abaqus經(jīng)典聲學分析例題l4-curve-fit

1、Curve FittingLecture 4Copyright 2006 ABAQUS, Inc.L4.2OverviewIts Just Curve Fitting!Material StabilityCurve Fitting Demonstration in ABAQUS/CAE Deviatoric (shear) curve fittingVolumetric Curve FittingModeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.Its Just Curve Fitting!Cop

2、yright 2006 ABAQUS, Inc.L4.4Its Just Curve Fitting!Curve fitting the tension test dataWe use linear or nonlinear least squares curve fit procedure.Minimize relative error normn()2thtestE =1- TTiii=1Linear least squares for polynomial and reduced polynomial forms.Nonlinear curve fit for all others (O

3、gden, Arruda-Boyce, Van der Waals).Nonlinear curve fit uses a Levenberg-Marquardt algorithm similar to that used in Twizell and Ogden (1986).Exception: the Marlow model requires no curve fitting!Modeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L4.5Its Just Curve Fitting!Reme

4、mber all the things learned about polynomial least squares curve fitting.Material models, especially the phenomenological ones, have no basis in rubber physics, not material “l(fā)aw.”Data points are nothing but weight points in the procedure.To enhance fit in certain strain range, increase the number o

5、f data points in that range (or reduce the number of data points elsewhere).ABAQUS/Standard and ABAQUS/Explicit do the curve fitting as part of the datacheck phase of a job. The material evaluation capability of ABAQUS/CAE automates this. To manually perform the curve fits and generate stress-strain

6、 data for plotting, see ABAQUS Benchmark Problem 3.1.4, Fitting of rubber test data.Modeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L4.6Its Just Curve Fitting!Visually check the curve fit response. ABAQUS/CAE automates this process by automatically generating plots of force

7、-displacement (Engineering Stress vs. Engineering Strain). If you dont have ABAQUS/CAE, you still need to do this!You should check tensile and compressive response.Check Stability. The curve fitting process does not guarantee a stable material model. It is up to you to check. Besides a visual check,

8、 you can check the stability limits in the Material Parameters and Stability Limit Information dialog box of ABAQUS/CAE or in the data (.dat) file.We have made some comments about model coefficients as an indicator of material stability; in general, a set of all positive coefficients guarantees stab

9、ility. However, some negative coefficients do not necessarily mean the model is unstable (just means it might be unstable). Typically lower order models have less stability problems.Modeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.Material StabilityCopyright 2006 ABAQUS, Inc

10、.L4.8Material StabilityStabilityWhat do we mean by material stability? Drucker postulate: s e 0.Graphically, in a stress vs. strain plot:Instability PointStressStrainModeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L4.9Material StabilityStability Checks in ABAQUS ABAQUS chec

11、ks the stability in the stretch range 0.1 l 10.0 (nominal strain range of -0.9 e 9) for the following deformation modes:-Uniaxial tension and compressionEquibiaxial tension and compressionPlanar tension and compressionModeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L4.10Mat

12、erial StabilityStability Checks in ABAQUSIn addition, ABAQUS checks the following deformation modes for foams:-Volumetric tension and compression-Simple Shear-If an instability is found, the preprocessor issues a warning message in the .dat file and prints the smallest nominal strains at which the i

13、nstability occurs in a particular deformation mode.-This same information is printed in the Material Parameters and Stability Limit Information dialog box in ABAQUS/CAE when the automatic material evaluation capability is used.If no instability is found, no messages will be printed.If an instability

14、 is likely to occur at the strain levels expected in the analysis, the material model should be revised.-Modeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L4.11Material StabilityStability warnings in ABAQUS/CAEModeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQ

15、US, Inc.L4.12Material StabilityGuaranteeing stability for various material modelsThe Neo-Hookean material model is always stable if C10 is positive.In general, the full or reduced polynomial material models will be materially stable if all the Cij are positive. However, some negative coefficients do

16、 not necessarily mean themodel is unstable (it just means it might be unstable). Typically lower order models have less stability problems.For the Yeoh model the C20 term is typically negative to help capture the S-shape feature of the stress-strain curve. If there are stability problems, reducing t

17、he absolute value of C20 or magnifying the value of C10 will help make the Yeoh model more stable.If all of the mi terms are positive the Ogden material model is guaranteed to be stable.Modeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L4.13Material StabilityGuaranteeing stab

18、ility for various material models For positive values of the initial shear modulus, m , and the locking stretch, lm, the Arruda-Boyce model is always materially stable. For positive values of the initial shear modulus, m , and the locking stretch, lm, the stability of the Van der Waals model depends

19、 on the global interaction parameter, a.All of the above comments are about material stability.Realize that geometric instabilities such as buckling, collapse, or snap- through may still occur in your analyses.Modeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.Curve Fitting De

20、monstration in ABAQUS/CAECopyright 2006 ABAQUS, Inc.L4.15Curve Fitting Demonstration in ABAQUS/CAETo define a hyperelastic material:In the Model Tree double-click theMaterials container.Modeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L4.16Curve Fitting Demonstration in ABAQ

21、US/CAEThe Material EditorIn the Edit Material dialog box a default material name Material-1 appears. 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, selec

22、t MechanicalElasticity Hyperelastic.Modeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L4.17Curve Fitting Demonstration in ABAQUS/CAEThe parameters and data corresponding to hyperelasticity appear in the option definition area below the option menus, and the word Hyperelastic

23、appears in the Material Options list at the top of the dialog box.In the option definition area accept Test data as the Input source selection.Note that the Strain energy potential button defaults to the value Unknown. Click Test Data, and select Uniaxial Test Data from the list that appears.Modelin

24、g Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L4.18Curve Fitting Demonstration in ABAQUS/CAEThe Test Data Editor appearsNote that data required are Engineering (Nominal) Stress in column 1 and Engineering Strain in column 2.To display context-sensitive help for specific buttons,

25、 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 File from the list that appears.Modeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L4.19C

26、urve Fitting Demonstration in ABAQUS/CAE In the Read Data from ASCII File dialog box you may type the name of the file or use the Select button to browse for the file. Click Select. From the ASCII File Selection dialog box, chose the file named st_treloar_abq.txt.= simple tensionst_treloar= test dat

27、a from Treloar= stress strain format_abq Click OK in the ASCII File Selectiondialog box. Click OK in the Read Data from ASCII File dialog box.Modeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L4.20Curve Fitting Demonstration in ABAQUS/CAEFinished reading in the experimental d

28、ataWe 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 Data values.There should be 14 data pairs, with maximum stress of 1.95 MPa and maximum strain value of 4.37 (437% strain).Modeling Ru

29、bber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L4.21Curve Fitting Demonstration in ABAQUS/CAESaving the test data set for use in VisualizationAlthough the test data have been read in, they have not been saved as XY data.Click mouse button 3 in the first cell of the table, and select

30、Create XY Data from the list that appears.Modeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L4.22Curve Fitting Demonstration in ABAQUS/CAENaming the XY data setType in the name st_treloar in the Create XY Data dialog box. We will use this named data set later in the Visualiza

31、tion module.Click OK in the Create XY Datadialog box.Click OK in the Test Data Editor.Modeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L4.23Curve Fitting Demonstration in ABAQUS/CAEDone with Test Data inputWe are now back at the Edit Material dialog box.If we wanted to read

32、in more test data, we would repeat this process, selecting Biaxial Test Data, Planar Test Data, or Volumetric Test Data from the Test Data pull-down menu.We are finished with test data input, so click OK in the Edit Material dialog box.Modeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 AB

33、AQUS, Inc.L4.24Curve Fitting Demonstration in ABAQUS/CAEBack to the Model TreeThis puts us back to the Model Tree. Having read in the uniaxial data,we are ready to Evaluate the material.The Evaluate option is useful in the following scenarios:Comparing test data with the behavior predicted by a part

34、icular strain energy potential.Evaluating multiple strain energy potentials.Viewing behavior predicted by coefficients for a particular strain energy potential.Modeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L4.25Curve Fitting Demonstration in ABAQUS/CAE The default setting

35、s for Test Setup are shown below:The upper area shows the available test data to work with.The lower area allows you to choose which standard stress-strain responses to generate and the strain limits in tension and compression.Modeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc

36、.L4.26Curve Fitting Demonstration in ABAQUS/CAEThe defaults for Strain Energy Potentials are shown here.There are five major categories.For Polynomial, Ogden, and Reduced Polynomial you must select the number of terms, N, in the energy function.You may choose one or more models to evaluate.In genera

37、l selecting more than three models makes viewing the results difficult.Modeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L4.27Curve Fitting Demonstration in ABAQUS/CAEEvaluate Material FunctionRather than take the defaults, lets choose 3 models:Mooney-Rivlin (Polynomial Form,

38、 N = 1).Ogden Form, N = 2.Neo-Hookean (Red. 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 OK in the Evaluate Material dialog box.This will launch the curve fitting process. Curve fit results

39、will automatically be displayed when ready.Modeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L4.28Curve Fitting Demonstration in ABAQUS/CAEMaterial stabilityMaterial coefficients and stability information for each of the selected models is automatically displayed in the Mater

40、ial Parameters and Stability Limit Information dialog box.Modeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L4.29Curve Fitting Demonstration in ABAQUS/CAEDefault results plotting of evaluate materialThe default results plotting uses three new viewports to display XY plots of

41、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.Modeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L4.30Curve Fitting Demonstration in ABAQUS/CAENondefault results

42、 plotting: VisualizationThe 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)

43、viewport.Modeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L4.31Curve Fitting Demonstration in ABAQUS/CAEThe XY Data ManagerThe XY Data Manager dialog box may be rather small. Grab an edge or corner and make it bigger. Grab the vertical bar that separates Name from Descriptio

44、n and enlarge the Name area. 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 withthe Rename option.Notice that our named data set st_treloar (the test data) is also listed. All oth

45、er data sets are simply strain-strain response curves to particular curve fits. Note that all of these data sets persist only in this ABAQUS/CAE session.Modeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L4.32Curve Fitting Demonstration in ABAQUS/CAEThe XY Data Manager: plotti

46、ngClick the st_treloar data set, then Control+Click on all the Uniaxial data setsClick 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 Manager window out of the way to s

47、ee the plot.Modeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L4.33Curve Fitting Demonstration in ABAQUS/CAEXY data plots: manipulationThe XY Curve Options can be used to modify the line and symbol attributes for each data set. Line color, line style, and line thickness can b

48、e 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 Oran

49、ge, the symbol type to +, and the symbol size to small.Deselect the Show line attribute. Click Apply.Select the other three data sets (use Shift+Click or Control+Clickselections), and increase the line thickness one level. Modify the line colors as follows: Neo-Hooke is set to Red; Mooney is set to

50、Blue; OGDEN_N2 is set to Green.Click OK.Modeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L4.34Curve Fitting Demonstration in ABAQUS/CAEXY Data Plots: ManipulationUnder XY Plot Options you can do things like add titles, change the axis scales (auto-scale or Specify scale), ch

51、ange color and thickness attributes for various grid lines.Click the Titles tab and:Set X-Axis Title Source: User-SpecifiedSet Y-Axis Title Source: User-SpecifiedClick the Scale tab and:Add X-Axis Title “Engineering Strain.”Y-Axis Title “Engineering Stress (MPa).”Set the X-Axis scale to Specify; max

52、 value=4.5, min value=0.0Set the Y-Axis scale to Specify; max value=2.0, min value=0.0 Click OKThe legend attributes The legend location can be modified using commands under Viewport Viewport Annotation Options (from the main menu bar). Select the Legend tab, and modify legend attributes.Modeling Ru

53、bber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L4.35Curve Fitting Demonstration in ABAQUS/CAEUniaxial XY data plots, manipulatedShown below 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 materia

54、l model gives the best fit to uniaxial data?How was the background color changed to white?Modeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L4.36Curve Fitting Demonstration in ABAQUS/CAEEquibiaxial curve fit responseWe can repeat the plotting process using the XY Data Manager

55、. If you have lost your Manager window, just go back to ToolsXY Data Manager from the main menu bar.Choose the st_treloar data set and all the curve fit response Biaxial data sets.What can we conclude from this plot?Modeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L4.37Curve Fitting Demonstration in ABAQUS/CAEPlanar curve fit response plotsHere we have selected the st_treloar data set and all the curve fit response Planar data setsWhat can we conclude fromthis plot?Modeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L4.38Curve Fitting Demons