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# Example

This example (see Figure 32.4.1–1) illustrates the use of the DCOUP3D element to impart a rotation to the surface of a structure that is expected to deform in a general way. In this case warping and motion within the plane of the end surface are expected to occur.

```matlab
* ELEMENT, TYPE=DCOUP3D, ELSET=ROTATEELEMENT
1001, 1
* DISTRIBUTING COUPLING, ELSET=ROTATEELEMENT
COUPLESET, 1.0
...
* STEP, NLGEOM
...
* BOUNDARY
1, 6, 6, 1.0
...
* END STEP 
```

# Defining the load distribution

The element distributes loads such that the resultants of the forces on the coupling nodes are equal to the forces and moments on the element node. For cases of more than a few coupling nodes, the distribution of the forces is not determined by equilibrium alone, and the user-specified weight factors are used to define the distribution. The weight factors are dimensionless and are normalized within each element so that the sum of all weight factors is one. As a consequence, the normalized weight factors describe the proportion of the total element force and moment that is transmitted through the particular coupling node. In the case of transmission of forces alone, the proportion of force transmitted through the node is simply the normalized weight factor. In the general case of transmission of forces and moments, the force distribution follows that of a classic bolt-pattern analysis, where the weight factors could be considered the areas of particular bolt cross-sections. Refer to “Distributing coupling constraints,” Section 3.9.8 of the Abaqus Theory Guide, for specific details of the load distribution.

In the example shown in Figure 32.4.1–1 the weight factor distribution chosen is homogeneous, with a value of 1.0. For the rotation depicted, a more accurate load distribution would reflect the fact that the shear forces on nodes near the edge of the slot will diminish to zero, which could be described by choosing individual weight factors for nodes near the slot edge. If the loading on the element were along the axis of the structure, the homogeneous distribution shown would be appropriate. For cases where different loading modes require different descriptions of the weight factor distribution, multiple distributing coupling elements with different element nodes and different weight factors can be used.

# Colinear coupling node arrangements

The distributing coupling element transmits moments at the element node as a force distribution among the coupling nodes, even if these nodes have rotational degrees of freedom. Thus, when the coupling node arrangement is colinear, the element is not capable of transmitting all components of a moment

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at the element node. Specifically, the moment component that is parallel to the colinear coupling node arrangement will not be transmitted. When this case arises, a warning message is issued that identifies the axis about which the element will not transmit a moment.

# Use with nonuniform meshes

When the distributing coupling element is used with coupling nodes attached to elements of varying size, care should be taken in selecting the weight factors. The weight factor selected for a node should generally scale with the size of the elements attached to that node.

# Output

Element nodal forces (the force the element places on the element and coupling nodes) are available through element variable NFORC. Element kinetic energy is available in dynamic procedures through the whole element variable ELKE.

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# 32.4.2 DISTRIBUTING COUPLING ELEMENT LIBRARY

Product: Abaqus/Standard

References 

<table><tr><td>• “Distributing coupling elements,” Section 32.4.1</td></tr><tr><td>• *DISTRIBUTING COUPLING</td></tr></table>

Overview

This section provides a reference to the distributing coupling elements available in Abaqus/Standard.

Element types 

<table><tr><td>DCOUP2D</td><td>Two-dimensional distributing coupling element</td></tr><tr><td>DCOUP3D</td><td>Three-dimensional distributing coupling element</td></tr></table>

<table><tr><td>Active degrees of freedom</td></tr><tr><td>DCOUP2D: 1, 2, 6</td></tr><tr><td>DCOUP3D: 1, 2, 3, 4, 5, 6</td></tr></table>

<table><tr><td>Additional solution variables</td></tr><tr><td>None.</td></tr></table>

Nodal coordinates required 

<table><tr><td>DCOUP2D: X, Y</td></tr><tr><td>DCOUP3D: X, Y, Z</td></tr></table>

Element property definition

You must identify a minimum of two nodes to which the distributing coupling element distributes loads and mass; in addition, you can specify the element mass.

Input File Usage: \*DISTRIBUTING COUPLING

Element-based loading 

<table><tr><td>None.</td></tr></table>

Element output

ELKE Element kinetic energy.

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NFORC

Element nodal forces.

# Nodes associated with the element

1 node is defined with the element. Additional nodes forming the coupling are defined in the element property definition.

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# 32.5 Cohesive elements

• “Cohesive elements: overview,” Section 32.5.1   
• “Choosing a cohesive element,” Section 32.5.2   
• “Modeling with cohesive elements,” Section 32.5.3   
• “Defining the cohesive element’s initial geometry,” Section 32.5.4   
• “Defining the constitutive response of cohesive elements using a continuum approach,” Section 32.5.5   
• “Defining the constitutive response of cohesive elements using a traction-separation description,” Section 32.5.6   
• “Defining the constitutive response of fluid within the cohesive element gap,” Section 32.5.7   
• “Defining the constitutive response of fluid transitioning from Darcy flow to Poiseuille flow,” Section 32.5.8   
• “Two-dimensional cohesive element library,” Section 32.5.9   
• “Three-dimensional cohesive element library,” Section 32.5.10   
• “Axisymmetric cohesive element library,” Section 32.5.11

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# 32.5.1 COHESIVE ELEMENTS: OVERVIEW

Abaqus offers a library of cohesive elements to model the behavior of adhesive joints, interfaces in composites, and other situations where the integrity and strength of interfaces may be of interest.

# Overview

Modeling with cohesive elements consists of:

• choosing the appropriate cohesive element type (“Choosing a cohesive element,” Section 32.5.2);   
• including the cohesive elements in a finite element model, connecting them to other components, and understanding typical modeling issues that arise during modeling using cohesive elements (“Modeling with cohesive elements,” Section 32.5.3);   
• defining the initial geometry of the cohesive elements (“Defining the cohesive element’s initial geometry,” Section 32.5.4); and   
• defining the mechanical, and optionally the fluid, constitutive behavior of the cohesive elements.

The mechanical constitutive behavior of the cohesive elements can be defined:

• with a continuum-based constitutive model (“Modeling of an adhesive layer of finite thickness” in “Defining the constitutive response of cohesive elements using a continuum approach,” Section 32.5.5),   
• with a uniaxial stress-based constitutive model useful in modeling gaskets and/or single adhesive patches (“Modeling of gaskets and/or small adhesive patches” in “Defining the constitutive response of cohesive elements using a continuum approach,” Section 32.5.5), or   
• by using a constitutive model specified directly in terms of traction versus separation (“Defining the constitutive response of cohesive elements using a traction-separation description,” Section 32.5.6).

When pore pressure cohesive elements are used in soils procedures in Abaqus/Standard, the fluid constitutive behavior of the cohesive elements can be defined (“Defining the constitutive response of fluid within the cohesive element gap,” Section 32.5.7, and “Defining the constitutive response of fluid transitioning from Darcy flow to Poiseuille flow,” Section 32.5.8):

• by defining the tangential fluid flow relationship, and   
• by defining a fluid leak-off coefficient that accounts for caking or fouling effects in rock fracture.

# Typical applications

Cohesive elements are useful in modeling adhesives, bonded interfaces, gaskets, and rock fracture. The constitutive response of these elements depends on the specific application and is based on certain assumptions about the deformation and stress states that are appropriate for each application area. The nature of the mechanical constitutive response may broadly be classified to be based on:

• a continuum description of the material;   
• a traction-separation description of the interface; or

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• a uniaxial stress state appropriate for modeling gaskets and/or laterally unconstrained adhesive patches.

Each of these constitutive response types is discussed briefly below.

# Continuum-based modeling

The modeling of adhesive joints involves situations where two bodies are connected together by a gluelike material (see Figure 32.5.1–1). A continuum-based modeling of the adhesive is appropriate when the glue has a finite thickness. The macroscopic properties, such as stiffness and strength, of the adhesive material can be measured experimentally and used directly for modeling purposes (see “Defining the constitutive response of cohesive elements using a continuum approach,” Section 32.5.5, for details). The adhesive material is generally more compliant than the surrounding material. The cohesive elements model the initial loading, the initiation of damage, and the propagation of damage leading to eventual failure in the material.

![](images/page-828_b9bf123e06123e15a602ee4639b7fa9047cc60d8eaeeb18d3cdb884f69fbcb30.jpg)

<details>
<summary>text_image</summary>

patches of adhesive
</details>

Figure 32.5.1–1 Typical peel test using cohesive elements to model finite-thickness adhesives.

In three-dimensional problems the continuum-based constitutive model assumes one direct (through-thickness) strain, two transverse shear strains, and all (six) stress components to be active at a material point. In two-dimensional problems it assumes one direct (through-thickness) strain, one transverse shear strain, and all (four) stress components to be active at a material point.

# Traction-separation-based modeling

The modeling of bonded interfaces in composite materials often involves situations where the intermediate glue material is very thin and for all practical purposes may be considered to be of zero thickness (see Figure 32.5.1–2). In this case the macroscopic material properties are not relevant directly, and the analyst must resort to concepts derived from fracture mechanics—such as the amount of energy required to create new surfaces (see “Defining the constitutive response of cohesive elements using a traction-separation description,” Section 32.5.6, for details). The cohesive elements model the

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![](images/page-829_bf46561d02f22693132c3a7d8a05cabbdbff44bdd0184fd574585e98248eb48d.jpg)

<details>
<summary>text_image</summary>

stiffener
skin
bond line
debonding
Debonding along skin-stringer interface.
</details>

Figure 32.5.1–2 Debonding along a skin-stringer interface: typical situation for traction-separation-based modeling.

initial loading, the initiation of damage, and the propagation of damage leading to eventual failure at the bonded interface. The behavior of the interface prior to initiation of damage is often described as linear elastic in terms of a penalty stiffness that degrades under tensile and/or shear loading but is unaffected by pure compression.

You may use the cohesive elements in areas of the model where you expect cracks to develop. However, the model need not have any crack to begin with. In fact, the precise locations (among all areas modeled with cohesive elements) where cracks initiate, as well as the evolution characteristics of such cracks, are determined as part of the solution. The cracks are restricted to propagate along the layer of cohesive elements and will not deflect into the surrounding material.

In three-dimensional problems the traction-separation-based model assumes three components of separation—one normal to the interface and two parallel to it; and the corresponding stress components are assumed to be active at a material point. In two-dimensional problems the traction-separation-based model assumes two components of separation—one normal to the interface and the other parallel to it; and the corresponding stress components are assumed to be active at a material point.

# Modeling of gaskets and/or laterally unconstrained adhesive patches

Cohesive elements also provide some limited capabilities for modeling gaskets (see Figure 32.5.1–3). The constitutive response of gaskets modeled with cohesive elements can be defined using only macroscopic properties such as stiffness and strength (see “Defining the constitutive response of cohesive elements using a continuum approach,” Section 32.5.5, for details). No specialized gasket behavior (typically defined in terms of pressure versus closure) is available. Compared to the class

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![](images/page-830_5a3c4b4f2d89259d22181fb3ad898bb2229c1be3b3415e065d7c225f674b2bba.jpg)

<details>
<summary>text_image</summary>

flanges
gasket
gasket
fasteners
</details>

Figure 32.5.1–3 Typical application involving gaskets.

of gasket elements available in Abaqus/Standard (“Gasket elements: overview,” Section 32.6.1), the cohesive elements

• are fully nonlinear (can be used with finite strains and rotations);   
• can have mass in a dynamic analysis; and   
• are available in both Abaqus/Standard and Abaqus/Explicit.

It is assumed that the gaskets are subjected to a uniaxial stress state. A uniaxial stress state is also appropriate for modeling small adhesive patches that are unconstrained in the lateral direction.

Any material model in Abaqus that is available for use with a one-dimensional element (beams, trusses, or rebars)—including, for example, the hyperelastic and the elastomeric foam material models (useful in this context for modeling gaskets, sealants, or shock absorbers made out of poron)—can be used with this approach.

# Spatial representation of a cohesive element

Figure 32.5.1–4 demonstrates the key geometrical features that are used to define cohesive elements. The connectivity of cohesive elements is like that of continuum elements, but it is useful to think of cohesive elements as being composed of two faces separated by a thickness. The relative motion of the bottom and top faces measured along the thickness direction (local 3-direction for three-dimensional elements; local 2-direction for two-dimensional elements—see “Defining the cohesive element’s initial geometry,” Section 32.5.4, for further details on local directions) represents opening or closing of the interface. The relative change in position of the bottom and top faces measured in the plane orthogonal to the thickness
