Appendix C - MCT State Variables for Composite Materials

View specifics of the MCT state variables for composite materials.

This appendix provides a description of all solution-dependent MCT state variables. There are a total of 35 MCT state variables for unidirectional composites and 91 MCT state variables for woven composites in Abaqus/Standard. There are 17 state variables for unidirectional composites and 13 for woven composites in Abaqus/Explicit. Analyses using the progressive fatigue feature can have 31 MCT state variables for unidirectional materials and 94 MCT state variables for woven materials. These solution-dependent state variables are computed or updated by the Helius PFA User-Defined Material Subroutine at each integration point within each finite element. Click here to view the state variables used in Advanced Material Exchange.

Abaqus stores the converged values of solution-dependent MCT state variables in the same manner it stores values for typical element outputs such as stress and strain. Unless the MCT state variables are explicitly renamed via the *DEPVAR statement in the input file, the Abaqus default naming convention for the MCT solution-dependent state variables is SDVi, where i=1,2,3,…,# of state variables. This appendix provides a complete description of all MCT state variables. For both unidirectional composites and woven composites, the first state variable (SDV1) has the same interpretation; however, the interpretation of the remaining state variables (SDV2, SDV3, ...) depends on the type of composite material (unidirectional or woven) and the analysis options. The following list describes each of the MCT state variables for unidirectional and woven composite materials.

Note: A unique file (jobname.mct) is generated for each analysis. This file contains a complete list of the SDVs that apply to the particular combination of user material constants for each material in the model. This file is the best reference for understanding the meaning of each SDV.

SDV1

SDV1 (often renamed as MAT_STATE) is a real variable that represents the discrete damage state of the composite material. It assumes a finite number of discrete values between 1 and 3. The number of discrete values assumed by SDV1 and the interpretation of those discrete values depend upon the type of composite material (i.e. unidirectional or woven) and the specific set of material nonlinearity features employed to describe the material's response. The following tables provide the interpretation for each allowable discrete value of SDV1 for each possible combination of composite material type and set of material nonlinearity features.

Unidirectional Composite Material

Progressive Failure Analysis (activated)
Pre-Failure Nonlinearity (deactivated)
Energy-Based Degradation (deactivated)

Allowable Discrete Values for SDV1	Discrete Composite Damage State
1.0	Undamaged Matrix, Undamaged Fiber
2.0	Failed Matrix, Undamaged Fiber
3.0	Failed Matrix, Failed Fiber

Unidirectional Composite Material

Progressive Failure Analysis (activated)
Pre-Failure Nonlinearity (activated)
Energy-Based Degradation (deactivated)

Allowable Discrete Values for SDV1	Discrete Composite Damage State
1.0	Undamaged Matrix, Undamaged Fiber
1.25	Matrix Pre-Failure Degradation Level 1, Undamaged Fiber
1.5	Matrix Pre-Failure Degradation Level 2, Undamaged Fiber
1.75	Matrix Pre-Failure Degradation Level 3, Undamaged Fiber
2.0	Failed Matrix, Undamaged Fiber
3.0	Failed Matrix, Failed Fiber

Unidirectional Composite Material

Progressive Failure Analysis (activated)
Pre-Failure Nonlinearity (deactivated)
Energy-Based Degradation (activated)

Allowable Discrete Values for SDV1	Discrete Composite Damage State
1.0	Undamaged Matrix, Undamaged Fiber
2.0	Matrix Post-Failure Degradation Level 1, Undamaged Fiber
2.038	Matrix Post-Failure Degradation Level 2, Undamaged Fiber
...
2.923	Matrix Post-Failure Degradation Level 25, Undamaged Fiber
2.962	Failed Matrix (Crack Saturation), Undamaged Fiber
3.0	Fiber Post-Failure Degradation Level 1
3.038	Fiber Post-Failure Degradation Level 2
...
3.923	Fiber Post-Failure Degradation Level 25
3.962	Complete Fiber Failure

Unidirectional Composite Material

Progressive Failure Analysis (activated)
Pre-Failure Nonlinearity (activated)
Energy-Based Degradation (activated)

Allowable Discrete Values for SDV1	Discrete Composite Damage State
1.0	Undamaged Matrix, Undamaged Fiber
1.25	Matrix Pre-Failure Degradation Level 1, Undamaged Fiber
1.5	Matrix Pre-Failure Degradation Level 2, Undamaged Fiber
1.75	Matrix Pre-Failure Degradation Level 3, Undamaged Fiber
2.0	Matrix Post-Failure Degradation Level 1, Undamaged Fiber
2.038	Matrix Post-Failure Degradation Level 2, Undamaged Fiber
...
2.923	Matrix Post-Failure Degradation Level 25, Undamaged Fiber
2.962	Failed Matrix (Crack Saturation), Undamaged Fiber
3.0	Fiber Post-Failure Degradation Level 1
3.038	Fiber Post-Failure Degradation Level 2
...
3.923	Fiber Post-Failure Degradation Level 25
3.962	Complete Fiber Failure

Woven Composite Material

Progressive Failure Analysis (activated)
Pre-Failure Nonlinearity (deactivated)
Post-Failure Nonlinearity (not supported)
Energy-Based Degradation (not supported)

Allowable Discrete Values for SDV1	Discrete Composite Damage State
1.0	Undamaged Matrix, Undamaged Fiber
1.4	Fill Matrix Failure, Undamaged Warp
1.6	Warp Matrix Failure, Undamaged Fill
2.0	Matrix Failure in Warp and Fill
2.2	Fill Fiber and Matrix Failure, Undamaged Warp
2.3	Warp Fiber and Matrix Failure, Undamaged Fill
2.7	Fill Fiber and Matrix Failure, Warp Matrix Failure
2.8	Warp Fiber and Matrix Failure, Fill Matrix Failure
3.0	Completely Failed

Woven Composite Material

Progressive Failure Analysis (activated)
Pre-Failure Nonlinearity (activated)
Post-Failure Nonlinearity (not supported)
Energy-Based Degradation (not supported)

Allowable Discrete Values for SDV1	Discrete Composite Damage State
1.0	Undamaged Matrix, Undamaged Fiber
1.057	Matrix Pre-Failure Degradation Level 1, Undamaged Fiber
1.114	Matrix Pre-Failure Degradation Level 2, Undamaged Fiber
1.171	Matrix Pre-Failure Degradation Level 3, Undamaged Fiber
1.229	Matrix Pre-Failure Degradation Level 4, Undamaged Fiber
1.286	Matrix Pre-Failure Degradation Level 5, Undamaged Fiber
1.343	Matrix Pre-Failure Degradation Level 6, Undamaged Fiber
1.4	Fill Matrix Failure, Undamaged Warp
1.6	Warp Matrix Failure, Undamaged Fill
2.0	Matrix Failure in Warp and Fill
2.2	Fill Fiber and Matrix Failure, Undamaged Warp
2.3	Warp Fiber and Matrix Failure, Undamaged Fill
2.7	Fill Fiber and Matrix Failure, Warp Matrix Failure
2.8	Warp Fiber and Matrix Failure, Fill Matrix Failure
3.0	Completely Failed

Note: The value of SDV1 behaves differently in Abaqus/Explicit analyses. Following a fiber failure event, the stiffness of the integration point is reduced to zero over some degradation time which is specified in UMC #11. After the degradation is complete, the value of SDV1 changes from 3.0 to 0.0. Refer to Special Considerations for Abaqus/Explicit Analyses for more information.

Unidirectional Composites - Static Analyses

For unidirectional composite materials, state variables SDV2, SDV3, ..., SDV35 have the following interpretations for static progressive failure analyses:

SDV2

SDV2 is a continuous real variable that ranges from 0.0 to 1.0 and is used to indicate the fraction of the matrix failure criterion that has been satisfied. For example, SDV2 = 0.0 implies that the matrix stress state is zero, while SDV2=1.0 implies that the matrix stress state has reached failure level. Numerically, SDV2 is computed as

which is recognized as the left hand side of the matrix failure criterion (see the MCT Constituent-Based Failure Criteria section of the Theory Manual).

SDV3

SDV3 is a continuous real variable that ranges from 0.0 to 1.0 and is used to indicate the fraction of the fiber failure criterion that has been satisfied. For example, SDV3 = 0.0 implies that the fiber stress state is zero, while SDV3 = 1.0 implies that the fiber stress state has reached failure level. Numerically, SDV3 is computed as

which is recognized as the left hand side of the fiber failure criterion (see the MCT Constituent-Based Failure Criteria section of the Theory Manual).

SDV4

SDV4 is used to indicate whether the axial strain in the fiber constituent was positive or negative when fiber failure occurred. If the axial strain was positive, SDV4 = 1.0. If the axial strain was negative, SDV4 = -1.0.

SDV5

SDV5 is the fourth term in the MCT matrix failure criterion and is used in the pre-failure nonlinearity feature (see the Theory Manual). This state variable is used internally for analyses conducted in Abaqus/Explicit.

SDV6

If Energy-Based Degradation is activated, SDV6 is defined as a composite effective strain measure at fiber failure.

SDV7

If Energy-Based Degradation is activated, SDV7 is defined as a composite effective stress measure at fiber failure.

SDV8

SDV8 is a measure of the progress of degradation of the composite after a fiber failure event. If Energy-Based Degradation is not activated, SDV8 is not used.

SDV9

SDV9 is defined as a composite effective strain measure at matrix failure. If Energy-Based Degradation is not activated, SDV9 is not used.

SDV10

SDV10 is defined as a composite effective stress measure at matrix failure. If Energy-Based Degradation is not activated, SDV10 is not used.

SDV11

SDV11 is a measure of the progress of degradation of the composite after a matrix failure event. If Energy-Based Degradation is not activated, SDV11 is not used.

For the case of unidirectional composites, the remaining MCT state variables are used to store the individual components of the matrix average stress and strain states and the fiber average stress and strain states.

Unidirectional Composites - Progressive Fatigue Analyses

For unidirectional composite materials, state variables SDV2, SDV3, ..., SDV35 have the following interpretations for progressive fatigue analyses:

SDV2: SDV2 is the number of cycles accompanying the given load increment. This value is always updated unless the fiber has failed (SDV1=3.0), in which case the number of cycles to failure is set to that at fiber failure.
SDV3: SDV3 is a continuous real variable that ranges from 0.0 to 1.0 and is used to indicate damage in the form of longitudinal cracking. A value of 0.0 indicates no damage and a value of 1.0 indicates a longitudinal crack.
SDV4: SDV4 is a continuous real variable that ranges from 0.0 to 1.0 and is used to indicate damage in the form of transverse cracking. A value of 0.0 indicates no damage and a value of 1.0 indicates a transverse crack.
SDV5: SDV5 represents the material temperature for longitudinal cracking that is used for hysteresis heating computations.
SDV6: SDV6 represents the material temperature for transverse cracking that is used for hysteresis heating computations.
SDV7: Unused

For the case of a progressive fatigue analysis with unidirectional materials, SDV8 through SDV31 are used to store the individual components of the matrix average stress and strain states and the fiber average stress and strain states (equivalent to SDV12 through SDV35 for static analyses).

Woven Composites - Static Analyses

For woven composite materials, state variables SDV2, SDV3, ..., SDV91 have the following interpretations for static progressive failure analyses:

SDV2: SDV2 (also known as FI_FILL_MATRIX) is a continuous real variable that ranges from 0.0 to 1.0. It is used to indicate the fraction of the matrix failure criterion that has been satisfied for the matrix constituent within the fill tows.
SDV3: SDV3 (also known as FI_FILL_FIBER) is a continuous real variable that ranges from 0.0 to 1.0. It is used to indicate the fraction of the fiber failure criterion that has been satisfied for the fiber constituent within the fill tows.
SDV4: SDV4 (also known as FI_WARP_MATRIX) is a continuous real variable that ranges from 0.0 to 1.0. It is used to indicate the fraction of the matrix failure criterion that has been satisfied for the matrix constituent within the warp tows.
SDV5: SDV5 (also known as FI_WARP_FIBER) is a continuous real variable that ranges from 0.0 to 1.0. It is used to indicate the fraction of the fiber failure criterion that has been satisfied for the fiber constituent within the warp tows.
SDV6: Not Used
SDV7: SDV7 is the second term in the MCT matrix failure criterion for woven composites and is used in the pre-failure nonlinearity feature. SDV7 is unused if pre-failure nonlinearity is turned off.

For the case of woven composites, the remaining MCT state variables are used to store the individual components of the average stress and strain states in the various superconstituents and constituents (e.g., fill = fill tow superconstituent, warp = warp tow superconstituent, matrix-pocket = matrix constituent of the intertow matrix pockets, fill-matrix = the matrix constituent of the fill tow, warp-matrix = the matrix constituent of the warp tow, fill-fiber = the fiber constituent of the fill tow, warp-fiber = the fiber constituent of the warp tow).

Woven Composites - Progressive Fatigue Analyses

For woven composite materials, state variables SDV2, SDV3, ..., SDV91 have the following interpretations for progressive fatigue analyses:

SDV2: SDV2 is the number of cycles accompanying the given load increment. This value is always updated unless the fiber has failed (SDV1=3.0), in which case the number of cycles to failure is set to that at fiber failure.
SDV3: SDV3 is a continuous real variable that ranges from 0.0 to 1.0. It is used to indicate damage in the form of longitudinal cracking in the fill-matrix constituent. A value of 0.0 indicates no damage and a value of 1.0 indicates a longitudinal crack in the fill-matrix.
SDV4: SDV4 is a continuous real variable that ranges from 0.0 to 1.0. It is used to indicate damage in the form of transverse cracking in the fill-matrix constituent. A value of 0.0 indicates no damage and a value of 1.0 indicates a transverse crack in the fill-matrix.
SDV5: SDV5 is a continuous real variable that ranges from 0.0 to 1.0. It is used to indicate damage in the form of longitudinal cracking in the warp-matrix constituent. A value of 0.0 indicates no damage and a value of 1.0 indicates a longitudinal crack in the warp-matrix.
SDV6: SDV6 is a continuous real variable that ranges from 0.0 to 1.0. It is used to indicate damage in the form of transverse cracking in the warp-matrix constituent. A value of 0.0 indicates no damage and a value of 1.0 indicates a transverse crack in the warp-matrix.
SDV7: SDV7 represents the material temperature for longitudinal cracking in the fill-matrix constituent used for hysteresis heating computations.
SDV8: SDV8 represents the material temperature for transverse cracking in the fill-matrix constituent used for hysteresis heating computations.
SDV9: SDV9 represents the material temperature for longitudinal cracking in the warp-matrix constituent used for hysteresis heating computations.
SDV10: SDV10 represents the material temperature for transverse cracking in the warp-matrix constituent used for hysteresis heating computations.

For the case of a progressive fatigue analysis with woven materials, SDV11 through SDV94 are used to store the individual components of the average stress and strain states in the various superconstituents and constituents (equivalent to SDV8 through SDV91 for static analyses).