Answers to Common ABAQUS Questions Summer 1999

ABAQUS / Answers

ContentsDistributing Coupling Elements and

Kinematic Coupling Constraints 1

Penalty Contact in ABAQUS/Explicit 2

Distributing Coupling Elements andKinematic Coupling ConstraintsCourtesy, Hibbitt, Karlsson & Sorensen (Michigan), Inc.

Distributing coupling elements (DCOUP2D, DCOUP3D)and kinematic coupling constraints, introduced withABAQUS/Standard Version 5.8, offer general capabilitiesfor transmitting loads and associating motions between onenode and a collection of “coupling” nodes.

Both options associate the coupling nodes with a singlenode in a “rigid body” sense; translations and rotations ofthe node (the distributing coupling element node orkinematic coupling reference node) are associated with thecoupling node group as a whole. The distinction between thetwo options is in how the rigid body association is enforced.

The following examples illustrate this distinction.

Kinematic Coupling ConstraintsThe ∗ KINEMATIC COUPLING option is a nonlineargeneralization of the NASTRAN RBE2 element. For thisconstraint the rigid body association between the couplingnodes and the independent reference node is exact, similarto a BEAM multi-point constraint. Unlike the latter,however, with kinematic coupling constraints the user isfree to constrain degrees of freedom selectively (in acorotational coordinate system when finite rotations occur)at the coupling nodes. The kinematic coupling generallyresults in a stiff constraint that can be tailored to specificneeds. For example, consider the assembly shown below.

A notched shaft slides onto a stiffened box section withprotrusions. A torque is applied to the stiff section, and wewish to understand the finite rotation response of the shaft,which is fixed at its far end. One approach to analyzing this

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Possible regions forkinematic couplingconstraints

z

y

x

Torque

assembly would involve modeling contact between therelatively stiff box section and the relatively compliant shaft.

However, a simplified modeling approach can be pursuedby using a kinematic coupling constraint to approximate theeffect of the rigid box section on the shaft. The shaft is seenas transmitting only circumferential motion, which isachieved by constraining only the circumferential degree offreedom on the slots to the rigid body motion of a referencenode on the cylinder axis.

The constraint on the circumferential displacement can bedefined as follows (assuming a positive rotation about thez-direction):*orientation,system=cylindrical,name=kc0.0, 0.0, 0.0, 0.0, 0.0, 1.0*kinematic coupling,ref node=500,orientation=kcred_nodes, 2

The axial and radial displacements on the coupling nodesare not affected by this constraint. ABAQUS imposes theconstraint on the circumferential displacement byeliminating that degree of freedom at the coupling nodes.(As with MPCs and equations, once any combination oftranslational or rotational degrees of freedom at a couplingnode is constrained, additional translational or rotationalconstraints cannot be applied to that node.)

Distributing Coupling ElementsDistributing coupling elements, DCOUP2D andDCOUP3D, are nonlinear generalizations of theNASTRAN RBE3 elements. DCOUP elements influencethe response of a collection of coupling nodes via a singlenode, which forms the DCOUP element. The connection iscreated by using the ∗ DISTRIBUTING COUPLINGoption.NASTRAN is a registered trademark of NASA.

Reference node 500

z

The rigid body motion of thereference node is transmittedto selected degrees of freedomof the coupling nodes. Forpositive rotation about thez-direction, only the red noderegions would be included inthe constraint.

r

z

θ

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The DCOUP element, unlike the kinematic couplingconstraint, enforces a rigid body association between thecoupling nodes and the element node in an average sense;and the user is free, through the use of nodal weight factors,to control the averaging. The user-defined averaging can beused to distribute applied forces and moments to the couplingnodes, to prescribe an average displacement and rotation tothe coupling nodes, to distribute mass to the coupling nodes,and to create a flexible connection between the structural andsolid elements. This average association between the nodes’motions has some desirable properties:

• The structure to which the coupling nodes are attachedwill not be stiffened by the DCOUP element.

• Forces transmitted through the element, either throughthe application of a ∗ CLOAD at the element node orthrough the force of the rigid body constraint, will beproportional to “weight” factors assigned to the couplingnodes. This proportionality is generally complex, butphysically motivated, and similar to force distributions ina classic bolt-pattern analysis.

• The element node is constrained to follow the averagemotion of the coupling nodes, but no strict constraint isimplied in the opposite sense. Individual coupling nodesare not constrained to follow the rigid body motion of theelement node, only the coupling node group as a whole.

• Boundary conditions can be prescribed to nodesreferenced by the ∗ DISTRIBUTING COUPLINGoption.

These distributing coupling elements are appealing whena load transfer path is known but it is feasible or desirable tosuppress geometric details for the analysis at hand.

For example, consider the case of a global-local analysisof an offshore oil structure. A global beam or frame elementmodel can provide resultant axial, bending, torsion, andshear forces near a complex connection. We can then usedistributing coupling elements to apply those loads to a local,detailed shell model of the connection region. The use of theDCOUP element in an analysis such as this means that thecut sections are still free to ovalize and warp as the jointresponds to the resultant forces and moment; thus, cuts canbe made closer to the joint without adversely affecting thesolution due to unnatural stiffening as would occur if a beamMPC or the kinematic coupling option was used.

Using the ∗ CLOAD option, the relevant section forcesfrom the global model can be applied to nodes located at thecentroid of each cut section of the connection region. Theseforces and moments should be applied in local coordinatesystems (defined with ∗ TRANSFORM) that correspond tothe beam axis and normal directions in the global model.

Each of the centroidal nodes is used to define a distributingcoupling element (DCOUP3D) that references thecircumferential nodes of the relevant cut section via the∗ DISTRIBUTING COUPLING option.

To ensure that the shell model is in global equilibrium, wedefine minimal boundary conditions to constrain rigid bodymotion. The reaction forces in each of the six degrees offreedom chosen for this purpose should be minimal if theapplied loads and moments are in equilibrium.

Penalty Contact in ABAQUS/ExplicitA penalty contact algorithm was introduced inABAQUS/Explicit Version 5.8 as an optional alternative tothe default kinematic contact algorithm. The addition ofpenalty contact expands the range of contact problems thatcan now be addressed with ABAQUS/Explicit.

There are fundamental differences in the way in which thekinematic and penalty contact algorithms enforce contactconstraints. These differences can be illustrated with thesimple diagrams shown in Figure 1. This figure illustrates asingle slave node that is about to come into contact with afixed master surface.

A detail of a tubular joint with resultantforces and moments applied throughdistributing coupling elements.

f i

md pred

i

∆t( )2--------------------=

f i 1+ kdcuri 1+

=

d pred

fi

i+1

i n

predictedconfiguration

d cur

n

fi+1

i

i+1

Figure 1: (a) Kinematic contact (b) Penalty contact

(a)

(b)

ABAQUS/Answers Page 3

The kinematic algorithm is a predictor/corrector method.When kinematic contact is active in an analysis,ABAQUS/Explicit carries out a predictor phase and acorrector phase in each time increment. In the predictorphase the kinematic state of the model is advanced byignoring any contact conditions. This can result inoverclosure or penetration, as shown by the predictedconfiguration of the slave node in Figure 1a. In the correctorphase of the time increment, an acceleration correction isapplied to the slave and master nodes to correct for thispredicted penetration, while conserving momentum. Thiscorrection results in a final configuration for increment i inwhich the slave node is exactly in compliance with the mastersurface. It can be seen that the kinematic algorithm isessentially implicit—it seeks to eliminate the contactpenetration at the end of each time increment.

The penalty algorithm uses an explicit approach toenforcing contact constraints. Figure 1b illustrates the sameslave node penetrating the fixed master surface at the end ofincrement i (beginning of increment i+1). However, incontrast to the kinematic algorithm, a corrector phase is notprocessed for increment i. Rather, an interface “spring” isinserted automatically between the slave node and the masterface in increment i+1 to minimize the contact penetration.The force associated with the interface spring is equal to thespring stiffness multiplied by the penetration distance. Asmall residual penetration will, therefore, exist, since contactforces are not generated unless there is some amount ofpenetration at the beginning of the increment. Thus, theexplicit nature of the penalty algorithm is apparent, since itseeks to resolve contact penetrations that exist at thebeginning of each time increment.

Because the kinematic algorithm is implicit, it has noeffect on the ongoing calculation of the stable time incrementduring the analysis. The penalty algorithm may have theeffect of reducing the stable time increment, since thepenalty springs increase the overall stiffness acting on the

interface nodes. This added stiffness can reduce the stabletime increment in the same manner that increasing thestiffness of a material can.

ABAQUS/Explicit automatically computes a defaultspring (penalty) stiffness using the mass and stiffness of thecontacting bodies. The default penalty stiffness is calculatedto minimize residual penetration, while reducing the stabletime increment by no more than 4%. It is possible to overridethe default penalty stiffness by scaling it upward ordownward using the ∗ CONTACT CONTROLS, SCALEPENALTY=value option. If the penalty stiffness is scaled upsignificantly, the automatic time incrementation algorithm inABAQUS/Explicit will account for this and automaticallyreduce the stable time increment accordingly.

Though there are significant differences in the kinematicand penalty contact algorithms, for most problems they willyield similar results. Figure 2 shows the deformedconfigurations of a beam discretized with shell elements asit is crushed axially and collapses onto itself. Contact occursbetween the shells and flat rigid bodies attached to either endof the beam (not shown), as well as between the differentregions of the shell itself (self-contact). The twoconfigurations shown are quite similar, even though differentcontact algorithms are used in each analysis. In addition, thechoice of contact algorithm has little effect on thecomputational cost, since the overall CPU times are nearlyidentical in these two cases.

Penalty contact is invoked by adding the PENALTYparameter to the ∗ CONTACT PAIR option.

vo

(a) (b)

Figure 2: Intermediate configuration of a frame rail impactinga rigid wall: (a) Kinematic contact (b) Penalty contact

(a)

(b)

Figure 3: Forging example(a) Kinematic contact (Pure master-slave)(b) Penalty contact (Balanced master-slave)

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

Copyright 1999, Hibbitt, Karlsson & Sorensen, Inc.No part of this document may be reproduced in any form or distributed in any way withoutprior written agreement with Hibbitt, Karlsson & Sorensen, Inc.

ABAQUS

It is possible to use a combination of kinematic contactpairs and penalty contact pairs in the same analysis.

One advantage of penalty contact is that it allows abalanced master-slave approach for contact between facetedrigid bodies and deformable bodies. Figure 3 shows a two-dimensional forging model, in which the billet must flowaround two sharp corners in the rigid forging dies. Using therequired pure master-slave approach for kinematic contactbetween a deformable and a rigid body, noticeablepenetration of one of these corners into the billet occurs, evenwith adaptive meshing invoked for the billet. However, usinga balanced master-slave approach with penalty contact, thispenetration is greatly reduced, since the nodes at each cornerof the rigid dies can now be considered as slave nodes in thecontact algorithm. In Version 5.8 ABAQUS/Explicit uses abalanced master-slave approach by default for all penaltycontact pairs between discretized surfaces.

Penalty contact also provides the capability to simulatecontact between two rigid bodies. At least one of the bodiesmust be discretized with elements (contact between twoanalytical rigid surfaces is not possible). Figure 4 shows asimple mechanism modeled in ABAQUS/Explicit.

The primary goal of the analysis is to evaluate thekinematic motion and forces associated with actuating themechanism. The stresses in each component are not critical,and the corresponding elastic deformations are considerednegligible; hence, it is possible to consider each componentas rigid. Since a rigid body in ABAQUS/Explicit can be anycollection of nodes and elements assigned by the user,components of a model can be discretized initially withdeformable elements, then designated as rigid using the∗ RIGID BODY option. The rigid vs. rigid contact approachallows the simulation to run much faster than if eachcomponent were considered deformable, since expensive

element calculations are not required and larger timeincrements can generally be used. Figure 5 shows timehistories of displacement and reaction force obtained whenboth the cam and cam follower are considered as rigid.

The main disadvantage of penalty contact is that thecontact constraints are not enforced exactly—there is a smallresidual penetration that exists while two bodies are incontact. In most applications this residual penetration has anegligible impact on the solution of interest. However, insome small-deformation, displacement-driven Hertz contactproblems, this small residual penetration may have a moresignificant effect on the predicted stresses in the contactingbodies. In such cases the default kinematic contact algorithmshould be used.

The following guidelines can, thus, be establishedregarding the choice of kinematic or penalty contact for aparticular problem:

• In most cases the two algorithms will yield very similarresults at similar computational expense.

• Penalty contact allows a balanced master-slave approachfor all contact pairs between two discretized surfaces.This feature can be used to avoid contact penetrations thatsometimes develop due to a pure master-slave approach.

• If contact between two rigid bodies is desired, penaltycontact must be used.

• Kinematic contact should usually be considered in small-deformation, displacement-driven Hertz contactproblems.

1

2

3

Cam node3530

Spring compressed

Cam pinnedand rotated

Followerpinned

Figure 4: A simple timing mechanism.

Figure 5: (a) Normalized displacement time history ofnode 3530 on the cam. (b) Time history of normalized reaction

force at the rigid body reference node of the cam.

(b)(a)