Engineer students, engineer designers, and whoever is working with finite element software, especially the ABAQUS, heard the word “Convergence” or “convergence issues.” Here, we will explain what does that all mean and answer the common questions such as “what is the convergency?”, “how to identify the ABAQUS convergence issues?”Â etc.

# 1Â Â Â Â Â Â Â Finite element software

If you are an engineer, you always have design problems. When you are starting to solve the problems, you could do it in a conventional way: using ideal models, simple physical models, writing equations on papers, etc. But nowadays, in the real world, we use computers and software to design. With finite element software, you can design complex models and solve complicated equations to have actual results in the fastest way possible. So be a pro engineer and solve the problem in real conditions with the help of finite element software.

When you are using finite element software, you will encounter issues. Don’t worry; this is an ordinary matter. Here you will learn how to find these issues and deal with them.

# 2Â Â Â Â Â Â Â Convergency in finite element

The finite element method uses this main equation to solve a problem:

The “K” is the stiffness matrix, the “U” is called the displacement matrix, and the “F” is the force matrix (see figure 1 as an example). When this equation is solved correctly, we will have accurate results, and here we use the term “the problem is convergence”. If by any means the equation cannot be solved or has some issues which give us inaccurate results, we use the term “there are some convergence issues.”

Figure 1 an example of a stiffness matrix with the dimension 6Ã—6

## 3Â Â Â Â Â Â Â Symptoms for the ABAQUS convergence issues

Now, how do we know there is a convergence issue? You could see the solving procedure when running a job by clicking on the “monitor.” As you see (figure2), there are “Error” and “Warning” tabs. You can see some messages that inform you about your issues. Also, you could find more information in “.msg” (Standard solver), “.dat,” and “. sta” (Explicit solver) files. These issues are more in nonlinear models than the linear ones. Some examples of these symptoms are shown in figure 1.

Figure 2: some warnings in monitor window

## 4Â Â Â Reason behind the ABAQUS convergence issues

This section will explain the reasons for the ABAQUS convergence issues. It may be more than we explain here, but we discussed the most important and common ones.

Incomplete and defective modeling in FE is the most common reason for convergence issues; for example:

- Defining inappropriate constraints that may cause conflicts in boundary conditions or contact conditions.
- Using wrong elements.
- Defining inadequate material in the property module.
- Defining inappropriate boundary conditions or contacts.
- Modeling an unstable physical system.
- Set an improper increment size.

Now, we intend to explain one or two of these conflicts. See figure 3 for an example. Imagine you have a box, and an amount of pressure is applied to it.Â You want to calculate the stress; if you do not define the boundary condition, the box moves and the software cannot calculate the stress, and you will see an error. Note that this only happens when you analyze a static problem and use the Static step. Another example is if you constrain a surface and apply pressure on it simultaneously (see figure 4), the software will show an error; because it is not possible to have the surface fixed and apply pressure at the same time (inappropriate boundary conditions).

Figure 3: pressurized box without boundary conditions

Figure 4 inappropriate boundary conditions

# 5Â Â Â Â Â Â Â Identifying ABAQUS convergence issues

Here, we intend to present some recommendations to identify which symptoms and reasons are caused the issues, the “Errors” and the “Warnings.” The general way is to list the top potential reasons and then check them to see the changes in the software. In the end, start to fix them one at a time. Now, some of our recommendations:

## 5.1Â Â Â Â Â Â One of the best ways is to simulate a simpler model:

- If possible, make a 2D model or a linear one to have fewer details and elements.
- If possible, do not enter Plasticity or Nonlinear geometry to understand the model’s behavior.
- In a model with several pieces, insert one piece at a time to minimize the number of issues sources.

## 5.2Â Â Â Â Â Â Set increment values

Set appropriate increment values that include initial increment, minimum increment, maximum increment size, and the maximum number of increments. To learn more about increments click here.

Figure 5 Staticgeneral step window and Incrementation tab

When the ABAQUS standard solver starts to run a Job, it splits the step in the maximum number of increments you specified (system default is 100). According to the specified increment size (Figure 5), the solver starts to run the Job. In the case of increments, in ABAQUS standard solver, you usually encounter three Errors:

“Too many attempts made for this increment”; means the solver attempted several times to calculate the equations for this increment, but the convergence conditions were not satisfied; so, you either look into the “Increment size” again and modify it or look somewhere else to overcome this Error.

“Too many increments needed to complete the step”; means the solver needs more increments; therefore, you have to increase the “Maximum number of increments.”

“Time increment required is less than the minimum specified”; in this Error, you have to decrease the “Minimum” in “Increment size” to satisfy the convergence conditions.

## 5-3Â Â Â Â See the reasons for convergence issues

See the reasons of convergence issues reported in the .dat, .sta, .msg, and .odb files.

You can add more information in the message files. For example, use the keyword command “*PRINT, CONTACT=YES” in the input file of the model (-.inp) to get contact information in the message file. Or use the command “*PRINT, PLASTICITY=YES” to get the integration point numbers and element output for material issues. You can use the “*PRINT” command to add more information in message files (.msg, .sta). Be patient, and we will explain to you how to use this command.

First, you need to know the input file (.inp). The Input file is one of the ABAQUS files that contains model data such as load, step, etc. It is like the “.cae” file but has less size, and you can open it in a text file and change whatever you want. When you have created your model completely and then created a Job for it, before you run it, you can create an input file for the model by clicking on the “Write Input” button in the “Job Manager” window (see figure 6). You can open the input file in a text file and change whatever you want; then, to use it in the ABAQUS, open the file according to Figure 7.

Figure 6 Create an input file

Figure 7: Open the Input file in the software

Now, as you know what an input file is, let’s use the “*PRINT” command. You can find the instructions about the “*PRINT” command or any other keywords in the Keywords in the ABAQUS documentation (Figure 8).

Figure 8 Finding PRINT keyword in ABAQUS documentation

As you can see in Figure 9, open your input file through the Edit Keywords window; then, find the lines that define the loading conditions; after these lines and before “*END STEP,” you can add your “*PRINT” commands then click OK button. After running the Job, you would see the results in the .msg (Standard solver) and .sta (Explicit solver) files. Now, you know how to write an input file, use it, and modify it.

The next articles will discuss tools and methods to overcome the convergence issues.

Figure 9 Enter the PRINT command