# *DAMAGE EVOLUTION

 Specify material properties to define the evolution of damage. This option is used to provide material properties that define the evolution of damage leading to eventual failure. It must be used in conjunction with the DAMAGE INITIATION option. It can be utilized for materials defined for cohesive elements, for enriched elements, for elements with plane stress formulations (plane stress, shell, continuum shell, and membrane elements) used with the damage model for fiber-reinforced materials, for ductile bulk materials associated with any element type in a low-cycle fatigue analysis, and, in Abaqus/Explicit, for elastic-plastic materials associated with any element type. It can also be used in conjunction with the SURFACE INTERACTION and DAMAGE INITIATION options to define a contact property model that allows modeling of progressive failure for cohesive surfaces.
 Related Topics In Other Guides Damage evolution and element removal for ductile metals Damage evolution and element removal for fiber-reinforced composites Damage evolution for ductile materials in low-cycle fatigue Defining the constitutive response of cohesive elements using a traction-separation description Contact cohesive behavior Modeling discontinuities as an enriched feature using the extended finite element method

ProductsAbaqus/StandardAbaqus/ExplicitAbaqus/CAE

TypeModel data

LevelModel

Abaqus/CAEProperty module

## Required parameters

TYPE

Set TYPE=DISPLACEMENT to define the evolution of damage as a function of the total (for elastic materials in cohesive elements) or the plastic (for bulk elastic-plastic materials) displacement after the initiation of damage.

Set TYPE=ENERGY to define the evolution of damage in terms of the energy required for failure (fracture energy) after the initiation of damage.

Set TYPE=HYSTERESIS ENERGY to define the evolution of damage in terms of the inelastic hysteresis energy dissipated per stabilized cycle after the initiation of damage in a low-cycle fatigue analysis.

## Optional parameters

Set DEGRADATION=MAXIMUM (default) to specify that the current damage evolution mechanism will interact with other damage evolution mechanisms in a maximum sense to determine the total damage from multiple mechanisms.

Set DEGRADATION=MULTIPLICATIVE to specify that the current damage evolution mechanism will interact with other damage evolution mechanisms using the same value of the DEGRADATION parameter in a multiplicative manner to determine the total damage from multiple mechanisms.

DEPENDENCIES

Set this parameter equal to the number of field variables included in the definition of damage evolution. If this parameter is omitted, it is assumed that properties defining the evolution of damage are constant or depend only on temperature. See Material data definition for more information.

FAILURE INDEX

This parameter can be used only in conjunction with the user-defined damage initiation criterion.

Set this parameter equal to the corresponding failure mechanism specified in the user-defined damage initiation criterion for enriched elements.

MIXED MODE BEHAVIOR

This parameter is meaningful only when the DAMAGE EVOLUTION option is used to define the evolution of damage for materials associated with cohesive elements or for surface-based cohesive behavior. If this parameter is omitted, Abaqus assumes that the damage evolution behavior is mode independent.

Set MIXED MODE BEHAVIOR=TABULAR to specify the fracture energy or displacement (total or plastic) directly as a function of the shear-normal mode mix for cohesive elements. This method must be used to specify the mixed-mode behavior for cohesive elements when TYPE=DISPLACEMENT.

Set MIXED MODE BEHAVIOR=POWER LAW to specify the fracture energy as a function of the mode mix by means of a power law mixed mode fracture criterion.

Set MIXED MODE BEHAVIOR=BK to specify the fracture energy as a function of the mode mix by means of the Benzeggagh-Kenane mixed mode fracture criterion.

MODE MIX RATIO

This parameter can be used only in conjunction with the MIXED MODE BEHAVIOR parameter. The specification of the damage evolution properties (fracture energy or effective displacement) as a function of the mode mix depends on the value of this parameter. See Defining damage evolution data as a tabular function of mode mix or Defining damage evolution data as a tabular function of mode mix for further details.

Set MODE MIX RATIO=ENERGY (default for surface-based cohesive behavior in Abaqus/Standard and for materials associated with cohesive elements) to define the mode mix in terms of a ratio of fracture energy in the different modes. The fracture energy is computed based on the current state of deformation only, not the deformation history. This option can be used when MIXED MODE BEHAVIOR=POWER LAW or BK. This option is not available for surface-based cohesive behavior in Abaqus/Explicit.

Set MODE MIX RATIO=ACCUMULATED ENERGY (default for surface-based cohesive behavior in Abaqus/Explicit) to define the mode mix in terms of a ratio of fracture energy in the different modes. The fracture energy is computed based on the energy accumulated over the entire deformation history at an integration point. This option can be used when MIXED MODE BEHAVIOR=POWER LAW or BK.

Set MODE MIX RATIO=TRACTION to define the mode mix in terms of a ratio of traction components.

POWER

This parameter can be used only in conjunction with MIXED MODE BEHAVIOR=POWER LAW or MIXED MODE BEHAVIOR=BK.

Set this parameter equal to the exponent in the power law or the Benzeggagh-Kenane criterion that defines the variation of fracture energy with mode mix for cohesive elements.

RATE DEPENDENT

This parameter can be used only in conjunction with the DAMAGE INITIATION option used with CRITERION=MAXE, CRITERION=MAXS, CRITERION=QUADE, or CRITERION=QUADS for cohesive elements with traction separation behavior in Abaqus/Explicit.

Include this parameter to define the damage evolution criterion as a function of the effective rate of separation.

SOFTENING

Set SOFTENING=LINEAR (default) to specify a linear softening stress-strain response (after the initiation of damage) for linear elastic materials or a linear evolution of the damage variable with deformation (after the initiation of damage) for elastic-plastic materials.

Set SOFTENING=EXPONENTIAL to specify an exponential softening stress-strain response (after the initiation of damage) for linear elastic materials or an exponential evolution of the damage variable with deformation (after the initiation of damage) for elastic-plastic materials.

Set SOFTENING=TABULAR to specify the evolution of the damage variable with deformation (after the initiation of damage) in tabular form. SOFTENING=TABULAR can be used only in conjunction with TYPE=DISPLACEMENT.

## Data lines to specify damage evolution for TYPE=DISPLACEMENT, SOFTENING=LINEAR without the MIXED MODE BEHAVIOR and the RATE DEPENDENT parameters

First line
1. Effective total or plastic displacement at failure, measured from the time of damage initiation.

2. Temperature, if temperature dependent.

3. First field variable.

4. Second field variable.

5. Etc., up to six field variables.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than six)
1. Seventh field variable.

2. Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the total or the plastic displacement at failure as a function of temperature and other predefined field variables.

## Data lines to specify damage evolution for TYPE=DISPLACEMENT, SOFTENING=LINEAR, RATE DEPENDENT without the MIXED MODE BEHAVIOR parameter

First line
1. Effective total or plastic displacement at failure, measured from the time of damage initiation.

2. Effective rate of separation.

3. Temperature, if temperature dependent.

4. First field variable.

5. Second field variable.

6. Etc., up to six field variables.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than six)
1. Seventh field variable.

2. Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the total or the plastic displacement at failure as a function of temperature and other predefined field variables.

## Data lines to specify damage evolution for TYPE=ENERGY, SOFTENING=LINEAR without the MIXED MODE BEHAVIOR and the RATE DEPENDENT parameters

First line
1. Fracture energy.

2. Temperature, if temperature dependent.

3. First field variable.

4. Second field variable.

5. Etc., up to six field variables.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than six)
1. Seventh field variable.

2. Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the fracture energy as a function of temperature and other predefined field variables.

## Data lines to specify damage evolution for TYPE=ENERGY, SOFTENING=LINEAR, RATE DEPENDENT without the MIXED MODE BEHAVIOR parameter

First line
1. Fracture energy.

2. Effective rate of separation.

3. Temperature, if temperature dependent.

4. First field variable.

5. Second field variable.

6. Etc., up to six field variables.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than six)
1. Seventh field variable.

2. Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the fracture energy as a function of temperature and other predefined field variables.

## Data lines to specify damage evolution for TYPE=DISPLACEMENT, SOFTENING=LINEAR, MIXED MODE BEHAVIOR=TABULAR and without the RATE DEPENDENT parameter

First line
1. Total displacement at failure, measured from the time of damage initiation.

2. Appropriate mode mix ratio.

3. Appropriate mode mix ratio (if relevant, for three-dimensional problems with anisotropic shear behavior).

4. Temperature, if temperature dependent.

5. First field variable.

6. Second field variable.

7. Etc., up to four field variables.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than four)
1. Fifth field variable.

2. Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the total displacement at failure as a function of mode mix, temperature, and other predefined field variables.

## Data lines to specify damage evolution for TYPE=DISPLACEMENT, SOFTENING=LINEAR, MIXED MODE BEHAVIOR=TABULAR, RATE DEPENDENT

First line
1. Total displacement at failure, measured from the time of damage initiation.

2. Appropriate mode mix ratio.

3. Appropriate mode mix ratio (if relevant, for three-dimensional problems with anisotropic shear behavior).

4. Effective rate of separation.

5. Temperature, if temperature dependent.

6. First field variable.

7. Second field variable.

8. Etc., up to four field variables.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than four)
1. Fifth field variable.

2. Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the total displacement at failure as a function of mode mix, temperature, and other predefined field variables.

## Data lines to specify damage evolution for TYPE=ENERGY, SOFTENING=LINEAR, MIXED MODE BEHAVIOR=TABULAR and without the RATE DEPENDENT parameter

First line
1. Fracture energy.

2. Appropriate mode mix ratio.

3. Appropriate mode mix ratio (if relevant, for three-dimensional problems with anisotropic shear behavior).

4. Temperature, if temperature dependent.

5. First field variable.

6. Second field variable.

7. Etc., up to four field variables.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than four)
1. Fifth field variable.

2. Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the fracture energy as a function of mode mix, temperature, and other predefined field variables.

## Data lines to specify damage evolution for TYPE=ENERGY, SOFTENING=LINEAR, MIXED MODE BEHAVIOR=TABULAR, RATE DEPENDENT

First line
1. Fracture energy.

2. Appropriate mode mix ratio.

3. Appropriate mode mix ratio (if relevant, for three-dimensional problems with anisotropic shear behavior).

4. Effective rate of separation.

5. Temperature, if temperature dependent.

6. First field variable.

7. Second field variable.

8. Etc., up to four field variables.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than four)
1. Fifth field variable.

2. Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the fracture energy as a function of mode mix, temperature, and other predefined field variables.

## Data lines to specify damage evolution for TYPE=DISPLACEMENT, SOFTENING=EXPONENTIAL without the MIXED MODE BEHAVIOR and the RATE DEPENDENT parameters

First line
1. Effective total or plastic displacement at failure, measured from the time of damage initiation.

2. Exponential law parameter.

3. Temperature, if temperature dependent.

4. First field variable.

5. Second field variable.

6. Etc., up to five field variables.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than five)
1. Sixth field variable.

2. Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the total or the plastic displacement at failure and the exponential law parameter as a function of temperature and other predefined field variables.

## Data lines to specify damage evolution for TYPE=DISPLACEMENT, SOFTENING=EXPONENTIAL, RATE DEPENDENT without the MIXED MODE BEHAVIOR parameter

First line
1. Effective total or plastic displacement at failure, measured from the time of damage initiation.

2. Exponential law parameter.

3. Effective rate of separation.

4. Temperature, if temperature dependent.

5. First field variable.

6. Second field variable.

7. Etc., up to five field variables.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than five)
1. Sixth field variable.

2. Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the total or the plastic displacement at failure and the exponential law parameter as a function of temperature and other predefined field variables.

## Data lines to specify damage evolution for TYPE=ENERGY, SOFTENING=EXPONENTIAL without the MIXED MODE BEHAVIOR and the RATE DEPENDENT parameters

First line
1. Fracture energy.

2. Temperature, if temperature dependent.

3. First field variable.

4. Second field variable.

5. Etc., up to six field variables.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than six)
1. Seventh field variable.

2. Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the fracture energy as a function of temperature and other predefined field variables.

## Data lines to specify damage evolution for TYPE=ENERGY, SOFTENING=EXPONENTIAL, RATE DEPENDENT without the MIXED MODE BEHAVIOR parameter

First line
1. Fracture energy.

2. Effective rate of separation.

3. Temperature, if temperature dependent.

4. First field variable.

5. Second field variable.

6. Etc., up to six field variables.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than six)
1. Seventh field variable.

2. Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the fracture energy as a function of temperature and other predefined field variables.

## Data lines to specify damage evolution for TYPE=DISPLACEMENT, SOFTENING=EXPONENTIAL, MIXED MODE BEHAVIOR=TABULAR and without the RATE DEPENDENT parameter

First line
1. Total displacement at failure, measured from the time of damage initiation.

2. Exponential law parameter.

3. Appropriate mode mix ratio.

4. Appropriate mode mix ratio (if relevant, for three-dimensional problems with anisotropic shear behavior).

5. Temperature, if temperature dependent.

6. First field variable.

7. Second field variable.

8. Third field variable.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than three)
1. Fourth field variable.

2. Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the total displacement at failure and the exponential law parameter as a function of mode mix, temperature, and other predefined field variables.

## Data lines to specify damage evolution for TYPE=DISPLACEMENT, SOFTENING=EXPONENTIAL, MIXED MODE BEHAVIOR=TABULAR, RATE DEPENDENT

First line
1. Total displacement at failure, measured from the time of damage initiation.

2. Exponential law parameter.

3. Appropriate mode mix ratio.

4. Appropriate mode mix ratio (if relevant, for three-dimensional problems with anisotropic shear behavior).

5. Effective rate of separation.

6. Temperature, if temperature dependent.

7. First field variable.

8. Second field variable.

9. Third field variable.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than three)
1. Fourth field variable.

2. Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the total displacement at failure and the exponential law parameter as a function of mode mix, temperature, and other predefined field variables.

## Data lines to specify damage evolution for TYPE=ENERGY, SOFTENING=EXPONENTIAL, MIXED MODE BEHAVIOR=TABULAR and without the RATE DEPENDENT parameter

First line
1. Fracture energy.

2. Appropriate mode mix ratio.

3. Appropriate mode mix ratio (if relevant, for three-dimensional problems with anisotropic shear behavior).

4. Temperature, if temperature dependent.

5. First field variable.

6. Second field variable.

7. Etc., up to four field variables.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than four)
1. Fifth field variable.

2. Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the fracture energy as a function of mode mix, temperature, and other predefined field variables.

## Data lines to specify damage evolution for TYPE=ENERGY, SOFTENING=EXPONENTIAL, MIXED MODE BEHAVIOR=TABULAR, RATE DEPENDENT

First line
1. Fracture energy.

2. Appropriate mode mix ratio.

3. Appropriate mode mix ratio (if relevant, for three-dimensional problems with anisotropic shear behavior).

4. Effective rate of separation.

5. Temperature, if temperature dependent.

6. First field variable.

7. Second field variable.

8. Etc., up to four field variables.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than four)
1. Fifth field variable.

2. Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the fracture energy as a function of mode mix, temperature, and other predefined field variables.

## Data lines to specify damage evolution for TYPE=DISPLACEMENT, SOFTENING=TABULAR without the MIXED MODE BEHAVIOR and the RATE DEPENDENT parameters

First line
1. Damage variable.

2. Effective total or plastic displacement, measured from the time of damage initiation.

3. Temperature, if temperature dependent.

4. First field variable.

5. Second field variable.

6. Etc., up to five field variables.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than five)
1. Sixth field variable.

2. Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the damage variable as a function of the total or the plastic displacement, temperature, and other predefined field variables.

## Data lines to specify damage evolution for TYPE=DISPLACEMENT, SOFTENING=TABULAR, RATE DEPENDENT without the MIXED MODE BEHAVIOR parameter

First line
1. Damage variable.

2. Effective total or plastic displacement, measured from the time of damage initiation.

3. Effective rate of separation.

4. Temperature, if temperature dependent.

5. First field variable.

6. Second field variable.

7. Etc., up to five field variables.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than five)
1. Sixth field variable.

2. Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the damage variable as a function of the total or the plastic displacement, temperature, and other predefined field variables.

## Data lines to specify damage evolution for TYPE=DISPLACEMENT, SOFTENING=TABULAR, MIXED MODE BEHAVIOR=TABULAR and without the RATE DEPENDENT parameter

First line
1. Damage variable.

2. Effective total displacement, measured from the time of damage initiation.

3. Appropriate mode mix ratio.

4. Appropriate mode mix ratio (if relevant, for three-dimensional problems with anisotropic shear behavior).

5. Temperature, if temperature dependent.

6. First field variable.

7. Second field variable.

8. Third field variable.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than three)
1. Fourth field variable.

2. Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the damage variable as a function of the total displacement, mode mix, temperature, and other predefined field variables.

## Data lines to specify damage evolution for TYPE=DISPLACEMENT, SOFTENING=TABULAR, MIXED MODE BEHAVIOR=TABULAR, RATE DEPENDENT

First line
1. Damage variable.

2. Effective total displacement, measured from the time of damage initiation.

3. Appropriate mode mix ratio.

4. Appropriate mode mix ratio (if relevant, for three-dimensional problems with anisotropic shear behavior).

5. Effective rate of separation.

6. Temperature, if temperature dependent.

7. First field variable.

8. Second field variable.

9. Third field variable.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than three)
1. Fourth field variable.

2. Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the damage variable as a function of the total displacement, mode mix, temperature, and other predefined field variables.

## Data lines to specify damage evolution for TYPE=ENERGY, SOFTENING=LINEAR or EXPONENTIAL, MIXED MODE BEHAVIOR=POWER LAW or BK and without the RATE DEPENDENT parameter

First line
1. Normal mode fracture energy.

2. Shear mode fracture energy for failure in the first shear direction.

3. Shear mode fracture energy for failure in the second shear direction.

4. Temperature, if temperature dependent.

5. First field variable.

6. Second field variable.

7. Etc., up to four field variables.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than four)
1. Fifth field variable.

2. Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the fracture energy as a function of temperature and other predefined field variables.

## Data lines to specify damage evolution for TYPE=ENERGY, SOFTENING=LINEAR or EXPONENTIAL, MIXED MODE BEHAVIOR=POWER LAW or BK, RATE DEPENDENT

First line
1. Normal mode fracture energy.

2. Shear mode fracture energy for failure in the first shear direction.

3. Shear mode fracture energy for failure in the second shear direction.

4. Effective rate of separation.

5. Temperature, if temperature dependent.

6. First field variable.

7. Second field variable.

8. Etc., up to four field variables.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than four)
1. Fifth field variable.

2. Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the fracture energy as a function of temperature and other predefined field variables.

## Data lines to specify damage evolution for TYPE=ENERGY, SOFTENING=LINEAR for the damage model for fiber-reinforced materials

First line
1. Fracture energy of the lamina in the longitudinal tensile direction.

2. Fracture energy of the lamina in the longitudinal compressive direction.

3. Fracture energy of the lamina in the transverse tensile direction.

4. Fracture energy of the lamina in the transverse compressive direction.

5. Temperature, if temperature dependent.

6. First field variable.

7. Second field variable.

8. Third field variable.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than three)
1. Fourth field variable.

2. Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the dependence of fracture energies on temperature and other predefined field variables.

## Data lines to specify damage evolution for TYPE=HYSTERESIS ENERGY in a low-cycle fatigue analysis

First line
1. Material constant $c3$. (Units of $L/C⁢Y⁢C⁢L⁢E/Fc4⁢L-2⁢c4$)

2. Material constant $c4$.

3. Temperature, if temperature dependent.

4. First field variable.

5. Second field variable.

6. Etc., up to five field variables per line.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than five)
1. Sixth field variable.

2. Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the dependence of material constants on temperature and other predefined field variables.