Application of Abaqus in flexible structures

Many industry verticals such as transportation and mobility, aerospace and industrial machinery deal with challenges related to design of flexible structures. These structures could be cables, hoses, flexible pipes or anything similar.

Usually, they are not complex in geometry. Most of them are created in a CAD modeler using extrusion. They can be easily brick meshes using sweep meshing techniques. As most of these problems are large deformation type, initial configuration is not an indicator of contact interactions as simulation proceeds. As a result, a general contact approach is often required in an explicit simulation step.

The boundary conditions portion makes these problems nontrivial. These structures are often confined to a limited space in context of a large assembly. They should not clash with other parts in their vicinity. Hence efficient routing is required that has a direct impact on structural response. In such cases, it’s difficult to quantify boundary conditions. Such problems can be addressed by both prescribed displacement and force-based loading methods. Either way, the problem would require multiple steps to reach desired configuration iteratively.

Here we discuss a simple case of a long flexible cable to be routed in a specific way using force-based methods. We defined half a meter long flexible cable with a bundle of wires wrapped in a tape. These are copper wires with elastic and piecewise plastic material properties. The wires are modeled using beam elements with circular cross section. The objective is to route the cable to confine it to a space as shown below. The cable cross section is also shown.

The routed shape is an S shape structure in 3D space. The initial configuration is a straight cable of half meter length. We defined the routed shape as a hollow and rigid frictionless tube with a larger diameter than the outer diameter of cable. Next, we place the end of the cable at one opening of the tube and sweep it all through the next end of the tube using an appropriate follower force.

The problem is divided into four steps to have better control of the dynamic behavior of cable. In each step, the cable travels through a quarter of the tube. The follower force may require an adjustment during steps or may even require a counter force at the other end of the cable. We really don’t know these parameters. But we know the objective: Traverse the cable to the other end of the tube and release all forces when cable is contained in the tube.

Now, let’s see what type of loading scenario did the job in this model. As mentioned before, the routing is done in four steps namely: bending-a, bending-b, bending-c and bending-d. The applied forces and contacts are removed in the next two steps so that the cable can reach its equilibrium state after spring back. The applied force is 10 units initially along the axis of the cable. It’s a follower force which means its orientation changes to remain normal to the applied face all the time. In the last bending step, a counter force is applied at the rear of the cable to reduce the inertia as the cable slacks quite a bit.

The contact interactions remain active in all but the last step in which the cable is released from the tubes so it can gain its equilibrium state. A substantial spring back is observed in this step.

Each of the bending steps has a length of 5 seconds and each of the release steps has a length of 0.5 seconds.

Let’s have a look at the outputs: It’s worth to reiterate that user has two points of interest in the output. First, the deformed shape in equilibrium state to perform collision check. Second, the stresses in the equilibrium state that can predict structural failure or act as a reference state for further simulation.

The images below show the state of stress after four bending steps vs. the equilibrium state after spring back. Another set of images show the stress contours at the end section of the cable on covering as well as underlying wire bundle.

Conclusion: Abaqus did a wonderful job to solve this flexible cable-routing problem using a force-based approach. Below are the strong capabilities of Abaqus that played a key role in making this kind of work successful.

1. General Contact: The initial configuration is not a reference for future contact interactions due to number of wires in and out of contact status as simulation proceeds. An all-inclusive automatic contact detection is a must.
2. Beam Elements: The bundle is half a meter long and wires have an average diameter of 0.5 mm. Solving this model using 3D continuum elements for wires is an overkill and computationally very expensive. Beam element approach reduces the total elements count by 90 percent and replaces expensive solid elements with efficient beam elements. Some limitations do apply. Caution is recommended from fidelity perspective as beam elements cannot capture extreme local deformations and penetrations might occur.
3. Multi Step chaining: The problem requires modification in loading and contact definition from beginning to the end. Multi step approach allows users to modify loads and interactions in a given step while the steps are fully connected to each other to maintain loading continuity.

Based on the above capabilities, we strongly recommend Abaqus as a tool of choice for this kind of work that may be applicable in cables, hoses, pipes and other flexible structures.