, see the documentation for the
TB,CDM command, and Mullins Effect in the Mechanical APDL Theory Reference.
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