w1 Spherical Indentation Ia

8/3/2019 w1 Spherical Indentation Ia

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Workshop 1

Spherical Indentation

Interactive Version

Note: This workshop provides instructions on using contact interactions interms of the ABAQUS GUI interface. If you wish to use the ABAQUSKeywords interface instead, please see the Keywords version ofthese instructions.

Please complete either the Keywords or Interactive version of thisworkshop.

Introduction

When you complete this workshop you will be able to:

Define contact interactions in ABAQUS.

Debug models with numerical problems.

Compare the effects of the node-to-surface and surface-to-surface

formulations.

Understand the effect of small sliding versus finite sliding.

Define an analytical rigid surface.

Visualize results from contact analyses.

The workshop problems are modeled with very coarse meshes.

Such meshes are used because they clearly illustrate the strengths and

limitations of each modeling approach.

Results obtained from these levels of mesh refinement will be only

approximate.

Considerably finer meshes must be used to obtain accurate results.

Indentation of an axisymmetric rubber blank

This workshop models the indentation of a spherical punch into a rubber (hyperelastic)

blank. An axisymmetric model is used. The blank is 12 inches in diameter and 2 inches

thick. The punch has a radius of 2 inches and is much stiffer than the blank. It is moveddown 1.45 inches, which compresses the rubber blank. The meshed model is shown in

Figure W11. This problem is very similar to problem 1.1.4Indentation of anelastomeric foam specimen with a hemispherical punch from theABAQUS ExampleProblems Manual.

Copyright 2006 ABAQUS, Inc. Contact in ABAQUS/Standard


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Figure W11 Axisymmetric indenter and blank mesh.

Preliminaries

Enter the working directory for this workshop:

../contact/interactive/sphere

Run the script ws_contact_sphere.py using the following command:

abaqus cae startup=ws_contact_sphere.py

The above command creates an ABAQUS/CAE database namedsphere.cae

in the

current directory. The model geometry, material properties, and loading history have

already been created in the database in the model named indent.

Finite-sliding analysis with node-to-surface contact

In this section you perform a finite sliding analysis using the node-to-surface contactdiscretization. You will begin by adding the contact interactions in order to complete the

ABAQUS model. When the model definition is complete, you will run the analysis and

check for modeling errors.Before continuing, collapse the model named interf in the Model Tree so that only the

details of the model named indent appear. The following instructions refer to this

model unless otherwise noted.

1. Define the contact surfaces.

a. In the Model Tree, expand the Assembly. In the list that appears, double-clickSurfaces to open the Create Surface dialog box.

b. Name the surface Sphere and clickContinue.



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c. Select the contact surface on the spherical punch and clickDonein theprompt area.

d. Similarly, create a surface named Blank that includes the top edge of the

blank.

2. Define the contact property with the assumption that friction can be ignored.

Frictionless contact is the default contact property in ABAQUS.

a. In the Model Tree, double-clickInteraction Properties.

b. Name the propertyNoFric.

c. Accept the default property settings in the Edit Contact Property dialog

box.

3. Define the contact interaction between the steel sphere and the rubber blank using

the contact property and surfaces defined above.

a. In the Model Tree, double-clickInteractions.

b. Name the interaction Sphere-Blank. Define it in the Initial step and

accept Surface-to-surface contact (Standard)as the interaction type.c. When you are prompted to select the master surface, clickSurfaces in the

prompt area to access the Region Selection dialog box. Use this dialog

box to select the master and slave surfaces. Note that the slave surface in

this example is a surface, not a node region.

Question W11: Which surface should be chosen as the master surface?Remember the recommendations from Lecture 2. Which

surface is the slave surface?

d. Accept Node to surface as the constraint method as well as all other

default options in the Edit Interaction dialog box.

4. Once you have defined the contact condition, submit the job named indent foranalysis.

5. In the Model Tree, click mouse button 3 on the job name and select Monitorin

the menu that appears to monitor the job while it is running. Check for errors and

warnings messages under the Errors and Warnings tabs in the job monitor dialogbox.

Visualizing the job diagnostics

It is always a good idea to check the job diagnostic information to see if any problems

occurred during the analysis. In this section you will assess the analysis using the job

diagnostic tools available in the Visualization module.1. Once the analysis is complete, click mouse button 3 on the job name and select

Results in the menu that appears. ABAQUS/CAE loads the Visualization module

and opens output database file indent.odb.

2. From the main menu bar, select ToolsJob Diagnostics.



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An analysis summary is displayed in the Job Diagnostics dialog box. For

example, the summary from your analysis may be similar to the one shown in

Figure W12.

Figure W12 Job diagnostics summary.

If there are any numerical problems, you will have to understand why theyoccurred, correct them, and rerun the analysis.

Note: If encountered no errors in your analysis, please proceed to the next

section of this workshop Visualizing the node-to-surface results.

Question W12: Did you have any numerical problems in your analysis? If so,

use the Job History in the Job Diagnostics dialog box to

find the first iteration in which the problem occurred. Displaythe Warnings tabbed page for this iteration.

Does it look like this?



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Question W13: What is the cause of the zero pivot?

Note: Additional information regarding any numerical

problems may be found in the message (.msg) file. For

example, if you receive zero pivot warnings, the

overconstraint messages in the message file may help you

identify the cause.

3. If you answered yes to Question W12, it is likely that you did not define the

surfaces in the model correctly. A common error involves defining the punchcontact surface to include both the circular and vertical edges of the punch rather

than just the circular edge. To see the consequences of this modeling error using

the Visualization module, do the following:

a. From the main menu bar, select PlotDeformed Shape. (If the analysishas an error, this command may not work.)

The node on the upper left corner of the blank appears to violate thecontact constraint.

b. In the Results Tree, expand the contents of the output databaseindent.odb. Open the Surface Sets container and double-click the

master surface (SPHERE) to highlight it in the viewport.

With the master surface highlighted, it is clear that the contact condition

has not been violated.

Make the necessary corrections to the model (e.g., only include the circular edge

in the punch surface definition) and resubmit the job.

Visualizing the node-to-surface results

Once you have verified that the analysis completed without any problems, continue tostudy the analysis results.

1. Customize and display the deformed shape as follows:

a. Open the Common Plot Options dialog box (click the Common Options

tool in the toolbox).

b. Click the Labels tab and toggle on Show node symbols.

c. Click OK.

d. From the main menu bar, select PlotDeformed Shape; or use the

tool in the toolbox.

e. From the main menu bar, select ToolsColor Code (or click in the

toolbar). Change the color of the sphere part instance to cyan.

It should now be easier to see the results. Note that the slave nodes (on the

blank) do not penetrate the sphere. The master surface facets (on thesphere), however, show significant penetration into the blank. This is

common for the node-to-surface discretization when coarse meshes are

used.



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Question W14: The results are only approximate with this mesh. Which

portion of the model should be refined to obtain more accurate

resolution of the contact and, thus, more accurate results?

2. The variation of the contact pressure over the surface can be contoured. To makevisualization easier, you will remove the spherical punch from the display. Before

proceeding, however, suppress the node symbol display in the Common PlotOptions dialog box.

a. Click the Remove tool in the toolbar. In the prompt area select

Part instances as the entity type then click on the sphere. ClickDone tocomplete the operation.

b. From the main menu bar, select PlotContourson Deformed

Shape (or click in the toolbox).

c. From the main menu bar, select ResultField Output. In the

Primary Variable tabbed page, select CPRESS and clickOK.

d. From the main menu bar, select ViewODB Display Options. Inthe Sweep/Extrude tabbed page, toggle on Sweep elements and click

OK.

It should be much easier to visualize the results now. Use the view manipulationtools and the Views toolbox to resize and reposition the model as necessary. You

can also try contouring other variables such as Mises stress or a component of

stress.

Finite-sliding analysis with surface-to-surface contact

You will now perform a finite sliding analysis using the surface-to-surface contact

discretization.

1. Copy the model indent to a model named indent-s2s.

a. In the Model Tree, click mouse button 3 on indent and select Copy

Model in the menu that appears.

b. Enter indent-s2s as the name of the new model.

The following instructions refer to this model.

2. Modify the contact interaction so that the surface-to-surface contact discretizationis used.

a. In the Model Tree, double-clickSphere-Blank underneath the

Interactions container.b. In the Edit Interaction dialog box, change the constraint method to

Surface to surface and accept all the other options.

3. Create and submit a job for the surface-to-surface model as follows:

a. In the Model Tree, double-clickJobs.

b. Name the job indent-s2s and select indent-s2s as the model to be

analyzed. ClickContinue.



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c. In the Edit Job dialog box, enter the description Finite Sliding

Analysis of Sphere Indentation (s-to-s).

d. Submit the new model for analysis.

Question W15: Why does the surface-to-surface analysis model fail toconverge?

4. Modify the surface-to-surface model as follows:

a. In the Model Tree, expand the Steps container.

b. Double-click the step named Step-1.

c. In the step editor, open the Othertabbed page and select the

Unsymmetric equation solver.

d. Click OK to close the dialog box.

5. Resubmit the job.

Visualizing the surface-to-surface results

Once you have verified that the analysis completed without any problems, continue tostudy the analysis results.

Suppress the element sweeping activated in the last postprocessing session and reset the

view to the 1-2 plane. Then plot the deformed model shape.

Note that the level of penetration has been reduced significantly. This illustrates asignificant advantage of the surface-to-surface method over the node-to-surface method.

Small-sliding analysis

You will now run the model as a node-to-surface small-sliding analysis. (Surface-to-

surface small sliding is left as an optional exercise.)

The small sliding model is basically the same as the finite sliding model, except for the

modifications described below.

1. Copy the model indent to a model named indent-sm.

a. In the Model Tree, click mouse button 3 on indent and select Copy

Model in the menu that appears.

b. Enter indent-smas the name of the new model.


2. Modify the contact interaction so that the small sliding contact formulation is

used.

a. In the Model Tree, double-clickSphere-blank underneath the

Interactions container.

b. In the Edit Interaction dialog box, change the sliding formulation to

Small sliding and accept all the other options.

3. Create a job for the small sliding model as follows:

a. In the Model Tree, double-clickJobs.



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b. Name the job indent-smand select indent-smas the model to be

analyzed. ClickContinue.

c. In the Edit Job dialog box, enter the description Small Sliding

Analysis of Sphere Indentation.

d. In the General tabbed page of the Edit Job dialog box, toggle on Printcontact constraint data and Print model definition data so that details

regarding the model data and the internally generated contact elements

will be written to the printed output file.

e. Click OK.

4. Submit the new model for analysis. Use the job monitor to determine if there were

any problems during the analysis. If there were problems, use the informationprovided in the message and printed output files to isolate the problems and make

the necessary corrections.

Question W16: Does the use of the small-sliding formulation in this problem

require any change in the choice of the master or slave

surfaces?

5. When the analysis has completed, use the Visualization module to view the sameresults that you examined for the finite-sliding version of the analysis.

Question W17: Judging from the deformed shape plots, is a betterapproximation of the contact condition obtained with the

small-sliding model or with the finite-sliding model?

Display contours of the variable CPRESS.

Question W18: Can you explain why there are nonzero values of CPRESS at

the slave node, which, from the deformed shape, does not

appear to be contacting the sphere? Think about the local

contact plane that is formed at the start of the analysis.

Question W19: Where would that plane be located at the end of the analysis?

Question W110: Judging from the contours of CPRESS, which model has abetter approximation of the contact condition? Which model

produces the higher value of CPRESS?

Viewing the printed output file

Next, you will study the contact definition using the printed output file (.dat).

1. Open the printed output file indent-sm.dat in a text editor.

2. Find where the internally generated contact elements are defined. If you have aproblem, try searching for the string INTERNALLY.

Question W111: How many internal contact elements were generated?



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Modeling the spherical punch with a rigid surface

In this section you will replace the deformable, but very stiff, spherical punch with an

analytical rigid surface. You will then run the analysis and compare the results with theprevious versions of the model.

Node-to-surface contact

1. In the database sphere.cae, copy the model indent to a model named rigid.

A circular arc will be used to define the rigid spherical indenter. The center, start

and end point of the arc will have the same coordinates as the points used todefine the deformable indenter.


2. In the Model Tree, expand the Parts container and double-clicksphere. Identifythe coordinates of the points used to define the original deformable punch using

the point type query tool (ToolQuery).3. Create an axisymmetric analytical rigid part with a wire base feature. Name the

part Rigidand specify an approximate part size of30. Sketch a circular arc to

define the rigid surface using the coordinates queried in the previous step.

4. Create a reference point for the analytical rigid part at the center of the arc

(ToolsReference Point).5. In the Model Tree, expand the Assembly and double-clickInstances to create a

dependent instance of the rigid part (the choice of independent or dependent is ofno consequence in this problem and is chosen solely for consistency with the rest

of the assembly). In the list of instances, suppress sphere-1 so that the assembly

contains only the rigid sphere and the rubber blank. Figure W13 shows thecompleted assembly.

Figure W13 Assembly with rigid spherical punch.


(0, 4)

(0, 2)

(2, 4)


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6. Update the contact interaction as follows:

a. Edit the surface named Sphere to include the rigid sphere.

b. Edit the contact interaction to verify that the node-to-surface finite slidingformulation is used and check the contact surface definitions.

7. Apply boundary conditions to the rigid body reference point to constrain the rigidsurface.

a. For convenience, create a set named RefPt that contains the rigid body

reference point.

b. Edit the existing boundary condition namedpush.

c. Change the constrained region to refer to the rigid body reference point

and apply a 1.45 inch displacement in the vertical direction.Question W112: How many degrees of freedom does the rigid surface have?

Have you constrained the surface adequately?

8. The set xsymmis used to constrain the model to the axis of symmetry. In the

original model, this set contains the center edge of both the plate and thedeformable sphere. Redefine this set to contain only the left edge of the plate.

a. In the Model Tree, expand the Assembly and underneath the Sets

container, double-clickxsymm.

b. Reselect the left edge of the plate.

c. Click Done in the prompt area.

9. If necessary, remesh the blank (underneath the Parts container, expand the blank

and double-clickMesh; in the Mesh module, select MeshPart).10. Create a new job named rigidfor the rigid punch model.

Question W113: Did you define the rigid surface to have the correct surfacenormal, one that points toward the blank and not away fromit?

You can check to see if such modeling mistakes were made byrunning a data checkanalysis, as described below.

11. Edit the job rigidand choose Data check as the job type. Submit this job to

create an output database file with the model data as interpreted by ABAQUS.

Use the Visualization module to display the rigid surface normal direction.

a. Switch to the Visualization module and open rigid.odb.

b. From the main menu bar, selectOptionsCommon.c. Click the Normals tab, toggle on Show normals, and chose the On

surfaces option.

d. Click OK.

If you have any input mistakes, correct them and rerun the data check analysis.

12. When you are satisfied with the model definition, edit the job rigidand choose

Continueanalysis as the job type. Submit this job to continue the analysis,

without repeating the data check.



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13. Once the job completes, check the job diagnostic information in the Visualization

module to see if any numerical problems occurred during the analysis. Were there

any? Are there any clues regarding what might have gone wrong? Can you thinkof any corrections that need to be made?

If you found no clues explaining any analysis problems, plot the deformed shape.

Does it look correct? If it looks similar to Figure W14Error: Reference sourcenot found, you forgot to constrain the rotation of the rigid surface. Go back to the

Job Diagnostics dialog box, and look at the increment of rotation in any of thefirst increment equilibrium iterations (select an iteration, click the Residuals tab,

and select the Rotation variable.) Does the value make any sense?

Figure W14 Deformed shape if degree of freedom 6 is notconstrained at the rigid body reference node.

Make any modifications needed to your input to correct the modeling errorsand resubmit the model for analysis.

14. View the results in the Visualization module.

Question W114: How do the contours of CPRESS compare to those for thedeformable-to-deformable model?

Question W115: Based on the results, which representation of the spherical

punch is the best approximationdeformable or rigid?



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Surface-to-surface contact

1. Copy the model rigidto a model named rigid-s2s.

2. Edit the contact interaction to use the surface-to-surface method.3. Edit the step definition to use the unsymmetric solver.

4. Create and run a new job named rigid-s2s.

5. View the results in the Visualization module. You will again notice significantly

less penetration with this model than with the previous one.

Before exiting, save your ABAQUS/CAE model database (FileSave).

Additional exercises

If time permits, try doing some of the following exercises.1. Run an analysis with a more refined mesh for the rubber blank. Use the Mesh

module to remesh the blank with a smaller element seed size. Partition the blankto refine the mesh only in the area of contact.

Question W116: Is the peak value of CPRESS very different using the refinedmesh?

2. Try reversing the master and slave surfaces chosen for the different analyses.

3. Try modeling the spherical punch with a discrete rigid part, instead of ananalytical part. This procedure will be similar to replacing the deformable punch

with the analytical rigid punch. You will need to mesh the discrete rigid part with

axisymmetric rigid elements (RAX2).

Question W117: Is there a way to make the spherical punch behave as a rigid

body without replacing the deformable punch with a rigidpart?

4. Compare plots of the reaction forces required to push the sphere into the rubber

blank for the different analyses.

a. First you need to obtainXYdata for the variable RF (reaction force)

using one of two methods. You can create theXYdata from the field

output written to the ODB. Alternatively, you can rerun the analyses withadditional history output requests. For the rigid sphere models, obtain RF

data at the reference node. In the deformable sphere model, obtain RF datafor the top edge of the indenter.

b. Plot the history of the reaction force at the reference node for the rigid

sphere. For the deformable sphere operate on theXYdata to sum thereaction force at the nodes along the top edge of the indenter.



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Note: A script that creates the complete model described in these instructionsis available for your convenience. Run this script if you encounter difficultiesfollowing the instructions outlined here or if you wish to check your work. Thescript is named

ws_contact_sphere_answer.py

and is available using the ABAQUS fetch utility.


w1 Spherical Indentation Ia

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