Answers to Common ABAQUS Questions Spring 1996

ABAQUS / Answers

Selecting Solid Elements forStress Analysis inABAQUS/StandardThe solid (or continuum) elements in ABAQUS can beused for linear analysis and for complex nonlinear analysesinvolving contact, plasticity, and large deformations. Theyare available for stress, heat transfer, acoustic, coupledthermal-stress, coupled pore fluid-stress, piezoelectric, andcoupled thermal-electrical analyses.

Given the wide variety of element types available, it isimportant to select the correct element for a particularapplication. In this, the first of two articles about solids, weexplain the influence of an element’s interpolation order,basic formulation, and numerical integration scheme on itsperformance for stress analysis. In the next article we willaddress issues relating to coupled problems, compositesolids, and element output.

The solid element library includes full- and reduced-integration elements, with first- or second-orderinterpolation, in both normal and hybrid forms. Linearinterpolation, incompatible mode elements are alsoavailable. Chapter 3 of the User’s manual contains acomplete description of all solid elements, together with adescription of the properties required, applicable loadings,and output available.

Element SelectionChoosing an element for a particular analysis can besimplified by considering specific element characteristics:first- or second-order; full- or reduced-integration;hexahedra/quadrilaterals or tetrahedra/triangles; or normal,hybrid, or incompatible mode formulation. By consideringeach of these aspects carefully, we can arrive at the bestelement for a given analysis.

Elements formulated as quadrilaterals or hexahedraperform better if their shape remains approximately

rectangular with respect to their parametric coordinatesystems. When the elements are distorted, their accuracydeteriorates (see ABAQUS/Standard ExampleProblem 1.1.6). Therefore, try to use well-shaped elementsin regions of interest.

First- or Second-Order ElementsSecond-order elements provide higher accuracy than first-order elements for “smooth” problems that do not involvecomplex contact or impact, or severe element distortions.They capture stress concentrations more effectively and arebetter for modeling geometric features—they can model acurved surface with fewer elements. Finally, second-orderelements are very effective in bending-dominatedproblems.

First-order elements should be used in contact problemsbecause the contact forces are consistent with the directionof contact. First-order elements perform better in analysesinvolving impact because they have a lumped mass matrix.First-order elements also perform better in analysesrequiring large element distortions, such as the simulation ofcertain manufacturing processes or the response of rubbercomponents.

Bricks/Quadrilaterals or Tetrahedra/TrianglesTriangular and tetrahedral elements are geometricallyversatile and are used in many automatic meshingalgorithms. It is very convenient to mesh a complex shapewith tetrahedra or triangles, and the second-order versionsof these elements (C3D10, CAX6, etc.) are suitable forgeneral usage. However, a good mesh of hexahedralelements usually provides a solution of equivalent accuracyat less cost. Quadrilaterals and hexahedra have a betterconvergence rate than triangles and tetrahedra and are lesssensitive to mesh orientation.

The faces of second-order tetrahedra should not be part ofslave surfaces in contact problems because the equivalentnodal forces at the corners are zero, which leads toconvergence problems.

First-order triangles and tetrahedra are usually overlystiff, and extremely fine meshes are required to obtainaccurate results. As mentioned below, they also exhibitvolumetric locking in incompressible problems. As a rule,they should not be used except as filler elements in non-critical areas.

Full or Reduced IntegrationReduced-integration elements are less expensive thanequivalent fully integrated elements. Element type C3D20

ContentsSelecting Solid Elements for

Stress Analysis in ABAQUS/Standard 1

X–Y Plotting Improved 3

Running Jobs Sequentially 4

Compacting ABAQUS/Pre Databases 4

Page 2 ABAQUS/Answers

has 27 integration points, while C3D20R has only 8;therefore, element assembly is roughly 3.5 times morecostly for C3D20 than for C3D20R.

However, fully integrated elements are not necessarilymore accurate than those with reduced integration. With aregularly shaped mesh, reduced-integration elements canprovide results that are more accurate than those providedby fully integrated elements. This “super convergence”property is discussed in detail in many textbooks on finiteelements.

Hourglassing can be a problem with first-order, reduced-integration elements (CPS4R, CAX4R, C3D8R, etc.). Sincethe elements have only one integration point, it is possiblefor them to distort in such a way that the strains calculatedat the integration point are all zero; this leads to uncontrolleddistortion of the mesh. First-order, reduced-integrationelements in ABAQUS include hourglass control, but theyshould only be used with reasonably fine meshes.Hourglassing can also be minimized by distributing pointloads and boundary conditions over a number of adjacentnodes.

Shear locking occurs in first-order, fully integratedelements (CPS4, CPE4, C3D8, etc.) that are subjected tobending. The numerical formulation of the elements givesrise to shear strains that do not really exist—“parasitic”shear. This means these elements are far too stiff in bending;avoid them in bending-dominated problems.

Volumetric locking occurs in fully integrated elementswhen the material behavior is almost incompressible.Spurious pressure stresses develop at the integration points,causing an element to behave too stiffly for deformations thatshould cause no volume changes. If materials are almostincompressible (such as elastic-plastic materials for whichthe plastic strains are incompressible), second-order, fullyintegrated elements develop volumetric locking when theplastic strains are on the order of the elastic strains. However,since first-order, fully integrated quadrilaterals andhexahedra use selectively reduced integration (reducedintegration on the volumetric terms), these elements do notlock with almost incompressible materials. Reducedintegration, second-order elements develop volumetriclocking for almost incompressible materials only aftersignificant straining occurs. In this case, volumetric lockingis often accompanied by hourglassing. Frequently, thisproblem can be avoided by refining the mesh in regions oflarge plastic strain.

You should check the pressure stress at the integrationpoints (printed output) if you suspect volumetric locking,which is characterized by the pressure values showing acheckerboard pattern, changing significantly from oneintegration point to the next. Usually this cannot be seen withthe default smoothed contour plots in ABAQUS/Post, but itmay be visible in unaveraged plots (∗ SET, C QUILT=ON).

Normal or Hybrid ElementsHybrid elements are designed for use with incompressiblematerials where the bulk modulus is many times greaterthan the shear modulus (for example, in linear elasticmaterials where the Poisson’s ratio is greater than .495).

In hybrid elements the pressure is treated as anindependent solution variable. Because of this, hybridelements have more internal variables than their non-hybridcounterparts and are slightly more expensive.

Hybrid elements must be used if the material is fullyincompressible, except in the case of plane stress, such as ina shell element (since the incompressibility constraint canbe satisfied by varying element thickness). If the material isalmost incompressible and hyperelastic, hybrid elements arestill recommended. For almost incompressible, elastic-plastic materials and for compressible materials, hybridelements offer no advantages and, hence, should not be used.

Incompatible Mode ElementsIncompatible mode elements (C3D8I, CPE4I, etc.) are first-order quadrilateral and hexahedral elements that areparticularly useful for modeling bending problems. Theyinclude additional internal deformation modes that allowthem to perform almost as well as normal second-orderelements in bending-dominated analyses if they arereasonably close to being rectangular in shape. They havemore internal degrees of freedom than normal first-orderelements but are less expensive than the correspondingsecond-order elements.

Recommendations• If possible, use hexahedral elements in three-dimensional analyses since they give the best results forthe minimum cost. If an automatic tetrahedral meshgenerator is used, use second-order elements (C3D10).

• For linear and “smooth” nonlinear problems, usereduced-integration, second-order elements.

• Use second-order, fully integrated elements close tostress concentrations to capture the severe gradients inthese regions. However, avoid these elements in regionsof finite strain if the material response is nearlyincompressible.

• Use first-order elements for problems involving contactor large distortions. If the mesh distortion is severe, usereduced-integration, first-order elements.

• If the problem involves bending and large distortions,use a fine mesh of first-order, reduced-integrationelements.

• Incompatible mode elements can give accurate results inproblems dominated by bending if they are reasonablyrectangular in shape.

• Make all elements as “well shaped” as possible toimprove convergence and accuracy.

ABAQUS/Answers Page 3

X–Y Plotting ImprovedIn response to requests from users, we made a number ofimprovements to the X–Y plotting capabilities inVersion 5.5 of ABAQUS/Post. The enhancements, whichaddress functionality and utility, are primarily associatedwith three commands: ∗ GRAPH AXES, ∗ REPORT XYVALUES, and ∗ READ CURVE. This article highlightsthese changes and presents some examples.

The x- and y-values of a point in an X–Y plot may bedisplayed by using the ∗ REPORT XY VALUES commandand clicking on the point with the mouse.

When point 42 on curve LVD_1 is selected using the cursor,the output on the screen and in the report file (.rpt) is:

Curve:LVD_1, Point: 42,X=5.91792E-01, Y=1.89926E+10

If the INTERPOLATE parameter is used, any point on thecurve may be picked; otherwise, only the actual data pointsmay be selected.

Generic variables, such as S and U, may now be specifiedon the ∗ READ CURVE command for data being read fromthe results file or the selected results file. Previously, onlyindividual components could be read. Now, for example, ifstress values have been written to either the results file or theselected results file, the command

*read curve, name=stress, variable=s,element=100

creates a curve set containing histories of each componentof the stress tensor.

A list of nodes and node sets may be given using theNODE parameter on the ∗ READ CURVE command.Similarly, a list of elements and element sets may be givenusing the ELEMENT parameter. For example, the command

*read curve, name=disp, variable=u2,node=(101,201,lhend)

creates curves of the history of U2 for nodes 101, 201, andall the nodes in node set LHEND. The NSET and ELSETparameters, which were previously used to specify a nodeor element set for which multiple curves were required, areno longer used for this purpose.

0. 5. 10. 15. 20. 25. 30. 35.

DISPLACEMENT - U2

-120.

-80.

-40.

0.

40.

80.

REACTION FORCE - RF2

[x10 9]

x

xx

x

Data points arehighlighted whenselected with thecursor.

Point: 42

As an example, consider a plot of all the displacementcomponents for nodes 1, 5, and node set BASE. Compare thecommands necessary to generate and display these curveson one plot in Versions 5.4 and 5.5.Version 5.4 syntax:

*nset, nset=plot>1,5,base>*read curve, var=u1, nset=plot, name=dis1*read curve, var=u2, nset=plot, name=dis2*read curve, var=u3, nset=plot, name=dis3*display curve>dis1,dis2,dis3>

Version 5.5 syntax:*read curve, var=u, node=(1,5,base),

name=disp*display curve>disp>

The ∗ GRAPH AXES command controls the display ofaxis tickmarks, labels, and ranges on an X–Y plot. A numberof new parameters have been added to this command to allowall aspects of the graph display to be adjusted. The axes andaxis labels in the plot below were created with the followingABAQUS/Post command:

*graph axes,x max=4.e-5, xmin=0.,ymax=4.2e-3,ymin=0.,x tickmark=1.e-6,y tickmark=1.e-4,x label=10, y label=10,x digits=1, y digits=2,x intermediate grid=marks,y intermediate grid=marks,x grid=dashed, y grid=dashed

The Y TICKMARK and Y LABEL parameters specifythat tickmarks be plotted every 10-4 m and that every tenthtickmark be labeled. The Y INTERMEDIATE GRID andY GRID parameters cause a mark to be plotted at everyunlabeled tickmark and a dashed line at every labeled one.

0. 10. 20. 30. 40.

TOTAL TIME [x10 -6 ]

0.0

1.0

2.0

3.0

4.0

DISPLACEMENT - U1

[x10 -3 ] U1 for node_33

U1 for node_55

U1 for node_77

Page 4 ABAQUS/Answers

HIBBITT, KARLSSON & SORENSEN, INC.1080 Main Street, Pawtucket, RI 02860-4847Tel: 401 727 4200 Fax: 401 727 4208 E-mail: hks@hks.com

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Copyright 1996, Hibbitt, Karlsson & Sorensen, Inc.No part of this document may be reproduced in any form or distributed in any way without prior written agreement with Hibbitt, Karlsson & Sorensen, Inc.

http://www.abaqus.com

ABAQUS

The Y DIGITS parameter specifies that the labels are to beplotted with two significant digits.

Other X–Y Plotting Enhancements

• The parameters BTIME and ETIME have been added tothe ∗ READ CURVE command to allow partial timehistories to be read from the results and selected resultsfiles. These parameters may not be used in conjunctionwith BINC and EINC.

• If the NAME parameter is set equal to an existing curveset name, the new curve may now be appended to theexisting curve set. Other options in this case includeoverwrite (default) and cancel. This change affects the∗ READ CURVE, the ∗ DEFINE CURVE, and the ∗ PATHcommands.

• The values of and from a fracture mechanicsanalysis may be plotted. For example,

*read curve, name=curve1, variable=jint

creates a curve setCURVE1 containing the history contourintegrals for all contours requested in the analysis.

• The ∗ GRAPH LEGEND command provides additionalcontrol over the appearance of the graph legend.

• The ∗ SHOW, CURVE DATA command has been addedto display the data values for a specified curve on thescreen. The ∗ SHOW, CURVE command has beenrenamed to ∗ SHOW, CURVE ATTRIBUTES.

• The ∗ CURVE STYLE, SYMBOL TYPE command nowincludes both filled and hollow symbols.

• Limitations on the number of curves that can be readfrom the selected results file at one time have beenremoved.

Further details of these and other changes in the latestrelease of ABAQUS/Post are described in Section 6.4 of theVersion 5.5 Release Notes. Changes to output variables (notcovered here) are discussed in Section 6.5 of the ReleaseNotes.

J Ct

Running Jobs SequentiallyIf you need to run a number of ABAQUS jobs overnight orduring the weekend on an engineering workstation, it isbetter to run them sequentially rather than simultaneously.This ensures that the analyses do not compete for thecomputer’s memory and scratch disk space.

The following Unix script runs three jobs, run1.inp,run2.inp, and run3.inp, sequentially.

#!/bin/csh -fforeach job (run1 run2 run3)(abaqus job=${job} int) >& ${job}.logend

Create a file (e.g., runs.csh) containing this script.Ensure that the file has “execute” privilege:

chmod 777 runs.csh

and execute the script:

./runs.csh

Make sure that the input files for all the analyses are in thecurrent directory and that no output files are present.

Compacting ABAQUS/PreDatabasesThe performance of ABAQUS/Pre may degrade if youhave made many changes to a database, such as deletingand redefining large parts of a model. This causesinformation to be stored inefficiently as the databasebecomes fragmented. The size of the database will alsobecome larger than it has to be. If this occurs, trycompacting the database by using the Compact Databaseoption in the File menu. This must be selected before thedatabase is opened. ABAQUS/Pre will take a few minutesto compact the database, but it should produce a smallerdatabase file and improve performance whenABAQUS/Pre is used for further work on the model.