UMULLINS

User subroutine to define damage variable for the Mullins effect material model.

User subroutine UMULLINS:

can be used to define the damage variable for the Mullins effect material model, including the use of the Mullins effect approach to model energy dissipation in elastomeric foams;
will be called at all material calculation points of elements for which the material definition contains a user-defined Mullins effect; and
should be used when you do not want to use the Ogden and Roxburgh form of the damage variable, $η$ , that is used by Abaqus/Standard.

The following topics are discussed:

User subroutine interface
Variables to be defined
Variables that can be updated
Variables passed in for information

User subroutine interface

      SUBROUTINE UMULLINS(NUMPROPS,PROPS,UMAXNEW,UMAXOLD,SEDDEV,
     1 ETA,DETADW,DMGDISSOLD,DMGDISSNEW,SENERNEW,NUMSTATEV,STATEV,
     2 TEMP,DTEMP,NUMFIELDV,FIELDV,FIELDVINC,CMNAME,LINPER)
C
      INCLUDE 'ABA_PARAM.INC'
C
      CHARACTER*80 CMNAME
      DIMENSION PROPS(*),STATEV(*),FIELDV(*),FIELDVINC(*)

      user coding to define ETA, DETADW,
      and, optionally, DMGDISSNEW, SENERNEW, STATEV


      RETURN
      END

Variables to be defined

ETA: The damage variable, $η$ .
DETADW: The derivative of the damage variable with respect to the elastic strain energy density of the undamaged material, $\frac{d η}{d \tilde{U}}$ . This quantity is needed for the Jacobian of the overall system of equations and needs to be defined accurately to ensure good convergence characteristics.

Variables that can be updated

DMGDISSNEW: The energy dissipation density at the end of the increment. This quantity can be defined either in total form or in an incremental manner using the old value of the damage dissipation DMGDISSOLD and the increment in damage dissipation. This quantity is used for output purposes only.
SENERNEW: The recoverable strain energy density at the end of the increment. This quantity is used for output purposes only.
STATEV: Array containing the user-defined solution-dependent state variables at this point. These are supplied as values at the start of the increment or as values updated by other user subroutines (see About user subroutines and utilities) and must be returned as values at the end of the increment.

Variables passed in for information

UMAXNEW: The value, at the end of the increment, of the maximum primary strain energy density over its entire deformation history.
UMAXOLD: The value, at the beginning of the increment, of the maximum primary strain energy density over its entire deformation history.
SEDDEV: The value, at the end of the increment, of the deviatoric primary strain energy density when the primary material behavior is hyperelastic. The value, at the end of the increment, of the total primary strain energy density when the primary material behavior is hyperfoam.
DMGDISSOLD: The value of energy dissipated at the beginning of the increment.
CMNAME: User-specified material name, left justified.
NUMSTATEV: Number of solution-dependent state variables associated with this material (defined as described in Allocating space).
NUMPROPS: Number of material properties entered for this user-defined hyperelastic material.
PROPS: Array of material properties entered for this user-defined hyperelastic material.
TEMP: Temperature at the start of the increment.
DTEMP: Increment of temperature.
NUMFIELDV: Number of field variables.
FIELDV: Array of interpolated values of predefined field variables at this material point at the beginning of the increment based on the values read in at the nodes (initial values at the beginning of the analysis and current values during the analysis).
FIELDVINC: Array of increments of predefined field variables at this material point for this increment; this includes any values updated by user subroutine USDFLD.
LINPER: Linear perturbation flag. LINPER=1 if the step is a linear perturbation step. LINPER=0 if the step is a general step.