II. REQUERIMIENTOS DE INFORMACIÓN
2. NÓMINAS DE RESPALDO DEL INFORME FINANCIERO
• To define a hyperelastic material:
• In the Model Treedouble-click the Materialscontainer.
L4.16
Modeling Rubber and Viscoelasticity with Abaqus
Curve Fitting Demonstration in Abaqus/CAE
• The Material Editor
• In the Edit Material dialog box a default material name Material-1appears.
• Replace this default name by typing the name rubber.
• The material editor appears with a blank options list and option definition area.
• From the menu bar in the upper portion of the editor window, select Mechanical
→ Elasticity → Hyperelastic.
L4.17
Modeling Rubber and Viscoelasticity with Abaqus
Curve Fitting Demonstration in Abaqus/CAE
• The parameters and data corresponding to
hyperelasticity appear in the option definition area below the option menus, and the word Hyperelasticappears in the Material Optionslist at the top of the dialog box.
• In the option definition area accept Test dataas the Input sourceselection.
• Note that the Strain energy potentialdefaults to the value Unknown. Click Test Data, and select Uniaxial Test Datafrom the list that
appears.
L4.18
Modeling Rubber and Viscoelasticity with Abaqus
Curve Fitting Demonstration in Abaqus/CAE
• The Test Data Editor appears
• Note that data required are Engineering (Nominal) Stress in column 1 and Engineering Strain in column 2.
• To display context-sensitive help for specific buttons, text fields, and other options in the Test Data Editor, you must select the option of interest and then press F1.
• Click mouse button 3 in the first cell of the table, and select Read from Filefrom the list that appears.
L4.19
Modeling Rubber and Viscoelasticity with Abaqus
Curve Fitting Demonstration in Abaqus/CAE
• In the Read Data from ASCII Filedialog box you may type the name of the file or click Selectto browse for the file.
• Click Select.
• From the ASCII File Selectiondialog box, chose the file named
st_treloar_abq.txt.
St = simple tension
_treloar = test data from Treloar _abq = stress strain format
• Click OKin the ASCII File Selectiondialog box.
• Click OKin the Read Data from ASCII File dialog box.
L4.20
Modeling Rubber and Viscoelasticity with Abaqus
Curve Fitting Demonstration in Abaqus/CAE
• Finished reading in the experimental data
• We are back in the Test Data Editor, but the dialog box may be rather small.
• Grab an edge or corner of the box and expand it until you can see all the Uniaxial Test Datavalues.
• There should be 14 data pairs, with maximum stress of 1.95 MPa and maximum strain value of 4.37 (437%
strain).
L4.21
Modeling Rubber and Viscoelasticity with Abaqus
Curve Fitting Demonstration in Abaqus/CAE
• Saving the test data set for use in Visualization
• Although the test data have been read in, they have not been saved as X–Y data.
• Click mouse button 3 in the first cell of the table, and select Create XY Datafrom the list that appears.
L4.22
Modeling Rubber and Viscoelasticity with Abaqus
Curve Fitting Demonstration in Abaqus/CAE
• Naming the X–Y data set
• Type in the name st_treloar in the Create XY Datadialog box.
• We will use this named data set later in the Visualization module.
• Click OKin the Create XY Data dialog box.
• Click OKin the Test Data Editor.
L4.23
Modeling Rubber and Viscoelasticity with Abaqus
Curve Fitting Demonstration in Abaqus/CAE
• Done with Test Data input
• We are now back at the Edit Material dialog box.
• If we wanted to read in more test data, we would repeat this process, selecting Biaxial Test Data, Planar Test Data, or Volumetric Test Datafrom the Test Datapull-down menu.
• We are finished with test data input, so click OKin the Edit Material dialog box.
L4.24
Modeling Rubber and Viscoelasticity with Abaqus
Curve Fitting Demonstration in Abaqus/CAE
• Back to the Model Tree
• This puts us back to the Model Tree. Having read in the uniaxial data,
we are ready to Evaluatethe material.
• The Evaluateoption is useful in the following scenarios:
• Comparing test data with the behavior predicted by a particular strain energy potential.
• Evaluating multiple strain energy potentials.
• Viewing behavior predicted by coefficients for a particular strain energy potential.
L4.25
Modeling Rubber and Viscoelasticity with Abaqus
Curve Fitting Demonstration in Abaqus/CAE
• The default settings for Test Setup are shown below:
• The upper area shows the available test data with which to work.
The lower area allows you to choose which standard stress-strain
responses to generate and the strain limits in tension and compression.
L4.26
Modeling Rubber and Viscoelasticity with Abaqus
Curve Fitting Demonstration in Abaqus/CAE
• The defaults for Strain Energy Potentialsare shown here.
• There are six major categories.
• For Polynomial, Ogden, and Reduced Polynomialyou must select the number of terms N in the energy function.
• You may choose one or more models to evaluate.
• In general selecting more than three models makes viewing the results difficult.
L4.27
Modeling Rubber and Viscoelasticity with Abaqus
Curve Fitting Demonstration in Abaqus/CAE
• Evaluate Material Function
• Rather than take the defaults, let’s choose 3 models:
• Mooney-Rivlin(Polynomial Form, N = 1).
• Ogden Form, N = 2.
• Neo-Hookean (Reduced Polynomial Form, N = 1).
• Your screen should now look like this (you may need to expand the dialog box to see all models).
With these models selected, click OKin the Evaluate Materialdialog box.
• This will launch the curve fitting process.
Curve fit results will automatically be displayed when ready.
L4.28
Modeling Rubber and Viscoelasticity with Abaqus
Curve Fitting Demonstration in Abaqus/CAE
• Material stability
• Material coefficients and stability information for each of the selected models is automatically displayed in the Material Parameters and Stability Limit Informationdialog box.
L4.29
Modeling Rubber and Viscoelasticity with Abaqus
Curve Fitting Demonstration in Abaqus/CAE
• Default results plotting of evaluate material
• The default results plotting uses three new viewports to display X–Y plots of stress-strain for Uniaxial response, Equibiaxial response, and Planar Tension response. You may want to maximize each window in turn to better view the viewports.
L4.30
Modeling Rubber and Viscoelasticity with Abaqus
Curve Fitting Demonstration in Abaqus/CAE
• Nondefault results plotting: Visualization
• The plots are created in the Visualization module and all the response data calculated during the curve fit are available to us in this module.
• Before creating additional plots, delete the three viewports labeled Uniaxial, Planar, and Biaxial.
• Maximize the remaining (original) viewport.
L4.31
Modeling Rubber and Viscoelasticity with Abaqus
Curve Fitting Demonstration in Abaqus/CAE
• The XY Data Manager
• The XY Data Managerdialog box may be rather small. Grab an edge or corner and make it bigger. Grab the vertical bar that separates Name from Descriptionand enlarge the Namearea. Notice the default names given to all the response curves from the curve fit calculations. These default names are very long to ensure uniqueness. You may shorten them with the Rename option.
• Notice that our named data set st_treloar(the test data) is also listed. All other data sets are simply stress-strain response curves to particular curve fits. Note that all of these data sets persist only in this Abaqus/CAE session.
L4.32
Modeling Rubber and Viscoelasticity with Abaqus
Curve Fitting Demonstration in Abaqus/CAE
• The XY Data Manager: plotting
• Click the st_treloar data set, then [Control]+Clickall the Uniaxial data sets
• Click Plot. This will plot the actual simple tension test data along with the curve fit response for all the material models (energy
potentials) chosen.
• You may need to move the XY Data Managerwindow out of the way to see the plot.
L4.33
Modeling Rubber and Viscoelasticity with Abaqus
Curve Fitting Demonstration in Abaqus/CAE
• Curve options
• The XY Curve Optionscan be used to modify the line and symbol
attributes for each data set. Line color, line style, and line thickness can be modified. You can choose to show or not show the line. Several symbol types are available. You can choose to show symbols or not;
and you can modify the symbol types, symbol size, symbol color, and symbol frequency.
• Select the st_treloar data set, and click Show symbol. Set the symbol color to Orange, the symbol type to +, and the symbol size to Large. Suppress the visibility of the line.
• Select the other three uniaxial data sets ([Shift]+Click), and do the following:
• Choose a solid line style, increase the line thickness one level and toggle off Show symbol.
• Set the line color of R_POLY_N1 to red; POLY_N1 to blue; and OGDEN_N2 to green.
• Edit the legend text to remove rubber_1 at the end of the description.
L4.34
Modeling Rubber and Viscoelasticity with Abaqus
Curve Fitting Demonstration in Abaqus/CAE
• Axis options
• Double-click the X-axis; change the scale to range from a min value of 0.0to a max value of 4.5; change the axis font to 12 bold Arial and the title to Engineering Strain and the title font to 18 bold Arial.
• Double-click the Y-axis; change the scale to range from a min value of 0.0to a max value of 2.0; change the axis font to 12 bold Arial and the title to Engineering Stress (MPa) and the title font to 18 bold Arial.
• Legend options
• Double-click the legend.
• In the Contents tabbed page of the Chart Legend Options dialog box, change the legend font size to 12.
• In the Area tabbed page of the dialog box, toggle on Inset.
• Dismiss the dialog box.
• Drag the legend over the chart.
L4.35
Modeling Rubber and Viscoelasticity with Abaqus
Curve Fitting Demonstration in Abaqus/CAE
• Uniaxial X–Y data plots, manipulated
• Shown at right is the modified X-Y plot we have generated. All further X-Y plots of stress-strain curve fit responses will be shown in this style.
• What material model gives the best fit to uniaxial data?
L4.36
Modeling Rubber and Viscoelasticity with Abaqus
Curve Fitting Demonstration in Abaqus/CAE
• Equibiaxial curve fit response
• We can repeat the plotting process using the XY Data Manager. If you have lost your Managerwindow, select
Tools→XY Data →Manager from the main menu bar. Choose the st_treloardata set and all the curve fit response Biaxial data sets.
• What can we conclude from this plot?
L4.37
Modeling Rubber and Viscoelasticity with Abaqus
Curve Fitting Demonstration in Abaqus/CAE
• Planar curve fit response plots
• Here we have selected the st_treloardata set and all the curve fit response Planar data sets
• What can we conclude from this plot?
L4.38
Modeling Rubber and Viscoelasticity with Abaqus
Curve Fitting Demonstration in Abaqus/CAE
• What if I have model coefficients?
• In cases where you may have some model (Mooney, Ogden, etc.)
coefficients, you can use the evaluate function to see the stress-strain response from those
coefficients. First, double-click rubberin the Model Tree to open the Edit Materialdialog box. Change Input Sourceto Coefficients, select the Polynomialstrain energy
function, and enter the values 0.8, 0.2, and 0.0in the boxes for C10, C01, and D1, respectively. Click OK.
L4.39
Modeling Rubber and Viscoelasticity with Abaqus
Curve Fitting Demonstration in Abaqus/CAE
• What if I have model coefficients?
• Now Evaluatematerial again. Under Available Input Data, change the Sourceto Coefficients.
• Change the minimum nominal strain to 0.0and the maximum nominal strain to 1.0for uniaxial and deselect Planar (Pure shear) and Biaxial. Take a look under the Strain Energy Potentialtab; we will evaluate the Polynomial, N = 1 material model because it was the one chosen earlier in the material editor.
• Click OKto perform the evaluation.
L4.40
Modeling Rubber and Viscoelasticity with Abaqus
Curve Fitting Demonstration in Abaqus/CAE
• Default X–Y plot from coefficient fit
• This is the default X–Y plot that appears. Notice that only one viewport is created because we deselected Planarand Biaxial. The material test data are included in the plot since they were still available for comparison purposes. If we want, we could delete the material test data prior to the evaluate and then the test data will not appear.
• Conclusion: Mooney coefficients of 0.8and 0.2represent a material much stiffer in uniaxial tension than the material for which we have test data.