MultiPhysicsVault/.raw/AbaqusAnalysisUserGuide5/AbaqusAnalysisUserGuide5_070.md

The spot-welded nodes in node set WELDS are a subset of the nodes on surface A, which is the slave surface of the pure master-slave contact pair.

*NSET, NSET=WELDS node set definition *CONTACT PAIR, MECHANICAL CONSTRAINT=KINEMATIC, INTERACTION=A TO B, WEIGHT=0. slave surface A, master surface B *SURFACE INTERACTION, NAME=A TO B *BOND WELDS, F_{f}^{n} , F_{f}^{s} , d_{b} , T_{f} , u_{f}^{n} , u_{f}^{s} *OUTPUT, HISTORY, TIME INTERVAL=0.001 *CONTACT OUTPUT, NSET=WELDS BONDSTAT, BONDLOAD

Here T _ { f } must be specified if the time to failure model is used, or \boldsymbol { u } _ { f } ^ { n } and \boldsymbol { u } _ { f } ^ { s } must be specified if the damaged failure model is chosen.

37.1.10 SURFACE-BASED COHESIVE BEHAVIOR

Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE

References

• “Progressive damage and failure,” Section 24.1.1
• “Defining the constitutive response of cohesive elements using a traction-separation description,” Section 32.5.6
• “Defining contact pairs in Abaqus/Standard,” Section 36.3.1
• “Defining general contact interactions in Abaqus/Explicit,” Section 36.4.1
• “Mechanical contact properties: overview,” Section 37.1.1
• “Crack propagation analysis,” Section 11.4.3
• *COHESIVE BEHAVIOR
• *SURFACE INTERACTION
• *DAMAGE INITIATION
• *DAMAGE EVOLUTION
• *DAMAGE STABILIZATION
• *FRACTURE CRITERION
• “Specifying cohesive behavior properties for mechanical contact property options” in “Defining a contact interaction property,” Section 15.14.1 of the Abaqus/CAE User’s Guide, in the HTML version of this guide
• “Specifying cohesive damage properties for mechanical contact property options” in “Defining a contact interaction property,” Section 15.14.1 of the Abaqus/CAE User’s Guide, in the HTML version of this guide

Overview

The features described in this section allow the specification of generalized traction-separation behavior for surfaces. This behavior offers capabilities that are very similar to cohesive elements that are defined using a traction-separation law (see “Defining the constitutive response of cohesive elements using a traction-separation description,” Section 32.5.6). However, surface-based cohesive behavior is typically easier to define and allows simulation of a wider range of cohesive interactions, such as two “sticky” surfaces coming into contact during an analysis.

Surface-based cohesive behavior is primarily intended for situations in which the interface thickness is negligibly small. If the interface adhesive layer has a finite thickness and macroscopic properties (such as stiffness and strength) of the adhesive material are available, it may be more appropriate to model the response using conventional cohesive elements (see “Defining the constitutive response of cohesive elements using a continuum approach,” Section 32.5.5).

In Abaqus/Explicit the surface-based cohesive behavior framework can also be used to model crack propagation in initially partially bonded surfaces via linear elastic fracture mechanics principles (LEFM) as implemented using the Virtual Crack Closure Technique (VCCT).

Surface-based cohesive behavior:

• is defined as a surface interaction property;
• can be used to model the delamination at interfaces directly in terms of traction versus separation;
• can be used to model “sticky” contact (i.e., surfaces or parts of surfaces that are not initially in contact may bond on coming into contact; subsequently the bond may damage and fail);
• can be restricted to surface regions that are initially in contact and, in Abaqus/Standard, to portions of surface regions that are initially in contact;
• allows specification of cohesive data such as the fracture energy as a function of the ratio of normal to shear displacements (mode mix) at the interface;
• assumes a linear elastic traction-separation law prior to damage;
• assumes that failure of the cohesive bond is characterized by progressive degradation of the cohesive stiffness, which is driven by a damage process (in Abaqus/Explicit brittle fracture can also be modeled using a VCCT fracture crierion);
• allows specification of postfailure cohesive behavior if failed nodes re-enter contact;
• is implemented within the general contact algorithmic framework in Abaqus/Explicit and within the contact pair framework in Abaqus/Standard;
• can be used to enforce “rough friction” surface interactions, the “no separation” contact relationship, or a combined “no separation and rough friction” behavior within the general contact framework in Abaqus/Explicit;
• is enforced only for node-to-face contact interactions in Abaqus/Explicit and is not available for edge-to-edge and node-to-analytical rigid surface contact interactions;
• cannot be used in a coupled Eulerian-Lagrangian analysis in Abaqus/Explicit; and
• can be used for all Abaqus/Standard contact formulations except the finite sliding, surface-to-surface formulation;
• is an alternative way to tie surfaces in Abaqus/Explicit, especially if the surfaces are offset from one another.

Defining cohesive behavior in Abaqus/Explicit

Cohesive behavior in Abaqus/Explicit is defined as part of the surface interaction properties that are assigned to the applicable surfaces. General contact must be defined for the model.

Input File Usage:

Use the following options to define cohesive behavior between two surfaces in a general contact definition:

*SURFACE INTERACTION, NAME=name

*COHESIVE BEHAVIOR

*CONTACT

*CONTACT PROPERTY ASSIGNMENT

surface1, surface2, name

Abaqus/CAE Usage: Use the following option to define cohesive behavior between two surfaces:

Interaction module: contact property editor: Mechanical→Cohesive Behavior

Use the following option to define contact between two surfaces:

Interaction module: interaction editor: General contact (Explicit): specify Contact interaction property

Contact formulation for cohesive behavior in Abaqus/Explicit

In Abaqus/Explicit overconstraints can arise in certain situations if the balanced master-slave formulation is enforced in addition to the cohesive constraint. To prevent this from occurring, a pure master-slave formulation is enforced for surfaces with cohesive behavior in Abaqus/Explicit. If cohesive behavior is defined between two surfaces, the first surface defined in the contact property assignment is treated as a slave surface and the second surface as its corresponding master surface. For contact interactions between the cohesive surfaces and other parts of the general contact domain, the default contact formulation (balanced master-slave) is applicable, unless a nondefault general contact formulation has been defined (see “Contact formulation for general contact in Abaqus/Explicit,” Section 38.2.1). The surface-based cohesive behavior is available only for node-to-face contact interactions; it is not available for edgeto-edge interactions. Hence, it is not possible to define surface-based cohesion between edges of beam and truss elements. In addition, contact definitions related to thermal interactions are ignored when surface-based cohesive behavior is defined.

Care should be exercised when cohesive behavior is used in conjunction with stacked conventional shell elements. Depending on the load case, the specialized contact formulation may lead to approximate normal contact forces, which in turn may induce approximate transverse shear behavior in the stacked shells that affect the bending behavior of the stack. Continuum shells should be used instead of conventional shells in such modeling scenarios.

Resolving initial overclosures and gaps in Abaqus/Explicit

In many debonding applications using cohesive surfaces, it may be desirable to begin the analysis with the surfaces just touching each other. This requires the resolution of initial overclosures and gaps between the surfaces at the start of the analysis to ensure that the slave nodes are precisely in contact with the master surface. In Abaqus/Explicit small initial overclosures are set to zero by default. To resolve large initial overclosures or to close initial gaps between the surfaces, an appropriate contact clearance specification may be defined, as explained in “Controlling initial contact status for general contact in Abaqus/Explicit,” Section 36.4.4. Since a pure-master slave formulation is enforced for cohesive surfaces, only nodes of the slave surface will undergo strain-free corrections to resolve any initial overclosures or gaps with their master facets; the nodes of the master facets will not be moved.

Keeping initial overclosures and gaps in Abaqus/Explicit

In some applications using cohesive surfaces, you may want to establish contact without making any adjustments even when the surfaces are apart from each other or overclosed with respect to each other. Such a case may arise if cohesive contact is used to tie surfaces that are apart from one another or intersect one another. To maintain an initial gap or overclosure between the surfaces, an appropriate contact clearance specification can be defined, as explained in “Controlling initial contact status for general contact in Abaqus/Explicit,” Section 36.4.4.

Defining cohesive behavior in Abaqus/Standard

Cohesive behavior in Abaqus/Standard is defined as part of the surface interaction properties that are assigned to a contact pair. Cohesive behavior cannot be assigned to contact pairs using the finite sliding, surface-to-surface formulation (see “Contact formulations in Abaqus/Standard,” Section 38.1.1).

Input File Usage:	Use the following options to define cohesive behavior between the surfaces in a contact pair:
	*SURFACE INTERACTION, NAME=name
	*COHESIVE BEHAVIOR
	*CONTACT PAIR, INTERACTION=name
	surface1, surface2

Abaqus/CAE Usage:

Use the following option to define cohesive behavior between two surfaces:Interaction module: contact property editor: Mechanical→Cohesive BehaviorUse the following option to define surface-to-surface contact between two surfaces:Interaction module: interaction editor: Surface-to-surface contact(Standard): Bonding tabbed page: specify Contact interaction property

Resolving initial overclosures and gaps in Abaqus/Standard

As discussed above, it is often desirable in debonding applications for the cohesive surfaces to begin the analysis just touching each other. Abaqus/Standard offers some tools for adjusting slave nodes in a contact pair so that they precisely contact the master surface, thereby eliminating initial overclosures and gaps. If nodes are not adjusted, even an extremely small initial gap will cause the contact constraints to be initialized to inactive and, thus, not cohered. These tools are described in “Adjusting initial surface positions and specifying initial clearances in Abaqus/Standard contact pairs,” Section 36.3.5.

Controlling the set of cohered nodes

By default, cohesive constraint forces can potentially act on all nodes of the surfaces for which cohesive behavior is defined. Slave nodes that are initially contacting the master surface can experience cohesive forces at the start of the analysis, and slave nodes that are not initially contacting the master surface can

experience cohesive forces if they contact the master surface during the analysis. There may, however, be situations where it is desirable to enforce cohesive behavior only for portions of surfaces that are contacting at the start of the analysis.

Restricting cohesive behavior to initially contacting nodes

As part of the cohesive behavior definition, you can indicate that only those nodes that are in contact with the master surface at the start of the step should experience cohesive forces. Any new contacts that occur during the step will not experience cohesive constraint forces; they will be modeled only as compressive contact.

Input File Usage: *COHESIVE BEHAVIOR, ELIGIBILITY=ORIGINAL CONTACTS

Abaqus/CAE Usage: Interaction module: contact property editor: Mechanical→Cohesive Behavior: Only slave nodes initially in contact

Restricting cohesive behavior to specified nodes

In Abaqus/Standard you can specify a subset of initially slave nodes that should experience cohesive forces. Strain-free adjustments will be made for those nodes initially not in contact but specified in the node set. All slave nodes outside of this set (including those that are initially contacting the master surface) will experience only compressive contact forces over the course of the analysis. This method is particularly useful for modeling crack propagation along an existing fault line.

Input File Usage: Use both of the following options: *INITIAL CONDITIONS, TYPE=CONTACT *COHESIVE BEHAVIOR, ELIGIBILITY=SPECIFIED CONTACTS

Abaqus/CAE Usage: Interaction module: contact property editor: Mechanical→Cohesive Behavior: Specify the bonding node set in the surfaceto-surface (Standard) interaction

Interaction module: interaction editor: Bonding tabbed page: Limit bonding to slave nodes in sub-set

Interaction of traction-separation behavior with compressive and friction behavior

In the contact normal direction, the pressure overclosure relationship governing the compressive behavior between the surfaces does not interact with the cohesive behavior, since they each describe the interaction between the surfaces in a different contact regime. The pressure overclosure relationship governs the behavior only when a slave node is “closed” (i.e., it is in contact with the master surface); the cohesive behavior contributes to the contact normal stress only when a slave node is “open” (i.e., not in contact). In the case of “sticky” cohesive behavior—where the two surfaces are not initially in contact—cohesive effects are activated in the increment after the slave node status changes from open to closed.

In the shear direction, if the cohesive stiffness is undamaged, it is assumed that the cohesive model is active and the friction model is dormant. Any tangential slip is assumed to be purely elastic in nature and is resisted by the cohesive strength of the bond, resulting in shear forces. If damage has been defined,

the cohesive contribution to the shear stresses starts degrading with damage evolution. Once the cohesive stiffness starts degrading, the friction model activates and begins contributing to the shear stresses. The elastic stick stiffness of the friction model is ramped up in proportion to the degradation of the elastic cohesive stiffness. Prior to the ultimate failure of the cohesive bond, and following the initiation of the degradation of the cohesive bond, the shear stress is a combination of the cohesive contribution and the contribution from the friction model. Once maximum degradation has been reached, the cohesive contribution to the shear stresses is zero, and the only contribution to the shear stresses is from the friction model.

Applying cohesive material concepts to surface-based cohesive behavior

The formulae and laws that govern cohesive surface behavior are very similar to those used for cohesive elements with traction-separation constitutive behavior (“Defining the constitutive response of cohesive elements using a traction-separation description,” Section 32.5.6). The similarities extend to the linear elastic traction-separation model, damage initiation criteria, and damage evolution laws.

However, it is important to recognize that damage in surface-based cohesive behavior is an interaction property, not a material property. Concepts of strain and displacement (used in behavior model formulae for cohesive elements) are reinterpreted as contact separations; contact separations are the relative displacements between the nodes on the slave surface and their corresponding projection points on the master surface along the contact normal and shear directions. Stresses are defined for surface-based cohesive behavior as the cohesive forces acting along the contact normal and shear directions divided by the current area at each contact point.

The specifics of the surface-based cohesive behavior model are discussed in the sections that follow.

Linear elastic traction-separation behavior

The available traction-separation model in Abaqus assumes initially linear elastic behavior (see “Defining elasticity in terms of tractions and separations for cohesive elements” in “Linear elastic behavior,” Section 22.2.1) followed by the initiation and evolution of damage. The elastic behavior is written in terms of an elastic constitutive matrix that relates the normal and shear stresses to the normal and shear separations across the interface.

The nominal traction stress vector, , consists of three components (two components in two-dimensional problems): t _ { n } , t _ { s } , and (in three-dimensional problems) t _ { t } , which represent the normal (along the local 3-direction in three dimensions and along the local 2-direction in two dimensions) and the two shear tractions (along the local 1- and 2-directions in three dimensions and along the local 1-direction in two dimensions), respectively. The corresponding separations are denoted by \delta _ { n } , \delta _ { s } , and \delta _ { t } . The elastic behavior can then be written as

\mathbf {t} = \left\{ \begin{array}{l} t _ {n} \\ t _ {s} \\ t _ {t} \end{array} \right\} = \left[ \begin{array}{l l l} K _ {n n} & K _ {n s} & K _ {n t} \\ K _ {n s} & K _ {s s} & K _ {s t} \\ K _ {n t} & K _ {s t} & K _ {t t} \end{array} \right] \left\{ \begin{array}{l} \delta_ {n} \\ \delta_ {s} \\ \delta_ {t} \end{array} \right\} = \mathbf {K} \delta .

Uncoupled traction-separation behavior

The simplest specification of cohesive behavior generates contact penalties that enforce the cohesive constraint in both normal and tangential directions. By default, the normal and tangential stiffness components will not be coupled: pure normal separation by itself does not give rise to cohesive forces in the shear directions, and pure shear slip with zero normal separation does not give rise to any cohesive forces in the normal direction.

For uncoupled traction-separation behavior, the terms K _ { n n } , K _ { s s } , and K _ { t t } must be defined, as well as any dependencies on temperature or field variables. If these terms are not defined, Abaqus uses default contact penalties to model the traction-separation behavior.

Input File Usage: *COHESIVE BEHAVIOR, TYPE=UNCOUPLED (default)

Abaqus/CAE Usage: Interaction module: contact property editor: Mechanical→Cohesive Behavior: Specify stiffness coefficients: Uncoupled

Coupled traction-separation behavior

In its full generality, the elasticity matrix provides fully coupled behavior between all components of the traction vector and separation vector and can depend on temperature and/or field variables. All terms in the matrix must be defined for coupled traction-separation behavior.

Input File Usage: *COHESIVE BEHAVIOR, TYPE=COUPLED

Abaqus/CAE Usage: Interaction module: contact property editor: Mechanical→Cohesive Behavior: Specify stiffness coefficients: Coupled

Cohesive behavior in the normal or shear direction only

To restrict the cohesive constraint to act along the contact normal direction only, define uncoupled cohesive behavior and specify zero values for the shear stiffness components, K _ { s s } and K _ { t t } . Alternatively, if only tangential cohesive constraints are to be enforced, the normal stiffness term, K _ { n n } , can be set to zero, in which case the normal “separations” will not be constrained. Normal compressive forces are resisted as per the usual contact behavior.

Damage modeling

Damage modeling allows you to simulate the degradation and eventual failure of the bond between two cohesive surfaces. The failure mechanism consists of two ingredients: a damage initiation criterion and a damage evolution law. The initial response is assumed to be linear as discussed above. However, once a damage initiation criterion is met, damage can occur according to a user-defined damage evolution law. Figure 37.1.10–1 shows a typical traction-separation response with a failure mechanism. If the damage initiation criterion is specified without a corresponding damage evolution model, Abaqus evaluates the damage initiation criterion for output purposes only; there is no effect on the response of the cohesive surfaces (i.e., no damage will occur). Cohesive surfaces do not undergo damage under pure compression.

Damage of the traction-separation response for cohesive surfaces is defined within the same general framework used for conventional materials (see “Progressive damage and failure,” Section 24.1.1),

line

separation	traction
δ_n^o(δ_s^o, δ_t^o)	t_n^o(t_s^o, t_t^o)
δ_n^f(δ_s^f, δ_t^f)	0

Figure 37.1.10–1 Typical traction-separation response.

except the damage behavior is specified as part of the interaction properties for the surfaces. Multiple damage response mechanisms are not available for cohesive surfaces: cohesive surfaces can have only one damage initiation criterion and only one damage evolution law.

Input File Usage:	Use the following options to define damage initiation and damage evolution for cohesive surfaces:
	*SURFACE INTERACTION, NAME=name
	*COHESIVE BEHAVIOR
	*DAMAGE INITIATION
	*DAMAGE EVOLUTION

Abaqus/CAE Usage: Interaction module: contact property editor: Mechanical→Damage: Damage Initiation and Damage Evolution tabbed pages

Damage initiation

Damage initiation refers to the beginning of degradation of the cohesive response at a contact point. The process of degradation begins when the contact stresses and/or contact separations satisfy certain damage initiation criteria that you specify. Several damage initiation criteria are available and are discussed below.

Each damage initiation criterion also has an output variable associated with it to indicate whether the criterion is met. A value of 1 or higher indicates that the initiation criterion has been met. Damage initiation criteria that do not have an associated evolution law affect only output. Thus, you can use these criteria to evaluate the propensity of the material to undergo damage without actually modeling the damage process (i.e., without actually specifying damage evolution).