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MATS23702    An Introduction to Modelling in Abaqus Tutorial 2

In the last workshop, you have been introduced to Abaqus, and now have some experience of setting up and running mechanical simulations. In this workshop, you will be given a problem to model with only a limited number of instructions. You will be asked to generate a suitable simulation, and compare the results of your simulation against theory and experiment.
You will also be asked to perform a mesh sensitivity study on your Abaqus model – sometimes the result of an FE simulation can change depending on the mesh size, and a mesh sensitivity study can help you understand when this is happening.
You may find it useful to look back at the previous tutorial if you are unsure how to set up your model.
You should work individually for this tutorial.
There will be a preliminary report for this tutorial, and also a longer written report. The details of the longer written report are given at the end of this tutorial document.
You are not expected to finish this tutorial in only one three-hour session – it may take more time than this!
Learning Outcomes:
By the end of this tutorial, you should be able to:
• Use Abaqus to create a model of three-point bending with only limited guidance.
• Extract model prediction data from Abaqus and compare it against experimental data.
1 Problem Definition
Your task is to set up and run an Abaqus FE simulation of a polymer beam undergoing three-point elastic bending. The experimental set up is shown in the schematic, and photo, below:
A video of the bend test is provided on Canvas, together with the polyethylene (HDPE).
The test was performed such that a load was applied at the centre of the It is your task to produce a model of this three-point bending scenario that predicts the load vs. displacement behaviour.
You will set up your model in a very similar way to that in the previous on your model, before comparing your results to theory and experiment.
To create and run the simulation, you will need to:
• Create the beam and test fixture parts
• Create the material file for the beam
• Assign section properties to the beam
• Assemble the model
• Define the analysis steps
• Create the surfaces to use in contact interactions
• Define contact between regions of the model
• Apply boundary conditions and loads to the assembly
• Mesh the assembly
• Create and submit a job
• View and record the results of your analysis
• Vary the mesh size and re-run your model to determine mesh sensitivity
Some instructions for each of these tasks are given in the following sections.
Please refer to the Tutorial 2 - Supplementary Guidance document for further information on the specific tasks in Abaqus.
2 Create the Model Parts
1. Create the jig pieces and beam parts, with dimensions as shown in the schematic above. The beam should be a 3D deformable extrusion, whilst the jig parts can be made as a 3D discrete rigid extruded shell.
• All the jig pieces have the same geometry. Hence, you only need to create one part for this (you’ll just make three instances of it).
2. Partition your beam (find under Tools) into quarters as shown below. This will help when you come to applying boundary conditions later.
3. Add a Datum point (find under the Tools menu) at the centre of the top of the beam – this is where the top jig piece will first make contact with the beam.
4. Add two Datum points to the bottom surface of the beam, where the centre of the jig pieces will first contact the beam.
5. Add a Datum point at the middle of the curved surface of your jig piece (where it will first touch the beam).
6. Add a Reference Point (find under Tools menu) at some corner of your jig 
Note 1: You need to define a reference point on any rigid body in order to apply constraints to it (i.e., to prevent its movement in particular directions).
Note 2: You could have proceeded with this simulation without generating the parts of the three-point bending jig. You could have simulated their effect reasonably well simply by applying loads to the beam at given points. However, you’re asked to generate these parts here to try out your CAD skills.
3 Generate the Material
Unlike metals, polymers exhibit non-linear elastic behaviour – their stress vs. strain curves are often not straight lines in the elastic regime. A tensile engineering stress vs. engineering strain curve was measured for the HDPE behaviour was almost entirely elastic (i.e. reversible), pronounced non-linear behaviour is seen.
The data for this test in text format is available on Canvas.
The stresses that your beam will experience in this simulation should be small, less than 15 MPa.
1. Estimate the Young’s modulus of the HDPE that would be most appropriate for the bend test simulation, and use this to create the material file.
2. Use a Poisson’s ratio of 0.4 (or another one of similar size you find in from another source, HDPE is usually in the range 0.4 to 0.45).
4 Define and Assign a section
1. Define a homogeneous solid Section with the properties of the HDPE you just entered.
2. Assign the Section to the beam (in the Model Tree expand the beam part and look for Section Assignments).
• A set is created at the same time (see the prompt window). It’s called Set-1 by default, but you may wish to change this name.
• The beam will go an aqua colour when it has been assigned properties.
5 Assemble the model
To assemble the model, you need to first create instances of the parts required, then position the parts appropriately.
1. Create one instance of your beam piece to start with (dependent or independent, it doesn’t matter here).
2. Create one instance of the jig piece.
3. Position the first jig piece by using the Datum points and the Constraint → Coincident Point tool. You could also apply further constraints if you wish (for instance, you could constrain certain edges of the jig and beam to be parallel, to ensure the correct loading geometry).
4. Create two further instances of the jig piece, and position as appropriate.
• You may need to rotate the jig pieces. To do this, use the Rotate Instance tool
5. Create a new Set that includes only the reference point on the top jig piece. This reference point should be added only in the Assembly container within the model tree.
6 Define your analysis steps
Before you apply loads or boundary conditions to the model or define contact within the model, you must define the different steps in the analysis. Once the steps are created, you can specify in which steps loads, boundary conditions, and interactions should be applied.
The analysis that you perform on the beam-bending model will consist of an initial step (as generated by Abaqus automatically) and two general analysis steps:
• In the first general analysis step you allow contact to become established. You will ensure boundary conditions and contact interactions are active in this step.
• In the second general analysis step you will apply a displacement to the top jig piece of the model to simulate the three-point bending.
• You will need to toggle Nlgeom on in both the contact and displacement (loading) steps so that Abaqus can use your input material data correctly.
1. Create the contact analysis step. This should be a Static, General step with an initial increment size of 0.1.
2. Create a load step, with the same settings, apart from using an initial increment size of 0.001 (this will help you ensure that the initial movement of the top jig piece is not too large).
7 Request output
1. As you did in the previous tutorial, change the F-Output-1 settings such that outputs are only recorded at the Last increment of the contact step, but every step in the loading step.
2. Accept the default output variables selected for each step.
3. You need to record the load-displacement behaviour of the top jig piece. To do this, in the History Output Requests, create a new output in the loading step.
• For Domain, select Set, and select the reference point on the top jig.
• Select the output variables associated with displacement in the appropriate direction (it will be either U1, U2 or U3 along X, Y or Z respectively).
• Select the output variable associated with the reaction force in the appropriate direction (it will be either RF1, RF2 or RF3 along X, Y or Z respectively).
8 Define contact between regions of the model
Interactions are objects that you create to model mechanical relationships between surfaces that are in contact or closely spaced. Remember that mere physical proximity of two surfaces on an assembly is not enough to indicate any type of interaction between the surfaces.
You will need to define the contact interactions between each of the three jig pieces and the beam. You will assume there is no friction present between the jig pieces and the beam.
1. Create an Interaction property (contact type). Select Mechanical → Tangential Behavior and accept Frictionless.
2. Create the three surface-to-surface interactions from the contact step onwards. Make sure the jig piece is the master surface and the beam the slave (the master surface should always be the less-deformable one).
9 Apply boundary conditions and loads
Apply the following constraints from the contact step onwards: 
1. Constrain the two bottom jig pieces to be fixed in space and not rotate (Displacement/Rotation = 0). 
• You will need to apply the boundary condition to the reference points on each of the jig pieces. 
• Note in the prompt window that a set is created automatically when you create the constraint. Rename the set as appropriate.
• Hold [shift] to select more than one object.
2. Constrain the beam, as appropriate, to stop it slipping out of position. This may take some thought (hint: use the lines created by the partition). 
3. Constrain the top jig piece to only move in the vertical direction also (and no rotation).
4. From the load step onwards, apply a displacement of 2.5 mm to the top jig in the appropriate direction (probably this will be the negative y-direction). Again, you do this by applying the movement to the reference point. 
• If any of the other parts get in the way of selecting, you can go into the Assembly → Instances section of the Model Tree and hide them temporarily.
10 Mesh the beam
Select the Parts container → your beam:
1. Check the Mesh → Mesh Controls. Make sure Hex is the default Element Shape selection and Structured is the default Technique selection.
2. In the Element Type dialog box, check the Incompatible modes option to change the element type to C3D8I. Retain all other default values. (C3D8I are good for beam bending, and C3D8R can also be used, but you could also switch to quadratic elements – these are more expensive computationally, but more accurate in general. See more details here:
http://50.16.225.63/v6.14/books/usb/default.htm\
3. Seed the part with a global size of 2 and mesh it.
For the jig pieces:
4. Seed the parts will a mesh size of 0.5 or smaller (you can do this without impacting computing times significantly, since they are not solid objects).
11 Creating and submitting a job
Create and submit the job!
12 View results and export simulation data
1. Right click on the job and select Results.
2. Select to plot the results as contours on the parts.
3. From the top menu bar, select Animate → Time History to view the animation of your simulation.
4. To export data from the model, you first need to create the appropriate XY data:
• Double click on XYData in the Results Tree. Select ODB history output (the results are saved in an output database .obd file).
• Find the Reaction force for the top jig reference point (i.e., the load). Click Plot to view the data graphically, then click Save As… to save the data (this had not been exported yet). Do the same for the Spatial Displacement for the top jig reference point.
• Double click on XYData in the Results Tree. Select Operate on XY Data.
• Under Operators, select combine(X,X). Select the displacement data first to make this the X-axis data, then click the reaction force data to plot this data, then click Save As… to save the data.
• To export the data, go to Report → XY…, select the data you just created and click Apply. This will append your data to 
• If you get an error doing this, select to use the XY and click Apply.
13 Perform a mesh sensitivity analysis
The results obtained from FEM simulations can sometimes vary significantly with mesh size. In order to judge the impact of mesh size, a mesh results are compared against each other. Generally it will be the case that, as the mesh size decreases, the results obtained will converge to a constant value, such that a further decrease in mesh size makes little appreciable difference. Very small mesh sizes can take a long time to run, so it is advantageous to use the largest mesh size that gives the most consistent result.
1. Assess the results obtained for smaller mesh sizes, try 1 mm and 0.5 mm to begin with.
• Save the load vs displacement curves (see procedure in Section 13) for each of the mesh sizes.
2. Plot and compare these in an appropriate software package (e.g. Excel).
• Do they compare well? Do you think that decreasing the mesh size 
14 Further Tips
How to open your data in Excel:
1. If you follow the instructions given in the Tutorial 3 script, Abaqus exports your data as a .rpt file. This is exported to your working directory.
2. If you’re struggling to find where the .rpt file is, go into Abaqus and click File > Set Work Directory. You should be able to see where the file has been exported to (e.g. C:\work).
3. Open up Excel. Click Open, find the working directory. Select the type of file you can open to All Files (not just Excel files). You should now be able to see the .rpt file. Open it.
4. The Text Import Wizard opens. The data in the .rpt is delimited by a space (i.e., a space separates the columns). Accept the delimited option everything else and finish.
5. Your data should be displayed. If you have multiple sets of data, it’s because you’ve exported your data on multiple occasions, and Abaqus has simply appended it to the .rpt file.
If your data looks orders of magnitude out compared to my test data, make sure you're using the correct units for the Young's modulus you input (see bit on units in Tutorial 1).
If your plots show a different slope (i.e., a negative gradient, rather than positive like my experimental results), this is simply because we have defined our directions differently (e.g., my positive is your negative). You can flip your results in Excel if you want.
15 Preliminary Report
You should submit one screenshot and one file to Canvas.
1. A screenshot of your von Mises contour plot when the beam is in its position of maximum bending (best pasted into a Word document)
2. Your Abaqus CAE file (.cae) for the beam bending model. Upload this onto Canvas by the date specified in the assignment. To take a screenshot, you might wish to use the Snipping Tool, which is activated using the Windows + Shift + S key combination. Paste this into Word for easy viewing on Blackboard.
Continue to Section 16 for details of the written report…
Assessment criteria
Your submission will be marked /3, according to the following:
• 3 marks: full submission, correct.
• 2 marks: full submission, but with significant errors.
• 1 marks: partial submission (e.g., only the contour plot).
• 0 marks: no submission.
16 Written report - assessment brief
As part of your assessment for this course, you are asked to write and submit individually a report giving details of the simulation you created above and its results.
It should compare your simulation results to the experimental results for the beam bending you simulated, which are shown in the graph below (data for this available on Blackboard), and offer explanations for any discrepancies.
Your report should be no more than 3000 words, and no more than 8 pages including all figures, references and appendices. Font size no smaller than 11.
You need to upload your report via Canvas by the specified date. Please read all the information and guidance below.
You can split up your report into the following sections. The report should be written in the style of a standard lab report (see further guidance on BB for 
• Introduction and Aims. Provide a brief introduction to FE modelling 
• Simulation Set Up. Assume your reader is an experienced Abaqus for them to recreate your simulation? You do not need to give lots of detail here - no ‘this button was clicked’, ‘that button was clicked’ etc. This should be written in the past tense, in the same style as you would for a standard lab report.
• Results. Describe your results and present your figures (graphs, etc).
Remember to provide text describing your results.
• Discussion. Discuss possible reasons for what your results shows.
• Summary. Give a brief summary of the findings of your investigation. Include only the key points.
There is an analytical theory (i.e., an equation) that describes the force vs. deflection behaviour of a beam undergoing three-point bending. You may as to the experimental results.
Assessment criteria
Marks will be awarded according to the following:
• Introduction and Aims (10%): Whether you have provided a brief introduction explaining the aims of your work.
• Simulation Set Up (15%): Whether you have provided the reader with section).
• Model and Tutorial Execution (15%): Whether you have completed the tasks outlined in the tutorial script, created a working and representative FE model, and presented evidence of these.
• Results (20%): Whether you have presented your results in an appropriate and coherent manner.
• Discussion (30%): The quality of your discussions, including comparisons of model results to the experimental results and theory.
• Presentation and Writing (10%): The structure of your report and the quality of writing, as well as the presentation of your report, including the quality of figures.
See the rubric at the end of this document.
17 Learning Outcomes Assessed:
• Create a basic linear elastic finite-element model in Abaqus for a simple loading scenario.
• Describe the creation of your model so others can understand your approach and accurately reproduce it.
• Discuss the limitations of finite element models, and reasons for discrepancies between model and experiment.
• Present the results of finite element simulations in a coherent manner.
• Write reports of sufficient quality for industry.
18 Other general considerations:
• The style of your report should be similar to your experimental lab reports – e.g., the simulation set up paragraph should be written in the past tense.
• You should make sure the scales on your graphs and other results are readable.
• You should label all your figures (e.g., Figure 1), and refer to all of them from your text.
• You should always define any acronyms (e.g., FEM) at the first point of use.
• There should be a space between numbers and their units, as well as between different units. For example: 600 m s-1, not 600ms-1
• Think about how many decimal places (or significant figures) it is appropriate to quote your results in. Do not present the same results in both tabular form and in graphical form – choose one or the other.
• You should NOT copy work from other sources, including other students – the work should be entirely your own. If information appropriately.