### Introduction

When it comes to simulating physical connections in ABAQUS, the axial connector takes center stage. In this post, we delve into the intricacies of utilizing axial connectors, specifically focusing on scenarios where linear or non-linear stiffness is defined—a commonplace in engineering simulations.

**Introduction to Axial Connectors**

The AXIAL connection type establishes a link between two nodes, where relative displacement occurs along the line separating them. This connector models a range of physical connections, including axial springs, shock dampers, dashpots, or node-to-node contact resembling a gap.

**Node Positions and Initial Displacements**

Nodes ‘a’ and ‘b’ can initially reside in the same position or in different positions, though our focus here is primarily on cases where they start with distinct initial positions—a scenario encountered in 99% of applications.

**Coordinate System and Displacement Direction**

Upon creating an axial connector, a Cartesian coordinate system is automatically generated, with the origin at point ‘a’ and the x-axis directed from ‘a’ to ‘b’. The displacement in this direction is denoted as ‘u_{1},’ allowing for force exclusively along this axis. We will explore forces arising from variations in connector length, a key aspect when utilizing axial connectors.

**Setting Up Axial Connectors: Connector Section in ABAQUS**

To initiate an axial connector, defining the Connector Section in ABAQUS is imperative. This is where the behavioral properties are specified, such as axial stiffness (elasticity), damping, and reference length. For our current study, the pivotal properties to define are axial stiffness and reference length.

**Understanding Axial Stiffness and Reference Length**

The axial stiffness, termed Elasticity in ABAQUS, governs the relationship between length variation and axial force. For instance, if the elasticity is set at 10 N/mm, a 5 mm variation in length results in a force of 50 N.

The reference length signifies the length at which no axial force is present—akin to the relaxed state of a spring.

### Example of Axial Connector with Constant Stiffness

Let’s imagine a situation where the starting gap between nodes “a” and “b” is 50 mm, exactly matching the reference length (50 mm too). At the beginning, there’s no force acting on the connector. Now, let’s say we move one of the nodes 5 mm along the axial direction, making the gap between the nodes wider—now it’s 55 mm. This shift leads to a force calculation: 10 N/mm * 5 mm, resulting in a force of 50 N. But you might be wondering, in which direction does this force act?

To understand the force’s direction, think of it like a spring. If the final length ends up being more than the reference length, the axial connector experiences a pulling force. As a consequence, the connector will attempt to bring the nodes closer together. However, here’s the twist—there needs to be an external force applied to keep the nodes apart. So, while the connector wants to reconnect the nodes, an opposing force is necessary that tries to separate the nodes. This dynamic interaction defines how axial connectors respond to changes in distance between the nodes.

### Example of Axial Connector with Nonlinear Stiffness

When working with ABAQUS, setting up axial stiffness can be straightforward. You have two choices: make it a constant value, creating a simple linear relationship between force and displacement—similar to what we just practiced. Alternatively, you can opt for a more intricate approach by defining a nonlinear relationship. In this case, you’d need to create a curve using a table that outlines force versus displacement. It’s like choosing between a straight road and a curvy path, depending on the complexity you need for your simulation.

As an example, suppose we have the following table that relates force and displacement:

Notice that between the points specified in this table, a linear interpolation occurs, resulting in a plot resembling a piecewise first-order polynomial function.

Breaking down the interpretation, let’s say we have a positive displacement of 25 mm. This implies that the distance between points “a” and “b” is the reference length plus 25 mm. When the final length exceeds the reference length in 25 mm, the connector force becomes 200 N, drawing the nodes together in a tractive manner. Similarly, with a positive displacement of 15 mm, we find ourselves in a comparable scenario, but the force is now 150 N, reflecting the dynamic relationship between displacement and force.

If there’s a displacement of -25 mm, it indicates that the distance between points “a” and “b” is the reference length minus 25 mm. In this case, the final length is shorter than the reference length. This leads to a connector force of -1000 N, showing that it’s compressive in nature—meaning it’s pulling the nodes together (external force) instead of pushing them apart.

When the displacement goes beyond 25 mm or falls below -25 mm, ABAQUS steps in to extend the curve through a process called extrapolation. Essentially, it’s like predicting what happens beyond the measured data. Now, there are two ways ABAQUS can do this: constant or linear extrapolation.

#### Contant Extrapolation

In constant extrapolation, ABAQUS simply sticks with the last known value. For instance, if the displacement is 30 mm, the force remains constant at 200 N. Similarly, if the displacement is -30 mm, the force remains steady at -1000 N.

#### Linear Extrapolation

On the other hand, with linear extrapolation, ABAQUS takes the last linear trend and continues it. For example, if the displacement is 30 mm, it calculates a new force using the same slope as the last linear interpolation. So, plugging in the values:

This way, even when we’re outside the measured range, ABAQUS gives us a calculated force that follows the trend of the data.

Conclusion: Mastering Axial Connectors in ABAQUS

Conclusion: Mastering Axial Connectors in ABAQUS

In wrapping up our exploration of axial connectors in ABAQUS, we’ve delved into their fundamental role in simulating physical connections, emphasizing scenarios with linear or non-linear stiffness. From establishing the basics to understanding axial stiffness nuances, we’ve witnessed how these connectors respond to varying lengths and forces.

Our journey touched on extrapolation possibilities, offering insights into predicting connector behavior beyond measured values. While we’ve covered key aspects of axial connectors with axial stiffness, there’s more to unveil. The next chapter will unravel the complexities of axial connectors with defined damping properties.

Stay tuned for deeper insights, as we continue to harness the potential of axial connectors in diverse engineering simulations. The adventure continues, and the discoveries are boundless!

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## 6 thoughts on “Axial Connector in ABAQUS: A Comprehensive Guide”

Very nice – thanks!

I would very much appreciate if You could make a similar post of of the model a bolted connection using a connector to simulate the bolt. This connector should, in addition to the axial stiffness given in your present post, include stiffness for the bolt shear and bolt bending. I have tried to sort this out using the Abaqus documentation but find it very difficult.

Hello Geir,

I’m delighted to hear that you enjoyed it.

We’ve got a dedicated post on bolt-pretension in Abaqus using the translator connector (you can find it here: https://learnfea.com/bolt-pre-tension-techniques-in-abaqus/) for applying the pretension. However, in our current approach, both the bolt and nut are modeled as solid flexible bodies. Just to clarify, are you suggesting that I model the bolt using beam elements instead of solid elements? I want to ensure I understand your request correctly.