<!-- source-page: 911 -->

# 32.5.11 AXISYMMETRIC 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 axisymmetric cohesive elements available in Abaqus/Standard and Abaqus/Explicit.

# Element types

# General element

COHAX4 4-node axisymmetric cohesive element

Active degrees of freedom

1, 2 ( , )

Additional solution variables

None.

# Pore pressure element

COHAX4P(S) 6-node displacement and pore pressure axisymmetric cohesive element CODAX4P(S) 6-node displacement and pore pressure axisymmetric cohesive element with the transition from Darcy flow to Poiseuille flow

Active degrees of freedom

1, 2, 8

Additional solution variables

None.

# Nodal coordinates required

X,Y

<!-- source-page: 912 -->

# 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 calculates 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>BR</td><td>Body force</td><td> $FL^{-3}$ </td><td>Body force in radial direction.</td></tr><tr><td>BY</td><td>Body force</td><td> $FL^{-3}$ </td><td>Body force in axial direction.</td></tr><tr><td>BRNU</td><td>Body force</td><td> $FL^{-3}$ </td><td>Nonuniform body force in radial direction with magnitude supplied via user subroutine DLOAD in 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 axial 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></table>

<!-- source-page: 913 -->

<table><tr><td>Load ID (*DLOAD)</td><td>Abaqus/CAE Load/Interaction</td><td>Units</td><td>Description</td></tr><tr><td> $\text{CENTRIF}^{(S)}$ </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>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> $\text{SBF}^{(E)}$ </td><td>Not supported</td><td> $FL^{-5}T^2$ </td><td>Stagnation body force in radial and axial directions.</td></tr><tr><td> $\text{SPn}^{(E)}$ </td><td>Not supported</td><td> $FL^{-4}T^2$ </td><td>Stagnation pressure on face n.</td></tr><tr><td> $\text{VBF}^{(E)}$ </td><td>Not supported</td><td> $FL^{-4}T$ </td><td>Viscous body force in radial and axial directions.</td></tr><tr><td> $\text{VPn}^{(E)}$ </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></table>

<!-- source-page: 914 -->

<table><tr><td>Load ID(*DSLOAD)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</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.

# 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 through-thickness stress.</td></tr><tr><td>S33</td><td>Direct membrane stress.</td></tr><tr><td>S12</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:

<!-- source-page: 915 -->

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-915_a24aaffe9c23aaa2b4ed5b7a3a0e58acc0941707b0f3a7cce1cb11084e2013ce.jpg)

![](images/page-915_168ee7004f92073ae31c9c033b634ad2b344a84949ba0b1e30717323c9e8344d.jpg)

<details>
<summary>text_image</summary>

4 face 3
face 4
1 face 1 face 2
face 3
face 2
2
4 - node element
</details>

![](images/page-915_4246c8583e76c9e6f780104c5447d2dc285d9c04b89e006b22c612ce510991f3.jpg)

<details>
<summary>text_image</summary>

4
3
5
6
1
2
6 - node element
</details>

# Element faces

Face 1 1 – 2 face

Face 2 2 – 3 face

Face 3 3 – 4 face

Face 4 4 – 1 face

# Numbering of integration points for output

![](images/page-915_2e2f55acf19f3fadd8e5b88e7cfc2095e091d51b3a0c670000a7a6bae86564e3.jpg)

<details>
<summary>text_image</summary>

4
1×
1
3
×2
2
</details>

4 - node element

![](images/page-915_d50f2a2da54bdbff119784e35d517c7d0bd1ba402178a296abdbf90020e77fee.jpg)

<details>
<summary>text_image</summary>

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

6 - node element

<!-- source-page: 916 -->

<!-- source-page: 917 -->

# 32.6 Gasket elements

• “Gasket elements: overview,” Section 32.6.1   
• “Choosing a gasket element,” Section 32.6.2   
• “Including gasket elements in a model,” Section 32.6.3   
• “Defining the gasket element’s initial geometry,” Section 32.6.4   
• “Defining the gasket behavior using a material model,” Section 32.6.5   
• “Defining the gasket behavior directly using a gasket behavior model,” Section 32.6.6   
• “Two-dimensional gasket element library,” Section 32.6.7   
• “Three-dimensional gasket element library,” Section 32.6.8   
• “Axisymmetric gasket element library,” Section 32.6.9

<!-- source-page: 918 -->

<!-- source-page: 919 -->

Abaqus/Standard offers a library of gasket elements to model the behavior of gaskets.

# Overview

Gasket modeling consists of:

• choosing the appropriate gasket element type (“Choosing a gasket element,” Section 32.6.2);   
• including the gasket elements in a finite element model (“Including gasket elements in a model,” Section 32.6.3);   
• defining the initial geometry of the gasket (“Defining the gasket element’s initial geometry,” Section 32.6.4); and   
• defining the gasket behavior with either a material model (“Defining the gasket behavior using a material model,” Section 32.6.5) or a gasket behavior model (“Defining the gasket behavior directly using a gasket behavior model,” Section 32.6.6).

# Motivation for gasket elements

Gaskets are constructed in many ways and from many materials. Some types of gaskets consist of several layers of preformed metal, possibly with thin elastomeric coatings or elastomeric inserts (see Figure 32.6.1–1). Others use plastics together with elastomeric inserts.

![](images/page-919_12e8c65e7be314dae523838e5281be8a5be1d2bd0077bc2608e517457c3a06d4.jpg)

<details>
<summary>text_image</summary>

A
A
</details>

![](images/page-919_1c049173a0e066bfe49a788349551df5ead06aca8ff7b032622f311acf26cfca.jpg)

<details>
<summary>text_image</summary>

Section A-A
</details>

Figure 32.6.1–1 Typical gasket consisting of several layers of preformed metal.

Gaskets are usually very thin and act as sealing components between structural components. They are carefully designed to provide appropriate pressure-closure behaviors through their thickness (the thin direction of the gaskets) so that they maintain their sealing action as the components undergo deformations due to thermal and mechanical loads. It is difficult to use solid continuum elements

<!-- source-page: 920 -->

to model the through-thickness behavior of gaskets with the material library available. Therefore, Abaqus/Standard offers a variety of gasket elements that have through-thickness behaviors specifically designed for the study of gaskets.

The gasket behavior models are separate from the models in the material library and assume that the thickness-direction, transverse shear, and membrane behaviors are uncoupled (see “Defining the gasket behavior directly using a gasket behavior model,” Section 32.6.6, for details). For a gasket behavior that is not readily addressed by these special behavior models, such as occurs when coupled behaviors or through-thickness tensile behavior must be considered, Abaqus/Standard provides a versatile alternative by allowing a gasket element to use either a built-in or user-defined material model (see “Defining the gasket behavior using a material model,” Section 32.6.5, for details).

# Spatial representation of a gasket element

Figure 32.6.1–2 demonstrates the key geometrical features that are used to define gasket elements. Gasket elements are composed of two surfaces separated by a thickness. The relative motion of the bottom and top surfaces measured along the thickness direction to the gasket quantifies the thickness-direction (local 1-direction) behavior of the gasket element. The relative change in position of the bottom and top surfaces measured in the plane orthogonal to the thickness direction quantifies the transverse shear behavior of the gasket element. The stretching and shearing of the midsurface of the element (the surface halfway between the bottom and top surfaces) quantifies the membrane behavior of the gasket element.

![](images/page-920_4863242ad2e2e0ac03179798b7857159773e08411b55e58621a3b67d87c0fd91.jpg)

<details>
<summary>text_image</summary>

top face (SPOS)
normal
direction
gasket element node
bottom face (SNEG)
midsurface
</details>

Figure 32.6.1–2 Spatial representation of a gasket element.

# Local behavior directions defined at the integration points

The thickness direction defined at the integration points of gasket elements constitutes the local 1-direction. The transverse shear behavior is defined in the local 1–2 and 1–3 planes. The membrane behavior is defined in the 2–3 plane. The local 2- and 3-directions are not defined for elements that have nodes with only one degree of freedom because these elements consider only the thickness-direction behavior of a gasket. The local directions are used to specify the gasket behavior and for output of all
