5.3. Cohesive Zone Material Models

Several material models are available for use with cohesive zone elements or with Dash contact. These models are described in this section.

Traction separation models used for cohesive surface elements are input within BEGIN MATERIAL blocks in the same manner as continuum models. Although density is not a property used by cohesive zone elements, because of their specification within this block, all of these models currently require a density to be provided as part of their input. Output variables for Cohesive Zones can be found in Table Table 9.21. NOTE: while some of the variables do have x, y, and z components they are not related to the global coordinate system, but instead are related to normal and tangential directions.

5.3.1. Traction Decay

BEGIN PARAMETERS FOR MODEL TRACTION_DECAY
  NORMAL DECAY LENGTH = <real>
  TANGENTIAL DECAY LENGTH = <real>
END [PARAMETERS FOR MODEL TRACTION_DECAY]

The Traction Decay cohesive model is a simple model that gets initialized with a traction upon activation or insertion of the cohesive element. The traction then decays to zero over specified values of normal and tangential separation. This model is only valid to use in conjunction with dynamic cohesive zone activation through MPC deactivation or dynamic insertion of cohesive surface elements.

In the above command block:

  • The density of the material is defined with the DENSITY command line. Although this is not used in the model, it is currently a required input parameter.

  • The separation length over which the normal traction decays to zero is set by the NORMAL DECAY LENGTH command line.

  • The separation length over which the tangential traction decays to zero is set by the TANGENTIAL DECAY LENGTH command line.

The state variables for this model are listed in Table Section 5.3.1.

Table 5.31 State Variables for TRACTION DECAY Surface Model (Section 5.3.1)

Index

Name

Variable Description

0

MAX_SEPARATION_S

maximum separation in the first tangential direction

1

MAX_SEPARATION_T

maximum separation in the second tangential direction

2

MAX_SEPARATION_N

maximum separation in the normal direction

5.3.2. Tvergaard Hutchinson

BEGIN PARAMETERS FOR MODEL TVERGAARD_HUTCHINSON
  INIT TRACTION METHOD = {IGNORE|ADD|EXTRINSIC} (IGNORE)
  LAMBDA_1 = <real>
  LAMBDA_2 = <real>
  NORMAL LENGTH SCALE = <real>
  TANGENTIAL LENGTH SCALE = <real>
  PEAK TRACTION = <real>
  PENETRATION STIFFNESS MULTIPLIER = <real>
  USE ELASTIC UNLOADING = {NO|YES} (YES)
END [PARAMETERS FOR MODEL TVERGAARD_HUTCHINSON]

The Tvergaard Hutchinson cohesive model combines the normal and tangential separation into a single normalized separation and calculates a traction per unit length based on this value. This model then calculates normal and tangential traction based on the ratio of the normal and tangential length scales.

In the above command blocks:

  • For dynamically activated or dynamically inserted cohesive surface elements, an initial traction can be used to initialize the traction-separation model based on element properties specified in the ELEMENT DEATH or XFEM block. This is set via the INIT TRACTION METHOD. The default behavior is to ignore any initial tractions and let the traction-separation law dictate the behavior. Note that this does not maintain equilibrium upon cohesive element insertion. The ADD method offsets the traction-separation law by the initiation traction, which is linearly scaled to zero under further loading. The EXTRINSIC method initializes the state of the traction-separation law along the hardening branch. In the case that the initialization traction is greater than the specified peak traction, the traction-separation law is evaluated from the beginning of the traction plateau with the peak traction value rese to the initialization traction. Both the ADD and EXTRINSIC methods maintain equilibrium upon cohesive element insertion.

  • LAMBDA_1 indicates the normalized separation at which the traction response flattens with an additional increase in separation.

  • LAMBDA_2 indicates the normalized separation at which the traction begins to degrade with an additional increase in separation.

  • The separation at which failure occurs in the normal direction is prescribed using the NORMAL LENGTH SCALE command.

  • The maximum traction is specified through the PEAK TRACTION command.

  • The separation at which failure occurs in the tangential direction is prescribed using the TANGENTIAL LENGTH SCALE command.

  • The PENETRATION STIFFNESS MULTIPLIER command artificially increases the normal traction to help prevent interpenetration of cohesive surfaces when crack closure occurs. However, cohesive elements are not equipped to handle compression, and this penalty stiffness is an ad hoc approach to contact.

  • Set the USE ELASTIC UNLOADING command to YES to force this model to unload elastically.

The state variables for this model are listed in Table Table 5.32.

Table 5.32 State Variables for TVERGAARD HUTCHINSON Surface Model (Section 5.3.2)

Index

Name

Variable Description

1

PEAK_TRACTION

maximum traction the model can experience

2

LAMBDA_MAX

maximum lambda the model has experienced

3

TRACTION_AT_LAMBDA_MAX

traction at LAMBDA_MAX

4

G_AT_LAMBDA_MAX

the area under the traction separation curve up to LAMBDA_MAX

5.3.3. Thouless Parmigiani

BEGIN PARAMETERS FOR MODEL THOULESS_PARMIGIANI
  INIT TRACTION METHOD = {IGNORE|ADD|EXTRINSIC} (IGNORE)
  LAMBDA_1_N = <real>
  LAMBDA_1_T = <real>
  LAMBDA_2_N = <real>
  LAMBDA_2_T = <real>
  NORMAL LENGTH SCALE = <real>
  PEAK NORMAL TRACTION = <real>
  TANGENTIAL LENGTH SCALE = <real>
  PEAK TANGENTIAL TRACTION = <real>
  PENETRATION STIFFNESS MULTIPLIER = <real>
  USE ELASTIC UNLOADING = {NO|YES} (YES)
END [PARAMETERS FOR MODEL THOULESS_PARMIGIANI]

The Thouless Parmigiani model supports mixed-mode fracture more accurately than the Tvergaard Hutchinson model by separating the normal and tangential components, allowing one to fail independently of the other. Failure of this model is dependent on the energy release of both normal and tangential components. The shape of the traction-separation curve for this model is hardening, followed by a plateau, followed by softening.

In the above command block:

  • For dynamically activated or dynamically inserted cohesive surface elements, an initial traction can be used to initialize the traction-separation model based on element properties specified in the ELEMENT DEATH or XFEM block. This is set via the INIT TRACTION METHOD. The default behavior is to ignore any initial tractions and let the traction-separation law dictate the behavior. Note that this does not maintain equilibrium upon cohesive element insertion. The ADD method offsets the traction-separation law by the initiation traction, which is linearly scaled to zero under further loading. The EXTRINSIC method initializes the state of the traction-separation law along the hardening branch. In the case that the initialization traction is greater than the specified peak traction, the traction-separation law is evaluated from the beginning of the traction plateau with the peak traction value rese to the initialization traction. Both the ADD and EXTRINSIC methods maintain equilibrium upon cohesive element insertion.

  • LAMBDA_1_N indicates the normalized normal separation at which the traction response flattens with an additional increase in separation.

  • LAMBDA_1_T indicates the normalized tangential separation at which the traction response flattens with an additional increase in separation.

  • LAMBDA_2_N indicates the normalized normal separation at which the traction begins to decrease with an additional increase in separation.

  • LAMBDA_2_T indicates the normalized tangential separation at which the traction begins to decrease with an additional increase in separation.

  • The separation at which failure occurs in the normal direction is prescribed using the NORMAL LENGTH SCALE command.

  • The maximum normal traction is specified through the PEAK NORMAL TRACTION command.

  • The separation at which failure occurs in the tangential direction is prescribed using the TANGENTIAL LENGTH SCALE command.

  • The maximum tangential traction is specified through the PEAK TANGENTIAL TRACTION command.

  • The PENETRATION STIFFNESS MULTIPLIER command artificially increases the normal traction to help prevent interpenetration of cohesive surfaces when crack closure occurs. However, cohesive elements are not equipped to handle compression, and this penalty stiffness is an ad hoc approach to contact.

  • Set the USE ELASTIC UNLOADING command to YES to force this model to unload elastically.

The state variables for this model are listed in Table Table 5.33.

Table 5.33 State Variables for THOULESS PARMIGIANI Surface Model (Section 5.3.3)

Index

Name

Variable Description

1

FRACTION_OF_FAILURE

current fraction of failure

2

PEAK_TRACTION_N

maximum normal traction the model can experience

3

PEAK_TRACTION_T

maximum tangential traction the model can experience

4

LAMBDA_MAX_N

maximum normal lambda the model has experienced

5

TRACTION_AT_LAMBDA_MAX_N

normal traction at LAMBDA_MAX_N

6

LAMBDA_MAX_T

maximum tangential lambda the model has experienced

7

TRACTION_AT_LAMBDA_MAX_T

tangential traction at LAMBDA_MAX_T

8

G_AT_LAMBDA_MAX_N

the area under the normal traction separation curve up to LAMBDA_MAX_N

9

G_AT_LAMBDA_MAX_T

the area under the tangential traction separation curve up to LAMBDA_MAX_T

5.3.4. Functional Interface Traction

BEGIN PARAMETERS FOR MODEL FUNCTIONAL_INTERFACE_TRACTION
  NORMAL LENGTH SCALE = <real> (1.0)
  TANGENTIAL LENGTH SCALE = <real> (1.0)
  NORMAL TRACTION FUNCTION = <string>
  TANGENTIAL TRACTION FUNCTION = <string>
END [PARAMETERS FOR MODEL FUNCTIONAL_INTERFACE_TRACTION]

The Functional Interface Traction model allows a general normal and tangential traction response law. The normal and tangential components of the traction are defined as functions of the normal and tangential components, respectively, of the separation displacement (appropriately normalized). The traction is evaluated given a separation displacement and subsequently applied. (Note: This model does not presently support some of the features of the other cohesive zone material models, such as elastic unloading and failure.)

The command block for the Functional Interface Traction model starts with the line:

BEGIN PARAMETERS FOR MODEL FUNCTIONAL_INTERFACE_TRACTION

and terminates with the line:

END [PARAMETERS FOR MODEL FUNCTIONAL_INTERFACE_TRACTION]

In the above command block:

  • The density of the material is defined with the DENSITY command line. Although this is not used in the model, it is currently a required input parameter.

  • The separation scale in the normal direction is specified using the NORMAL LENGTH SCALE command. This is not strictly necessary as this scaling may instead be effected directly within the normal traction response function. It is only provided for similarity with the other cohesive zone material models.

  • The separation scale in the tangential direction is specified using the TANGENTIAL LENGTH SCALE command. This is not strictly necessary as this scaling may instead be effected directly within the tangential traction response function. It is only provided for similarity with the other cohesive zone material models.

  • The normal traction response as a function of the (normalized) normal component of the separation displacement is specified through the NORMAL TRACTION FUNCTION command.

  • The tangential traction response as a function of the (normalized) tangential component of the separation displacement is specified through the TANGENTIAL TRACTION FUNCTION command.

5.3.5. Alves-Roehl

begin parameters for model quadshell_model_alves_roehl
  NORMAL LENGTH SCALE = <real>
  TANGENTIAL LENGTH SCALE 1 = <real>
  TANGENTIAL LENGTH SCALE 2 = <real>
  ROTATIONAL LENGTH SCALE = <real>

  # normal work of separation
  NORMAL WOS = <real>

  # tangential work of separation
  TANGENTIAL WOS 1 = <real>
  TANGENTIAL WOS 2 = <real>

  # rotational work of separation
  ROTATIONAL WOS = <real>

  USE ELASTIC UNLOADING = {NO|YES} (YES)
end

In the above command block:

  • The separation at which failure occurs in the normal direction is prescribed using the NORMAL LENGTH SCALE command.

  • The separation scale in the tangential direction 1 is specified using the TANGENTIAL LENGTH SCALE 1 command.

  • The separation scale in the tangential direction 2 is specified using the TANGENTIAL LENGTH SCALE 1 command.

  • The characteristic length for rotational bending is prescribed using the ROTATIONAL LENGTH SCALE command.

  • The normal work of separation (WOS) in the normal direction is set using the NORMAL WOS command.

  • The tangential work of separation in the tangential direction 1 is set using the TANGENTIAL WOS 1 command.

  • The tangential work of separation in the tangential direction 2 is set using the TANGENTIAL WOS 2 command.

  • The rotational work of separation (WOS) is set using the ROTATIONAL WOS command.

  • Set the USE ELASTIC UNLOADING command to YES to force this model to unload elastically.