_solutions_attach_ask-The-experts_Modeling Nonlinear Contact in ANSYS Mechanical and MAPDL R14

© 2011 ANSYS, Inc. April 18, 20121 Release 14.0

14. 0 Release

ANSYS Contact Technology New Features in R14

John Doyle

Technical Support


Agenda

Review of Contact Technology

What’s new for R14

• Contact Stabilization Damping

• Surface projection based methods

• New “Program Controlled” defaults for Workbench

• Symmetry Conditions for Force Distributed Constraints

• Bolt pretension simulation via Joint Load

• Critical Bonding Temperature


A. Basic Concepts

Contact:

When two separate surfaces touch each other such that they become mutually tangent, they are said to be in contact.

In the common physical sense, surfaces that are in contact have these characteristics:

• They do not interpenetrate.

• They can transmit compressive normal forces and tangential friction forces.

• They often do not transmit tensile normal forces.

– They are therefore free to separate and move away from each other.

Contact is a changing-status nonlinearity. That is, the stiffness of the system depends on the contact status, whether parts are touching or separated.


How compatibility is enforced in a contact region:

Physical contacting bodies do not interpenetrate. Therefore, the program must establish a relationship between the two surfaces to prevent them from passing through each other in the analysis.

• When the program prevents interpenetration, we say that it enforces contact compatibility.

• Workbench Mechanical offers several different contact formulations to enforce compatibility at the contact interface.

F

TargetContact

Penetration occurs when contact

compatibility is not enforced.

F

... Basic Concepts


For nonlinear solid and surface body contact of faces and edges, Pure Penalty or Augmented Lagrange formulations can be used:

• Both of these are penalty-based contact formulations:

• Here, for a finite contact force Fnormal, there is a concept of contact stiffness knormal. The higher the contact stiffness, the lower the penetration xpenetration, as shown in the figure below

• Ideally, for an infinite knormal, one would get zero penetration. This is not numerically possible with penalty-based methods, but as long as xpenetration is small or negligible, the solution results will be accurate.

B. Contact Formulations

Fn

xp

npenetrationormalnormal xkF


The main difference between Pure Penalty and Augmented Lagrange methods is that the latter augments the contact force (pressure) calculations:

Because of the extra term l, the augmented Lagrange method is less sensitive to the magnitude of the contact stiffness knormal.

All things being equal, Augmented Lagrange should produce less penetration then Pure Penalty, but might take more iterations to converge.

npenetrationormalnormal xkF

l npenetrationormalnormal xkF

Pure Penalty:

Augmented Lagrange:

... Contact Formulations


Another available option is Lagrange multiplier Formulation:

• The Normal Lagrange Formulation adds an extra degree of freedom (contact pressure) to satisfy contact compatibility. Consequently, instead of resolving contact force as contact stiffness and penetration, contact force (contact pressure) is solved for explicitly as an extra DOF.

– Enforces zero/nearly-zero penetration with pressure DOF

– Does not require a normal contact stiffness (zero elastic slip)

– Requires Direct Solver, which can be more computationally expensive

F

DOFFnormal



For the specific case of “Bonded” and “No Separation” type of contact between two faces, a multi-point constraint (MPC) formulation is available.

• MPC internally adds constraint equations to “tie” the displacements between contacting surfaces

• This approach is not penalty-based or Lagrange multiplier-based. It is a direct, efficient way of relating surfaces of contact regions which are bonded.

• Large-deformation effects also are supported with MPC-based bonded contact



What is new in Release 14?

• Contact Stabilization Damping

• Surface projection based methods

• New “Program Controlled” defaults for Workbench

• Symmetry Conditions for Force Distributed Constraints

• Bolt pretension simulation via Joint Load

• Critical Bonding Temperature


What is new in Release 14?

• Rigid body motion often can occur in the beginning of a static analysis due to the fact that the initial contact condition is not well established.

• Contact Stabilization introduces a viscous damping traction proportional to but opposite to the relative pseudo velocities between the two surfaces along contact normal and/or tangential directions.

Where: = damping coefficient in normal direction

= damping coefficient in tangential direction

= pseudo velocity

Fn

Target

Contact

Ft

22

11

udP

udP

udP

td

td

nndn

Pdn

Pd1,d2

u

d

d

t

n


Contact Stabilization Damping

• The damping coefficients are calculated as a function of the opening gap and pinball as follows:

Where: FDMN = real constant scaling factor in normal direction (default =1.0)

FDMT = real constant scaling factor in tangential direction (default = 0.001)

PINB = Pinball radius

0

/)(**

0

/)(*

PINBUPINBFDMTFDMNd

PINBUPINBFDMNd

n

t

n

n

pinbnn

pinbn

UUU

UU

gt or 0 If

If

pinbnn

pinbn

UUU

UU

gt or 0 If

If



• Contact stabilization is inactive by default.

• As an exception, it will be activated automatically if ALL of the following conditions are met:

– Gauss point (KEYOPT(4) = 0) or surface projection based (KEYOPT(4) = 3) detection.

– AND the entire contact pair is in near field open status.

– AND a geometric penetration is detected at any contact nodal point, despite the initially open status.



• Users can activate contact stabilization damping manually by specifying real constants FDMN and FDMT.

rmodif,,31,5e-2

rmodif,,32,1e-3

Use positive values to specify scaling factors in the formulas presented earlier

Use negative values to define damping coefficient directly



• Additional controls with new KEYOPT(15):

– 0 Damping is activated only in first load step (default)

– 1 Deactivate automatic damping

– 2 Damping is activated for all load steps

– 3 Damping is activated at all times regardless of the contact status of previous steps

• When KEYOPT(15) = 0, 1, or 2, contact stabilization damping will not be applied in the current substep if any contact detection point had a closed status in the previous substep.

• However, when KEYOPT(15) = 3, stabilization damping is always applied as long as the current contact status is near-field open.



• Note that the Energy introduced into the model by Contact Stabilization Damping is artificial.

• It can alleviate convergence problems, but it can also affect solution accuracy if the applied stabilization energy generated by the damping forces are too large

– In most cases, the program automatically activates and deactivates contact stabilization damping and estimates reasonable damping forces.

– However, it is a good practice to check the stabilization energy and reaction forces.

• The contact stabilization energy can be post processed via the ETABLE command using the AENE label. This should be compared to element potential energy via SENE label on ETABLE.

For example: ETABLE,AE,AENE !save artificial energies associated with stabilization

ETABLE,SE,SENE !save strain energies to element table

SSUM !sum all element energies for comparison

PRETAB,AE,SE !print element table values



• Issue the NLDIAG,CONT,ON command to create a ‘Jobname.cnd’ file which

stores contact information for all defined contact pairs at all substeps.

Alternatively, you may issue one of the following commands to store contact

information at a specific frequency:

– NLDIAG,CONT,ITER to write at each iteration

– NLDIAG,CONT,SUBS to write at each substep (default)

– NLDIAG,CONT,LSTP to write at each load step

• Two new fields added to Jobname.cnd file related to contact damping:

– Maximum contact damping pressure

– Maximum tangential contact damping stress



What is available in Workbench Mechanical?

• WB-Mechanical GUI exposes access to real constant FDMN as a “Stabilization Damping Factor” in the Details Window of the Contact Region

• Stabilization Damping Factor is applied in the contact normal direction and it is valid only for nonlinear contact (frictionless, rough and frictional contacts).

– If this factor is 0 (default), the damping is activated under the conditions mentioned previously and only in the first load step (KEYOPT(15) = 0, the default)

– If its value is greater than 0, the damping is activated for all load steps (KEYOPT(15) = 2).

– KEYOPT (15) options are not directly exposed in GUI but can be set manually via command object.



Example: Consider a fixed pin interfacing with a hole in plate with initial radialclearance and under a force based load

– Stabilization captures localized stress distribution more accurately

Conventional Adjust to Touch Contact Stabilization Damping



• Contact Stabilization can be more challenging to converge as compared to “adjust-to-touch” option. Note also, it introduces some artificial energy into the model.




Mathematical adjustment to close gap causes rigid region to exist

No Gap


Example: Consider a hyperelastic seal against a hard surface


Projection based Contact Method extended to support 2D applications

• KEYOPT(4)=3: Recall this option enforces a contact constraint on an overlapping region of the contact and target surfaces in an averaging sense rather than on individual contact nodes (KEYOPT(4) = 1, 2) or Gauss points (KEYOPT(4) = 0).

– Now supports 2D applications

• The projection based method also now supports the HHT time integration method for implicit transient dynamic analysis

• Both accuracy and performance have been improved for transient dynamic analysis that include contact and the use of the HHT time-integration method


Projection Based MethodAdvantages over conventional detection methods• Less sensitive to the designation of contact and target surfaces

• In general, it provides more accurate contact results.

– Stress distribution across contacting interface is smoother.

• It meets moment equilibrium even when offset exists between contact and target surfaces with friction.

• Contact forces do not jump when contact nodes slide off the edge of target surface

Disadvantages:

• Computationally more expensive

• When a model has corner or edge contact, the averaged penetration/gap could be quite different than the real geometric penetration observed at contact nodes.

– In this situation, mesh refinement is usually required.


2D/3D Projection Based MPC

• Contact integration is done on overlapping area instead of whole contact element

• Advantages over conventional MPC contact

• Stress distribution across contacting interface is smoother.

• In general, it provides more accurate contact results .

• Disadvantage

• Computationally more expensive.


Existing contact: MPCDoes not pass the patch test

New projection based contact + MPC Results in constant VM stressPasses the patch test

2D/3D Projection Based MPC


Projection Based MPC

Existing surf-surf contact + MPC

New projection based contact + MPC



Hot Side ConvectionT = 2400 Fh = 50 BTU/(in-hr-F)Cold Side ConvectionT=1800 Fh = 16.67 BTU/(in-hr-F)E = 37e6 psiCTE = 2.3e-6 in/in/FK = 1.167 BTU/(in-hr-F)Element Type: SOLID70Contact Conductance: 145000

Bonded contact Between each two layers


Projection Based MPCTemperature (TCC)Existing surf-surf contact

Temperature (TCC)New projection based contact

Temperature (MPC)New projection based contact

Temperature (MPC)Existing surf-surf contact



Equivalent stress (LAG)Existing surf-surf contact

Equivalent stress (MPC)Existing surf-surf contact

Equivalent stress (LAG)New projection based contact

Equivalent stress (MPC)New projection based contact


Projection based Method

• In R14, WB-Mechanical GUI exposes access to all the detection methods, including Projection based


• For models built new in R14, WB-Mechanical has added more “Program Controlled” defaults for basic features

• More consistent with MAPDL defaults

• For models created and saved in R13, previous defaults will be preserved.

New Program Controlled defaults

Aug-Lagrange

Auto-asymmetric

Update between interations


Force-Distributed Constraint under Symmetric Conditions

• New KEYOPT(6) for target elements to set symmetry condition for constrained surfaces

– When the constrained surface is built on a symmetric geometry model instead of the “full” geometry model.

– Enter a three digit value that represents the symmetry conditions on the constrained surface.

– Symmetry is defined with respect to the nodal coordinate system of the pilot node.

– Available in WB-Mechanical via command object only


Critical Temperature for Bonding

• After materials around contacting surfaces exceed a critical temperature, the surfaces start to melt and bond with each other.

• The critical temperature is defined by the new TBND real constant on the contact elements.

• As soon as the temperature at the contact surface exceeds this melting temperature, the contact will change to “bonded” and will remain bonded for the rest of the analysis.

• Available in WB-Mechanical via command object only


Critical Temperature for Bonding

Tool

Plates of 304L Steel (Workpiece)

Contact interface

Temperature after Load Step3Friction Stir welding

with bonding temperature 1000◦C with bonding temperature 900◦C

Contact Status


Bolt Pretension via Joint Technology

• Supports Large rotation based pretension and pretorque loads

• Supports locking in subsequent loadsteps

• The preloaded Bolt needs to be sliced in advance of analysis.

• The two cut surfaces are connected by a cylinder joint.

• The pretension loading is applied via Joint load (FJ,,FZ)

• The pretorque loading is applied via Joint Load (FJ,,MZ)

• The loading can be locked via DJ,,UZ,%_FIX% and DJ,,ROTZ,%FIX%


Using cylindrical joint the stress appear without significant bending

Using conventional bolt pretension, the stresses appear with significant bending with rotation

Bolt Pretension via Joint Technology

_solutions_attach_ask-The-experts_Modeling Nonlinear Contact in ANSYS Mechanical and MAPDL R14

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