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# 31.1.4 CONNECTOR ELEMENT LIBRARY

Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE

# References

• “Connector elements,” Section 31.1.2   
• “Connection-type library,” Section 31.1.5   
• \*CONNECTOR BEHAVIOR   
• \*CONNECTOR LOAD   
• \*CONNECTOR SECTION

# Overview

This section provides a reference to the connector elements available in Abaqus/Standard and Abaqus/Explicit.

# Element types

# Connector in a plane

CONN2D2 Connector element between two nodes or ground and a node.

Active degrees of freedom

1, 2, 6 for the most general connection types.

Additional solution variables

In Abaqus/Standard there can be up to three additional constraint variables related to forces and a moment associated with the connector. The number of additional constraint variables depends on the connection type.

# Connector in space

CONN3D2 Connector element between two nodes or ground and a node.

Active degrees of freedom

1, 2, 3, 4, 5, 6 for the most general connection types.

Additional solution variables

In Abaqus/Standard there can be up to six additional constraint variables related to forces and moments associated with the connector. The number of additional constraint variables depends on the connection type.

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Nodal coordinates required

CONN2D2: X, Y

CONN3D2: X, Y, Z

Element property definition 

<table><tr><td>Input File Usage:</td><td>*CONNECTOR SECTION</td></tr><tr><td>Abaqus/CAE Usage:</td><td>Interaction module: Connector→Section→Create</td></tr></table>

Element-based loading

Use connector loads to apply loading to the available components of relative motion. Prescribe connector motion to specify relative kinematics (zero or nonzero values) for the available components of relative motion. See “Connector actuation,” Section 31.1.3, for details.

Element output   
Total force components 

<table><tr><td>CTF1</td><td>Total force in the 1-direction.</td></tr><tr><td>CTF2</td><td>Total force in the 2-direction.</td></tr><tr><td>CTF3</td><td>Total force in the 3-direction.</td></tr><tr><td>CTM1</td><td>Total moment about the 1-direction.</td></tr><tr><td>CTM2</td><td>Total moment about the 2-direction.</td></tr><tr><td>CTM3</td><td>Total moment about the 3-direction.</td></tr></table>

The total force is obtained as $\mathrm { C T F } = \mathrm { C E F } + \mathrm { C V F } + \mathrm { C U F } + \mathrm { C S F } + \mathrm { C R F } - \mathrm { C C F } .$

Elastic force components 

<table><tr><td>CEF1</td><td>Elastic force in the 1-direction.</td></tr><tr><td>CEF2</td><td>Elastic force in the 2-direction.</td></tr><tr><td>CEF3</td><td>Elastic force in the 3-direction.</td></tr><tr><td>CEM1</td><td>Elastic moment about the 1-direction.</td></tr><tr><td>CEM2</td><td>Elastic moment about the 2-direction.</td></tr><tr><td>CEM3</td><td>Elastic moment about the 3-direction.</td></tr></table>

Elastic relative displacement components 

<table><tr><td>CUE1</td><td>Elastic displacement in the 1-direction.</td></tr><tr><td>CUE2</td><td>Elastic displacement in the 2-direction.</td></tr></table>

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<table><tr><td>CUE3</td><td>Elastic displacement in the 3-direction.</td></tr><tr><td>CURE1</td><td>Elastic rotation about the 1-direction.</td></tr><tr><td>CURE2</td><td>Elastic rotation about the 2-direction.</td></tr><tr><td>CURE3</td><td>Elastic rotation about the 3-direction.</td></tr></table>

Plastic relative displacement components 

<table><tr><td>CUP1</td><td>Plastic relative displacement in the 1-direction.</td></tr><tr><td>CUP2</td><td>Plastic relative displacement in the 2-direction.</td></tr><tr><td>CUP3</td><td>Plastic relative displacement in the 3-direction.</td></tr><tr><td>CURP1</td><td>Plastic relative rotation about the 1-direction.</td></tr><tr><td>CURP2</td><td>Plastic relative rotation about the 2-direction.</td></tr><tr><td>CURP3</td><td>Plastic relative rotation about the 3-direction.</td></tr></table>

Equivalent plastic relative displacement components 

<table><tr><td>CUPEQ1</td><td>Equivalent plastic relative displacement in the 1-direction.</td></tr><tr><td>CUPEQ2</td><td>Equivalent plastic relative displacement in the 2-direction.</td></tr><tr><td>CUPEQ3</td><td>Equivalent plastic relative displacement in the 3-direction.</td></tr><tr><td>CURPEQ1</td><td>Equivalent plastic relative rotation about the 1-direction.</td></tr><tr><td>CURPEQ2</td><td>Equivalent plastic relative rotation about the 2-direction.</td></tr><tr><td>CURPEQ3</td><td>Equivalent plastic relative rotation about the 3-direction.</td></tr><tr><td>CUPEQC</td><td>Equivalent plastic relative motion for a coupled plasticity definition.</td></tr></table>

Kinematic hardening shift force components 

<table><tr><td>CALPHAF1</td><td>Kinematic hardening shift force in the 1-direction.</td></tr><tr><td>CALPHAF2</td><td>Kinematic hardening shift force in the 2-direction.</td></tr><tr><td>CALPHAF3</td><td>Kinematic hardening shift force in the 3-direction.</td></tr><tr><td>CALPHAM1</td><td>Kinematic hardening shift moment about the 1-direction.</td></tr><tr><td>CALPHAM2</td><td>Kinematic hardening shift moment about the 2-direction.</td></tr><tr><td>CALPHAM3</td><td>Kinematic hardening shift moment about the 3-direction.</td></tr></table>

Viscous force components 

<table><tr><td>CVF1</td><td>Viscous force in the 1-direction.</td></tr><tr><td>CVF2</td><td>Viscous force in the 2-direction.</td></tr><tr><td>CVF3</td><td>Viscous force in the 3-direction.</td></tr><tr><td>CVM1</td><td>Viscous moment about the 1-direction.</td></tr></table>

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CVM2 Viscous moment about the 2-direction.

CVM3 Viscous moment about the 3-direction.

# Uniaxial force components

Connector uniaxial behavior can be defined only in Abaqus/Explicit; therefore, there is no uniaxial force output available in Abaqus/Standard.

CUF1 Uniaxial force in the 1-direction.

CUF2 Uniaxial force in the 2-direction.

CUF3 Uniaxial force in the 3-direction.

CUM1 Uniaxial moment about the 1-direction.

CUM2 Uniaxial moment about the 2-direction.

CUM3 Uniaxial moment about the 3-direction.

# Friction force components

CSF1 Force due to frictional stress in the 1-direction.

CSF2 Force due to frictional stress in the 2-direction.

CSF3 Force due to frictional stress in the 3-direction.

CSM1 Frictional moment about the 1-direction.

CSM2 Frictional moment about the 2-direction.

CSM3 Frictional moment about the 3-direction.

CSFC Force due to frictional stress in the instantaneous slip direction. Available only for predefined or user-defined coupled friction interactions.

# Contact force components generating friction

CNF1 Contact force generating friction in the 1-direction.

CNF2 Contact force generating friction in the 2-direction.

CNF3 Contact force generating friction in the 3-direction.

CNM1 Contact moment generating friction about the 1-direction.

CNM2 Contact moment generating friction about the 2-direction.

CNM3 Contact moment generating friction about the 3-direction.

CNFC Contact force generating friction in the instantaneous slip direction.

# Total overall damage components

CDMG1 Overall damage variable in the 1-direction.

CDMG2 Overall damage variable in the 2-direction.

CDMG3 Overall damage variable in the 3-direction.

CDMGR1 Overall damage variable about the 1-direction.

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CDMGR2 Overall damage variable about the 2-direction.

CDMGR3 Overall damage variable about the 3-direction.

Connector force-based damage initiation criteria 

<table><tr><td>CDIF1</td><td>Connector force-based damage initiation criterion in the 1-direction.</td></tr><tr><td>CDIF2</td><td>Connector force-based damage initiation criterion in the 2-direction.</td></tr><tr><td>CDIF3</td><td>Connector force-based damage initiation criterion in the 3-direction.</td></tr><tr><td>CDIFR1</td><td>Connector force-based damage initiation criterion about the 1-direction.</td></tr><tr><td>CDIFR2</td><td>Connector force-based damage initiation criterion about the 2-direction.</td></tr><tr><td>CDIFR3</td><td>Connector force-based damage initiation criterion about the 3-direction.</td></tr><tr><td>CDIFC</td><td>Connector force-based damage initiation criterion in the instantaneous slip direction.</td></tr></table>

Connector motion-based damage initiation criteria 

<table><tr><td>CDIM1</td><td>Connector motion-based damage initiation criterion in the 1-direction.</td></tr><tr><td>CDIM2</td><td>Connector motion-based damage initiation criterion in the 2-direction.</td></tr><tr><td>CDIM3</td><td>Connector motion-based damage initiation criterion in the 3-direction.</td></tr><tr><td>CDIMR1</td><td>Connector motion-based damage initiation criterion about the 1-direction.</td></tr><tr><td>CDIMR2</td><td>Connector motion-based damage initiation criterion about the 2-direction.</td></tr><tr><td>CDIMR3</td><td>Connector motion-based damage initiation criterion about the 3-direction.</td></tr><tr><td>CDIMC</td><td>Connector motion-based damage initiation criterion in the instantaneous slip direction.</td></tr></table>

Connector plastic motion-based damage initiation criteria 

<table><tr><td>CDIP1</td><td>Connector plastic motion-based damage initiation criterion in the 1-direction.</td></tr><tr><td>CDIP2</td><td>Connector plastic motion-based damage initiation criterion in the 2-direction.</td></tr><tr><td>CDIP3</td><td>Connector plastic motion-based damage initiation criterion in the 3-direction.</td></tr><tr><td>CDIPR1</td><td>Connector plastic motion-based damage initiation criterion about the 1-direction.</td></tr><tr><td>CDIPR2</td><td>Connector plastic motion-based damage initiation criterion about the 2-direction.</td></tr><tr><td>CDIPR3</td><td>Connector plastic motion-based damage initiation criterion about the 3-direction.</td></tr><tr><td>CDIPC</td><td>Connector plastic motion-based damage initiation criterion in the instantaneous slip direction.</td></tr></table>

Connector lock or stop status

CSLSTi Flags for connector stop and connector lock status .

Friction-related accumulated slip

CASU1 Accumulated frictional slip in the 1-direction.

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<table><tr><td>CASU2</td><td>Accumulated frictional slip in the 2-direction.</td></tr><tr><td>CASU3</td><td>Accumulated frictional slip in the 3-direction.</td></tr><tr><td>CASUR1</td><td>Accumulated frictional rotation about the 1-direction.</td></tr><tr><td>CASUR2</td><td>Accumulated frictional rotation about the 2-direction.</td></tr><tr><td>CASUR3</td><td>Accumulated frictional rotation about the 3-direction.</td></tr><tr><td>CASUC</td><td>Accumulated frictional slip in the instantaneous slip direction.</td></tr></table>

# Frictional instantaneous velocity in the slip direction (available only if friction is defined in the slip direction)

CIVC Friction-related instantaneous velocity in the slip direction.

# Reaction force components due to kinematic constraints, connector locks, connector stops, and prescribed connector motion

<table><tr><td>CRF1</td><td>Connector reaction force in the 1-direction.</td></tr><tr><td>CRF2</td><td>Connector reaction force in the 2-direction.</td></tr><tr><td>CRF3</td><td>Connector reaction force in the 3-direction.</td></tr><tr><td>CRM1</td><td>Connector reaction moment about the 1-direction.</td></tr><tr><td>CRM2</td><td>Connector reaction moment about the 2-direction.</td></tr><tr><td>CRM3</td><td>Connector reaction moment about the 3-direction.</td></tr></table>

# Connector concentrated force components due to connector loads

<table><tr><td>CCF1</td><td>Connector concentrated force in the 1-direction.</td></tr><tr><td>CCF2</td><td>Connector concentrated force in the 2-direction.</td></tr><tr><td>CCF3</td><td>Connector concentrated force in the 3-direction.</td></tr><tr><td>CCM1</td><td>Connector concentrated moment about the 1-direction.</td></tr><tr><td>CCM2</td><td>Connector concentrated moment about the 2-direction.</td></tr><tr><td>CCM3</td><td>Connector concentrated moment about the 3-direction.</td></tr></table>

# Relative position components

<table><tr><td>CP1</td><td>Relative position in the 1-direction.</td></tr><tr><td>CP2</td><td>Relative position in the 2-direction.</td></tr><tr><td>CP3</td><td>Relative position in the 3-direction.</td></tr><tr><td>CPR1</td><td>Relative angular position in the 1-direction.</td></tr><tr><td>CPR2</td><td>Relative angular position in the 2-direction.</td></tr><tr><td>CPR3</td><td>Relative angular position in the 3-direction.</td></tr></table>

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Relative displacement components 

<table><tr><td>CU1</td><td>Relative displacement in the 1-direction.</td></tr><tr><td>CU2</td><td>Relative displacement in the 2-direction.</td></tr><tr><td>CU3</td><td>Relative displacement in the 3-direction.</td></tr><tr><td>CUR1</td><td>Relative rotation in the 1-direction.</td></tr><tr><td>CUR2</td><td>Relative rotation in the 2-direction.</td></tr><tr><td>CUR3</td><td>Relative rotation in the 3-direction.</td></tr></table>

Constitutive displacement components 

<table><tr><td>CCU1</td><td>Constitutive displacement in the 1-direction.</td></tr><tr><td>CCU2</td><td>Constitutive displacement in the 2-direction.</td></tr><tr><td>CCU3</td><td>Constitutive displacement in the 3-direction.</td></tr><tr><td>CCUR1</td><td>Constitutive rotation in the 1-direction.</td></tr><tr><td>CCUR2</td><td>Constitutive rotation in the 2-direction.</td></tr><tr><td>CCUR3</td><td>Constitutive rotation in the 3-direction.</td></tr></table>

Relative velocity components 

<table><tr><td>CV1</td><td>Relative velocity in the 1-direction.</td></tr><tr><td>CV2</td><td>Relative velocity in the 2-direction.</td></tr><tr><td>CV3</td><td>Relative velocity in the 3-direction.</td></tr><tr><td>CVR1</td><td>Relative angular velocity in the 1-direction.</td></tr><tr><td>CVR2</td><td>Relative angular velocity in the 2-direction.</td></tr><tr><td>CVR3</td><td>Relative angular velocity in the 3-direction.</td></tr></table>

Relative acceleration components 

<table><tr><td>CA1</td><td>Relative acceleration in the 1-direction.</td></tr><tr><td>CA2</td><td>Relative acceleration in the 2-direction.</td></tr><tr><td>CA3</td><td>Relative acceleration in the 3-direction.</td></tr><tr><td>CAR1</td><td>Relative angular acceleration in the 1-direction.</td></tr><tr><td>CAR2</td><td>Relative angular acceleration in the 2-direction.</td></tr><tr><td>CAR3</td><td>Relative angular acceleration in the 3-direction.</td></tr></table>

Connector failure status 

<table><tr><td>CFAILSTi</td><td>Flags for connector failure status (i = 1,6).</td></tr></table>

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# 31.1.5 CONNECTION-TYPE LIBRARY

Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE

# References

• “Connector elements,” Section 31.1.2   
• “Connector element library,” Section 31.1.4   
• \*CONNECTOR BEHAVIOR   
• \*CONNECTOR SECTION

# Overview

The connection-type library contains:

• translational basic connection components, which affect translational degrees of freedom at both nodes and may affect rotational degrees of freedom at the first node or at both nodes on the connector element;   
• rotational basic connection components, which affect only rotational degrees of freedom at both nodes on the connector element;   
• specialized rotational basic connection components, which in addition to rotational degrees of freedom affect other degrees of freedom at the nodes on the connector element;   
• assembled connections, which are predefined combinations of translational and rotational or translational and specialized rotational basic connection components; and   
• complex connections, which affect a combination of degrees of freedom at the nodes on the connector element and cannot be combined with any other connection component.

# Using the connection-type library

Each connection type is described in the connection-type library. Each library entry includes a figure, which relates the physical behavior to the idealized model and defines the local coordinate directions. Following the figure, each library entry defines kinematic constraints; constraint forces and moments internal to the connection; components of relative motion available for defining the connector behavior, connector motion, or connector loads (called available components); and kinetic forces and moments conjugate to the available components of relative motion. If appropriate, a discussion of the predicted Coulomb-like friction in the connection is included. Finally, the connection type is summarized in a table.

# Connection figures

A schematic drawing of each connection type is included along with the Abaqus idealization of the connection. The idealization indicates in what sense available components of relative motion are measured and how the nodes’ positions and orientation directions define the connection. When

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orientation directions are used to define the connection, the idealization shows these local directions at the appropriate nodes. If available components of relative motion exist in the connection, they are indicated in the figure as free relative motions. Figure 31.1.5–1 shows the connection figure for the REVOLUTE connection type, which affects only rotations. It has one available component (the rotation about the shared axis), requires an orientation at node ${ \pmb a } ,$ and allows an optional orientation at node b.

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Figure 31.1.5–1 Example connection type: REVOLUTE.

# Orientation directions

The orientation directions at node a (the first node on the connector element) are indicated as unit base vectors ${ \bf e } _ { i } ^ { a }$ , where $i \ = \ \{ 1 , 2 , 3 \}$ . Similarly, the orientation directions at node b are indicated as $\mathbf { e } _ { i } ^ { b }$ . When orientation directions are required at a node, you must define them as described in “Orientations,” Section 2.2.5. If orientation directions are optional but not provided at node ${ \pmb a } ,$ the global directions are used by default. If orientation directions are optional but not provided at node $\begin{array} { r } { \boldsymbol { b } , } \end{array}$ the orientation directions from node a are used by default.

Connector elements activate rotational degrees of freedom at the nodes to which they are attached if they do not exist already and an orientation is permitted at that node. The only exception is connection type JOIN, where an orientation is optional at node a but rotation degrees of freedom are not activated.

The orientation directions corotate with the rotation of the node to which they are attached (with the exception of connection type JOIN, which uses fixed directions when rotation degrees of freedom are not active at node a). If there are no elements with rotational degrees of freedom attached to the node, rotational multi-point constraints, or rotational equations, you must ensure that sufficient rotational boundary conditions are provided to avoid numerical singularities associated with unconstrained rotational degrees of freedom.

# Components of relative motion and connector forces and moments

The six components of relative motion, denoted $u _ { i }$ and $u r _ { i } \mathrm { f o r } i = \{ 1 , 2 , 3 \}$ , are defined in the description for each connection, where needed. These components include constrained and available components of relative motion. Forces and moments are denoted and . These quantities are either constraint forces and moments, which enforce the kinematic constraints on the constrained components of relative motion, or kinetic forces and moments, which are the work conjugate variables to the available components of
