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# Cohesive elements using a uniaxial stress state

Stress and other tensors (including strain tensors) are available for cohesive elements with uniaxial stress response. Both the stress tensor and the strain tensor contain true values. For the constitutive calculations using a uniaxial stress response, only the direct through-thickness stress is assumed to be nonzero. All the other stress components (i.e., the membrane and transverse shear stresses) are assumed to be zero (see “Modeling of gaskets and/or small adhesive patches” in “Defining the constitutive response of cohesive elements using a continuum approach,” Section 32.5.5, for details). All tensors have the same number of components. For example, the stress components are as follows:

S22

Direct through-thickness stress.

# Cohesive elements using a traction-separation response

Stress and other tensors (including strain tensors) are available for elements with traction-separation response. Both the stress tensor and the strain tensor contain nominal values. The output variables E, LE, and NE all contain the nominal strain when the response of cohesive elements is defined in terms of traction versus separation. All tensors have the same number of components. For example, the stress components are as follows:

S22

Direct through-thickness stress.

S12

Transverse shear stress.

# Node ordering and face numbering on elements

![](images/page-901_1109e0dc5fb4b7ddbf71d2a794c8b45de97579592574dbe3d0711d127dff2a9f.jpg)

![](images/page-901_79f6289793684f278ce88093583dc900d6975852ac98093439e85221f26a5e88.jpg)

<details>
<summary>text_image</summary>

face 3
face 4
face 2
face 1
face 1
1
2
3
4
</details>

4 - node element

![](images/page-901_225ecdca68b2b8b0fed1967363ac18e6c2014a63454c8499b207bb4f51deec6d.jpg)

<details>
<summary>text_image</summary>

4
5
1
3
6
2
</details>

6 - node element

Element faces 

<table><tr><td>Face 1</td><td>1 - 2 face</td></tr><tr><td>Face 2</td><td>2 - 3 face</td></tr><tr><td>Face 3</td><td>3 - 4 face</td></tr><tr><td>Face 4</td><td>4 - 1 face</td></tr></table>

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# Numbering of integration points for output

![](images/page-902_1c922d6a1d731fd5a67795970a2790541106504ca1ecdafce4f9ed352eecc55e.jpg)

<details>
<summary>text_image</summary>

4
1×
1
3
×2
2
</details>

4 - node element

![](images/page-902_1281e71bdadb7ddf60349f85833234726329814feed1411465a054fe15af7422.jpg)

<details>
<summary>text_image</summary>

4
5 1
1
3
2 6
2
</details>

6 - node element

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# 32.5.10 THREE-DIMENSIONAL COHESIVE ELEMENT LIBRARY

Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE

# References

• “Cohesive elements: overview,” Section 32.5.1   
• “Choosing a cohesive element,” Section 32.5.2   
• \*COHESIVE SECTION   
• Chapter 21, “Adhesive joints and bonded interfaces,” of the Abaqus/CAE User’s Guide

# Overview

This section provides a reference to the three-dimensional cohesive elements available in Abaqus/Standard and Abaqus/Explicit.

# Element types

# General elements

<table><tr><td>COH3D6</td><td>6-node three-dimensional cohesive element</td></tr><tr><td>COH3D8</td><td>8-node three-dimensional cohesive element</td></tr></table>

Active degrees of freedom

1, 2, 3

Additional solution variables

None.

# Pore pressure elements

<table><tr><td>COH3D6P(S)</td><td>9-node displacement and pore pressure three-dimensional cohesive element</td></tr><tr><td>COD3D6P(S)</td><td>9-node displacement and pore pressure three-dimensional cohesive element with the transition from Darcy flow to Poiseuille flow</td></tr><tr><td>COH3D8P(S)</td><td>12-node displacement and pore pressure three-dimensional cohesive element</td></tr><tr><td>COD3D8P(S)</td><td>12-node displacement and pore pressure three-dimensional cohesive element with the transition from Darcy flow to Poiseuille flow</td></tr></table>

Active degrees of freedom

1, 2, 3, 8 at nodes on the top and bottom faces   
8 at nodes on the middle face

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Additional solution variables

None.

Nodal coordinates required

X,Y,Z

# Element property definition

You can define the element’s initial constitutive thickness. The default initial constitutive thickness of cohesive elements depends on the response of these elements. For continuum response, the default initial constitutive thickness is computed based on the nodal coordinates. For traction-separation response, the default initial constitutive thickness is assumed to be 1.0. For response based on a uniaxial stress state, there is no default; you must indicate your choice of the method for computing the initial constitutive thickness. See “Specifying the constitutive thickness” in “Defining the cohesive element’s initial geometry,” Section 32.5.4, for details.

Abaqus computes the thickness direction automatically based on the midsurface of the element.

Input File Usage: \*COHESIVE SECTION

Abaqus/CAE Usage: Property module: Create Section: select Other as the section Category and Cohesive as the section Type

# Element-based loading

# Distributed loads

Distributed loads are specified as described in “Distributed loads,” Section 34.4.3.

<table><tr><td>Load ID (*DLOAD)</td><td>Abaqus/CAE Load/Interaction</td><td>Units</td><td>Description</td></tr><tr><td>BX</td><td>Body force</td><td> $FL^{-3}$ </td><td>Body force in global X-direction.</td></tr><tr><td>BY</td><td>Body force</td><td> $FL^{-3}$ </td><td>Body force in global Y-direction.</td></tr><tr><td>BZ</td><td>Body force</td><td> $FL^{-3}$ </td><td>Body force in global Z-direction.</td></tr><tr><td>BXNU</td><td>Body force</td><td> $FL^{-3}$ </td><td>Nonuniform body force in global X-direction with magnitude supplied via user subroutine DLOAD in Abaqus/Standard and VDLOAD in Abaqus/Explicit.</td></tr><tr><td>BYNU</td><td>Body force</td><td> $FL^{-3}$ </td><td>Nonuniform body force in global Y-direction with magnitude supplied via user subroutine DLOAD in</td></tr></table>

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<table><tr><td>Load ID (*DLOAD)</td><td>Abaqus/CAE Load/Interaction</td><td>Units</td><td>Description</td></tr><tr><td></td><td></td><td></td><td>Abaqus/Standard and VDLOAD in Abaqus/Explicit.</td></tr><tr><td>BZNU</td><td>Body force</td><td> $FL^{-3}$ </td><td>Nonuniform body force in global Z-direction with magnitude supplied via user subroutine DLOAD in Abaqus/Standard and VDLOAD in Abaqus/Explicit.</td></tr><tr><td> $CENT^{(S)}$ </td><td>Not supported</td><td> $FL^{-4}(ML^{-3}T^{-2})$ </td><td>Centrifugal load (magnitude is input as  $\rho\omega^{2}$ , where  $\rho$  is the mass density per unit volume,  $\omega$  is the angular velocity).</td></tr><tr><td> $CENTRIF^{(S)}$ </td><td>Rotational body force</td><td> $T^{-2}$ </td><td>Centrifugal load (magnitude is input as  $\omega^{2}$ , where  $\omega$  is the angular velocity).</td></tr><tr><td> $CORIO^{(S)}$ </td><td>Coriolis force</td><td> $FL^{-4}T (ML^{-3}T^{-1})$ </td><td>Coriolis force (magnitude is input as  $\rho\omega$ , where  $\rho$  is the mass density per unit volume,  $\omega$  is the angular velocity).</td></tr><tr><td>GRAV</td><td>Gravity</td><td> $LT^{-2}$ </td><td>Gravity loading in a specified direction (magnitude is input as acceleration).</td></tr><tr><td>Pn</td><td>Pressure</td><td> $FL^{-2}$ </td><td>Pressure on face n.</td></tr><tr><td>PnNU</td><td>Not supported</td><td> $FL^{-2}$ </td><td>Nonuniform pressure on face n with magnitude supplied via user subroutine DLOAD in Abaqus/Standard and VDLOAD in Abaqus/Explicit.</td></tr><tr><td> $ROTA^{(S)}$ </td><td>Rotational body force</td><td> $T^{-2}$ </td><td>Rotary acceleration load (magnitude is input as  $\alpha$ , where  $\alpha$  is the rotary acceleration).</td></tr><tr><td> $SBF^{(E)}$ </td><td>Not supported</td><td> $FL^{-5}T^{2}$ </td><td>Stagnation body force in global X-, Y-, and Z-directions.</td></tr><tr><td> $SPn^{(E)}$ </td><td>Not supported</td><td> $FL^{-4}T^{2}$ </td><td>Stagnation pressure on face n.</td></tr><tr><td> $VBF^{(E)}$ </td><td>Not supported</td><td> $FL^{-4}T$ </td><td>Viscous body force in global X-, Y-, and Z-directions.</td></tr></table>

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<table><tr><td>Load ID(*DLOAD)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</td></tr><tr><td> $VPn^{(E)}$ </td><td>Not supported</td><td> $FL^{-3}T$ </td><td>Viscous pressure on face  $n$ , applying a pressure proportional to the velocity normal to the face and opposing the motion.</td></tr></table>

Surface-based loading   
Distributed loads

Surface-based distributed loads are specified as described in “Distributed loads,” Section 34.4.3.

<table><tr><td>Load ID(*DSLOAD)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</td></tr><tr><td>P</td><td>Pressure</td><td> $FL^{-2}$ </td><td>Pressure on the element surface.</td></tr><tr><td>PNU</td><td>Pressure</td><td> $FL^{-2}$ </td><td>Nonuniform pressure on the element surface with magnitude supplied via user subroutine DLOAD in Abaqus/Standard and VDLOAD in Abaqus/Explicit.</td></tr><tr><td> $SP^{(E)}$ </td><td>Pressure</td><td> $FL^{-4}T^{2}$ </td><td>Stagnation pressure on the element surface.</td></tr><tr><td> $VP^{(E)}$ </td><td>Pressure</td><td> $FL^{-3}T$ </td><td>Viscous pressure applied on the element surface. The viscous pressure is proportional to the velocity normal to the element face and opposing the motion.</td></tr></table>

# Element output

Stress, strain, and other tensor components available for output depend on whether the cohesive elements are used to model adhesive joints, gaskets, or delamination problems. You indicate the intended usage of the cohesive elements by choosing an appropriate response type when defining the section properties of these elements. The available response types are discussed in “Defining the constitutive response of cohesive elements using a continuum approach,” Section 32.5.5, and “Defining the constitutive response of cohesive elements using a traction-separation description,” Section 32.5.6.

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# Cohesive elements using a continuum response

Stress and other tensors (including strain tensors) are available for elements with continuum response. Both the stress tensor and the strain tensor contain true values. For the constitutive calculations using a continuum response, only the direct through-thickness and the transverse shear strains are assumed to be nonzero. All the other strain components (i.e., the membrane strains) are assumed to be zero (see “Modeling of an adhesive layer of finite thickness” in “Defining the constitutive response of cohesive elements using a continuum approach,” Section 32.5.5, for details). All tensors have the same number of components. For example, the stress components are as follows:

<table><tr><td>S11</td><td>Direct membrane stress.</td></tr><tr><td>S22</td><td>Direct membrane stress.</td></tr><tr><td>S33</td><td>Direct through-thickness stress.</td></tr><tr><td>S12</td><td>In-plane membrane shear stress.</td></tr><tr><td>S13</td><td>Transverse shear stress.</td></tr><tr><td>S23</td><td>Transverse shear stress.</td></tr></table>

# Cohesive elements using a uniaxial stress state

Stress and other tensors (including strain tensors) are available for cohesive elements with uniaxial stress response. Both the stress tensor and the strain tensor contain true values. For the constitutive calculations using a uniaxial stress response, only the direct through-thickness stress is assumed to be nonzero. All the other stress components (i.e., the membrane and transverse shear stresses) are assumed to be zero (see “Modeling of gaskets and/or small adhesive patches” in “Defining the constitutive response of cohesive elements using a continuum approach,” Section 32.5.5, for details). All tensors have the same number of components. For example, the stress components are as follows:

S33 Direct through-thickness stress.

# Cohesive elements using a traction-separation response

Stress and other tensors (including strain tensors) are available for elements with traction-separation response. Both the stress tensor and the strain tensor contain nominal values. The output variables E, LE, and NE all contain the nominal strain when the response of cohesive elements is defined in terms of traction versus separation. All tensors have the same number of components. For example, the stress components are as follows:

<table><tr><td>S33</td><td>Direct through-thickness stress.</td></tr><tr><td>S13</td><td>Transverse shear stress.</td></tr><tr><td>S23</td><td>Transverse shear stress.</td></tr></table>

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![](images/page-908_7cfeb47aff0f896887d78d7bc403d35496d73c7dd476e7cfaab3cca6e2d55b62.jpg)

<details>
<summary>flowchart</summary>

```mermaid
graph TD
    1 --> 2
    1 --> 3
    2 --> 3
    2 --> 4
    3 --> 4
    3 --> 5
    4 --> 5
    4 --> 6
    5 --> 6
    6 --> 6
    5 --> 1
    5 --> 2
    5 --> 3
    5 --> 4
    5 --> 5
    6 --> 6
    6 --> 4
    4 --> 5
    5 --> 6
    6 --> 4
    4 --> 3
    3 --> 2
    2 --> 1
    1 --> 3
    3 --> 4
    4 --> 5
    5 --> 6
    6 --> 5
    5 --> 4
    4 --> 3
    3 --> 2
    2 --> 1
    1 --> 3
    3 --> 4
    4 --> 5
    5 --> 6
    6 --> 5
    5 --> 4
    4 --> 3
    3 --> 2
    2 --> 1
    1 --> 3
    3 -->|face 1| 2
    4 -->|face 2| 3
    5 -->|face 3| 1
    6 -->|face 4| 4
```
</details>

6 - node element

![](images/page-908_799a53254a610d569a69b7a4a0e096b853c14bf33fd0101006bbe7396b7b45ff.jpg)

<details>
<summary>flowchart</summary>

```mermaid
graph TD
    1 --> 2
    1 --> 3
    1 --> 4
    1 --> 5
    2 --> 3
    2 --> 4
    2 --> 5
    3 --> 4
    3 --> 5
    4 --> 5
    4 --> 6
    5 --> 6
    5 --> 7
    6 --> 7
    6 --> 8
    7 --> 8
    8 --> 2
    9 --> 6
    9 --> 3
```
</details>

9 - node element

![](images/page-908_6a0cf735de00bc2f0638ed88bf9b5f30d25eb1dc4289db06d32d9ee52836f634.jpg)

<details>
<summary>text_image</summary>

face 2
face 5
8
7
face 6
4
3
face 4
5
6
1
face 1
2
face 3
</details>

8 - node element

![](images/page-908_df2ecc24e94995346cf480390ced554353b483bcb61002d4e987cd9b9cc0d1db.jpg)

<details>
<summary>text_image</summary>

8
12
4
7
11
3
5
6
9
10
1
2
</details>

1 2 - node element

![](images/page-908_4f0d7ae72ef087a95bd381a0f5570f51a6121c5f68df5f2d69aa3d9ef8d7f3b4.jpg)

# Element faces for COH3D6

Face 1 1 – 2 – 3 face

Face 2 4 – 6 – 5 face

Face 3 $1 - 4 - 5 - 2$ face

Face 4 $2 - 5 - 6 - 3$ face

Face 5 $3 - 6 - 4 - 1$ face

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Element faces for COH3D8 

<table><tr><td>Face 1</td><td>1 - 2 - 3 - 4 face</td></tr><tr><td>Face 2</td><td>5 - 8 - 7 - 6 face</td></tr><tr><td>Face 3</td><td>1 - 5 - 6 - 2 face</td></tr><tr><td>Face 4</td><td>2 - 6 - 7 - 3 face</td></tr><tr><td>Face 5</td><td>3 - 7 - 8 - 4 face</td></tr><tr><td>Face 6</td><td>4 - 8 - 5 - 1 face</td></tr></table>

# Numbering of integration points for output

![](images/page-909_c00da83c8ddb32c982ea2f5061de9f010a9acbe3c526d9c213c08813d615a5d8.jpg)

<details>
<summary>flowchart</summary>

```mermaid
graph TD
    1 -->|1| 4
    1 -->|2| 2
    2 -->|3| 3
    2 -->|5| 5
    3 -->|6| 6
    4 -->|1| 5
    5 -->|3| 6
```
</details>

6 - node element

![](images/page-909_a0a8e204189347a89897201b335e37ad79f97c9ac7a14740b72ea42b154501e6.jpg)

<details>
<summary>flowchart</summary>

```mermaid
graph TD
    1 --> 2
    1 --> 3
    1 --> 4
    2 --> 5
    2 --> 6
    2 --> 8
    3 --> 5
    3 --> 6
    4 --> 5
    4 --> 6
    5 --> 8
    6 --> 9
    7 --> 1
    8 --> 2
    9 --> 3
```
</details>

9 - node element

![](images/page-909_3ca0fd158022e373f4ab59e915f3e97a2d01de3472afe87c6485cdeb0a869f82.jpg)

<details>
<summary>text_image</summary>

8
4
4
7
3
3
5
6
1
2
1
2
</details>

8 - node element

![](images/page-909_e25b723c7e079c2a817d6354b92eb616470a27b21934a98b376cbaebafee479f.jpg)

<details>
<summary>text_image</summary>

8
12
4
4
7
11
3
3
5
6
9
1
10
2
1
2
</details>

1 2 - node element

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