文本教程讲稿tire-l06contact

1、Lesson content:Overview of ContactContact DiscretizationContact EnforcementFinite Sliding of Deformable Bodies against Each Other Finite Sliding of Deformable Bodies against Rigid Bodies Additional Features Friction BasicsLesson 6: Modeling Contact1 hourOverview of Contact (1/4)Abaqus provides two a

2、lgorithms for modeling contact: General contactContact pairsGeneral contactAllows you to define contact between many or all regions of a model with a single interaction. The surfaces that can interact with one another are considered the contact domain and can span many disconnected regions of a mode

3、l (i.e., very general surface topology is allowed). Potential contact interactions are automatically detected.One contact domain in general contact*CONTACT*CONTACT INCLUSIONS*CONTACT PROPERTY ASSIGNMENTOverview of Contact (2/4)Contact pairsDescribe contact between two surfaces.Require more careful d

4、efinitions of contact; each possible contact pair interaction must be defined.Have many restrictions on the types of surface involved.Multiple contact pairs required*CONTACT PAIR, INTERACTION=.Overview of Contact (3/4)Basic features of a contact formulationContact discretizationWhere is the constrai

5、nt applied?Node-to-surface Surface-to-surfaceConstraint enforcementHow is the constraint enforced?Direct (Lagrange multipliers)Penalty method Augmented Lagrange (Lagrange multipliers + penalty method)Contact tracking (relative sliding)How does the constraint evolve?Finite sliding (arbitrary relative

6、 sliding and rotation of surfaces)Small sliding (assumes relatively little sliding between surfaces)Contact formulationOverview of Contact (4/4)Contact in Abaqus/Standard can be broken into five categories:Finite sliding of deformable bodies against each other (e.g., contact between tread blocks).Fi

7、nite sliding of deformable bodies against rigid bodies (e.g., contact between road-tread and bead-rim).Contact between a deformable body and itself (self-contact; e.g., tread blocks). Self-contact is always finite sliding.Small sliding of deformable bodies against each other.Small sliding of deforma

8、ble bodies against rigid bodies.Small-sliding contact and self-contact are rarely used for tire analysis. We, therefore, focus on finite-sliding contact (between deformable bodies, and between deformable and rigid bodies) in this lecture.Contact Discretization (1/5)The locations of the contact const

9、raints depend on the contact discretization technique used:Node-to-surface technique:Default method for contact pairsNot available for general contactNodes on one surface (the slave surface) contact the segments on the other surface (the master surface).Contact is enforced at discrete points (slave

10、nodes)Surface-to-surface techniqueOnly method for general contactAlternative method for contact pairsThe method considers the shape of both the master and slave surfaces. Contact is enforced in an average sense over the slave surface.Contact Discretization (2/5)Node-to-surface (N-to-S) contact discr

11、etizationTraditional “point-against-surface” methodContact is enforced between a node and surface facets local to the nodeThe node is referred to as a “slave” node; the opposing surface is called the “master” surfaceThis formulation is also called a strict master/slave formulationslavemasterThese no

12、des are free to penetrateContact Discretization (3/5)Key implications of the strict master/slave formulation:Slave nodes cannot penetrate master surface segments.Nodes on the master surface can penetrate slave surface segments.A gross penetration of a master surface into a coarsely meshed slave surf

13、ace causes solution inaccuracyRefinement of the slave surface improves contact resolutionAssignment of master and slave rolesThe more-refined surface should act as the slave surfaceThe stiffer body should be the masterThe active contact region should change most rapidly on the master surface (minimi

14、zes contact status changes )SlaveMasterMasterSlaveContact Discretization (4/5)Surface-to-surface (S-to-S) contact discretizationContact is enforced in a weighted sense, between the slave node and a larger number of master surface facets surrounding it.In effect, contact is smeared over a larger numb

15、er of facets.Contact is enforced in an average sense.More master surface nodes are involved in contact, reducing the likelihood of penetration.slavemasterContact Discretization (5/5)The surface-to-surface discretization offers many advantages over the node-to-surface discretization, including:Increa

16、sed contact stress accuracyReduced snagging of surfacesReduced surface penetrationsReduced sensitivity with respect to choice of master and slave rolesSlave and master surfaces switchedChoosing the slave surface to be the finer mesh will still yield better results; choosing the master surface to be

17、the more refined surface will tend to increase analysis costContact Enforcement (1/9)In Abaqus/Standard, the default contact behavior is “hard” contact“Hard” contact is depicted below; the behavior is described by a contact property known as the pressure-penetration curve (alternative behavior can b

18、e specified; not discussed here).The desired behavior (no penetration) is achieved using an enforcement methodh 0h = 0No penetration; no constraint requiredConstraint enforced; positive contact pressure- hp, contact pressureAny pressure possible when in contactNo pressureh, penetrationPhysically “ha

19、rd” pressure vs. penetration behaviorContact Enforcement (2/9)Three numerical methods are available in Abaqus/Standard to achieve or approximate “hard” contact conditions:Direct enforcement methodStrict enforcement of pressure-penetration relationship using the Lagrange multiplier methodPenalty meth

20、odApproximate enforcement using penalty stiffnessAugmented Lagrange methodApproximate enforcement using penalty method with augmentation iterations; not discussed further herep, contact pressureNo pressureh, penetrationDirect enforcementSome numerical “softening” with penalty or augmented Lagrange e

21、nforcementContact Enforcement (3/9)The penalty method is used by default for each of the following:General contactContact pairs with the finite-sliding, surface-to-surface formulationAutomatic contact pair detection capability in Abaqus/CAEThe augmented Lagrange is used by default for:3D self contac

22、t with node-to-surface discretizationOtherwise, direct enforcement is the defaultMutually exclusive parameters DIRECT, PENALTY & AUGMENTED LAGRANGE on the *SURFACE BEHAVIOR optionContact Enforcement (4/9)Direct enforcementLagrange multiplier method Constraint equations and Lagrange multipliers are a

23、dded to the system of equationsKCCT0ulf0=Kuf=Unconstrained system of equationsConstraint equations addedVector of Lagrange multiplier degrees of freedom (constraint forces)One per constraintContact Enforcement (5/9)Pros and cons of direct enforcement Advantages:Accuracyconstraint is satisfied exactl

24、yDisadvantages:Adds to equation solver costAdditional variable per contact constraint, which enlarges the system of equations to be solvedRestricts elimination order for sparse solver, which can degrade performancePotential convergence difficultiesAbrupt change from zero contact stiffness (while con

25、tact is inactive) to infinite contact stiffness (while contact is active)Difficulties with overconstraintsOverlap between contact constraints and MPCs, etc.Contact Enforcement (6/9)Penalty method The penalty method is a stiff approximation of hard contactp, contact pressureAny pressure possible when

26、 in contactNo pressureh, penetrationStrictly-enforced hard contactp, contact pressureNo pressureh, penetrationPenalty method approximation of hard contactk, penalty stiffnessContact Enforcement (7/9)Pros and cons of penalty method Advantages:Significantly improved convergence ratesBetter equation so

27、lver performanceNo Lagrange multiplier DOF unless contact stiffness is very highGood treatment of overlapping constraintsDisadvantages:Small amount of penetrationTypically insignificantMay need to adjust the penalty stiffness in some casesContact Enforcement (8/9)Penalty stiffness behavior can be .L

28、inear (default):Easier convergence.Better suited for problems involving firm contact.Difficult to choose stiffness appropriate for all regimesNonlinear:The lower initial stiffness makes it better suited for problems involving chattering.The higher final stiffness helps reduce penetrations.Convergenc

29、e overall can be more difficult.Contact pressureOver-closurec0=0e=d/3dKf=10KlinKlinKi=0.1KlinLinearNonlinear3% of characteristic facet length*SURFACE BEHAVIOR, PENALTY = LINEAR (default) / NONLINEARContact Enforcement (9/9)Default penalty stiffness Abaqus tries to strike a balance betweenToo low a p

30、enalty stiffness: Excessive penetrationsToo high a penalty stiffness: Converges rates degrade Lagrange multiplier DOF are needed to avoid ill-conditioningThe default penalty stiffness is based on a representative stiffness of the underlying elements. A scale factor is applied to this representative

31、stiffness to set the default penalty stiffness; its magnitude is higher in Abaqus/Standard than in Abaqus/Explicit.Finite Sliding of Deformable Bodies against Each OtherKinematically, finite sliding of deformable bodies against each other is the most general.Arbitrarily large sliding is allowed.Arbi

32、trarily large rotations and deformations of the surfaces are allowed.All contact pairs use finite sliding by default when geometric nonlinearity is chosen (NLGEOM specified on the *STEP option).Three-dimensional node-to-surface finite-sliding problems generate unsymmetric terms when contact occurs.T

33、hese terms are proportional to the curvature of the master surfacea highly curved master surface will produce large unsymmetric terms.Therefore, use of the unsymmetric solver (UNSYMM=YES) is advised for three-dimensional, node-to-surface finite-sliding problems with curved master surfaces.The surfac

34、e-to-surface contact discretization generates unsymmetric terms in the system of equations for both two- and three-dimensional problems.Note: inclusion of friction always results in unsymmetric Jacobian terms, both in two and three dimensions.Finite Sliding of Deformable Bodies against Rigid Bodies

35、(1/9)Abaqus has a general rigid body capability. A rigid body is a collection of nodes and elements whose motion is governed by the motion of a single node called a “reference node.”Any body or part of a body can be defined as a rigid body. A rigid body can undergo arbitrarily large rigid-body motio

36、ns.The geometry of the rigid body is defined: As a surface obtained by revolving or extruding a two-dimensional geometric profile (analytical rigid surface) orBy meshing the body with nodes and elements (discrete rigid body)Most of the continuum and structural element types, as well as the rigid ele

37、ment types, can be included in a rigid body definition.Rigid bodies are computationally efficient.Their motion is described completely by no more than six degrees of freedom.There are no element calculations for elements making up a rigid body.Model a body as rigid if it is much stiffer than the oth

38、er bodies it will come in contact with and if the stresses in the body are of no concern.Finite Sliding of Deformable Bodies against Rigid Bodies (2/9)Rigid body reference nodeThe reference nodes degrees of freedom represent the motion of the rigid surface.In two dimensions: three degrees of freedom

39、 (two translations, one rotation)In three dimensions: six degrees of freedom (three translations, three rotations)You can control the rigid bodys motion directly by prescribing boundary conditions (displacement, velocity, acceleration) to the reference nodes degrees of freedom. It is also possible t

40、o apply concentrated loads to the node.Finite Sliding of Deformable Bodies against Rigid Bodies (3/9)Rigid body reference node (contd)The rigid body can be made to rotate about the reference node by prescribing the rotational degrees of freedom.In dynamics problems where the rigid body moves freely,

41、 the reference node should be placed at the center of mass of the rigid body.The location of the reference node is irrelevant if its rotational degrees of freedom are suppressed.Elements can be connected to the reference node. For example:Attach MASS and/or ROTARYI elements to simulate mass and/or r

42、otary inertia of the rigid body in dynamic problems. Attach spring elements to remove rigid body motion or simulate a supporting structure.Rigid surfaces are always the master surface in a contact pair and should be smoothed to avoid convergence problems. For analytical rigid surfaces define a smoot

43、hing radius using the FILLET RADIUS parameter on the *SURFACE option.Finite Sliding of Deformable Bodies against Rigid Bodies (4/9)Analytical rigid surfacesDefined using *SURFACE.*SURFACE, TYPE=SEGMENTS: Two-dimensional segmented surface, composed of lines, circles, and/or parabolas.Three-dimensiona

44、l analytical surfaces require definition of a two-dimensional profile in a local coordinate system.*SURFACE, TYPE=CYLINDER: Three-dimensional infinite rectangular projection of a two-dimensional profile (road).*SURFACE, TYPE=REVOLUTION: Three-dimensional surface of revolution (rim).The *RIGID BODY o

45、ption must be used to assign the surface to a rigid body.Finite Sliding of Deformable Bodies against Rigid Bodies (5/9)Analytical rigid surfaces (contd)Add a reference node at part level and Abaqus/CAE automatically makes the part an analytical rigid surface, with the reference point already defined

46、.*SURFACE,TYPE=CYLINDER*SURFACE,TYPE=REVOLUTION*SURFACE,TYPE=SEGMENTSFinite Sliding of Deformable Bodies against Rigid Bodies (6/9)Discrete rigid bodiesMore general rigid surfaces can be constructed using discrete rigid bodies. Most element types can be part of a rigid body. For example, solid eleme

47、nts or rigid elements can be used to model the same effect as long as a *RIGID BODY option is used to assign the elements to the rigid body. Example of defining a rigid body containing solid elements:*ELEMENT, TYPE=C3D8R, ELSET=SOLID1.*SOLID SECTION, ELSET=SOLID1, MATERIAL=STEEL*MATERIAL, NAME=STEEL

48、*ELASTIC200.0E9, 0.3*DENSITY7800.0,*RIGID BODY, REF NODE=refPt, ELSET=SOLID1Finite Sliding of Deformable Bodies against Rigid Bodies (7/9)Discrete rigid bodies (contd)To add regions, pin sets, tie sets To add reference pointFinite Sliding of Deformable Bodies against Rigid Bodies (8/9)Rigid elements

49、Rigid (surface) elements provide an alternative approach to defining discrete rigid bodies for use in contact problems.The surface of the body can be meshed using:2-D: R2D2: planar stripRAX2: axisymmetric shell3-D: R3D3: triangular shellR3D4: quadrilateral shellXYZXY124332112R2D2 and RAX2R3D3R3D4Fin

50、ite Sliding of Deformable Bodies against Rigid Bodies (9/9)Rigid elements (contd)Rigid element normals are defined in the same way as shell or beam elements.Element numbering dictates positive normal direction.Positive normal direction = SPOS surface.Negative normal direction = SNEG surface.XYZXY124

51、312312nnnSPOSSPOSSPOSR2D2 and RAX2 elementsR3D3 elementR3D4 elementIn Abaqus/CAE: Property Module, Assign Shell/Membrane Normals can be used to change the normalsAdditional Features (1/6)Adjusting surfacesThe slave nodes of contact pair (or general contact interaction) can be “adjusted” automaticall

52、y so that they are initially exactly in contact or exactly a prescribed distance apart or overclosed.This process is useful when preprocessors do not place nodes in “exact” positions.Abaqus modifies coordinates of slave nodes before the analysis starts.The adjustment does not generate any strain.Add

53、itional Features (2/6)Tie constraintsA tie constraint (*TIE) is a simple way to bond surfaces together permanently.It is a powerful technique to handle patible mesh regions.Surface-to-surface algorithm is the default for tie constraintsUse *TIE, TYPE=NODE TO SURFACE to use the node-to-surface algori

54、thmSlave nodes involved in a node-to-surface tied contact pair cannot:Penetrate the master surfaceSeparate from the master surfaceSlide relative to the master surfaceSlave nodes not initially tied will remain unconstrained throughout the analysis; they will never “see” the master surface and will be able to penetrate it. Additional Features (3/6)Tie constraints (contd)Additional Features (4/6)Contact pair removal and reintroductionContact pairs have computational cost, even when they