Large Sliding Contact Analysis of a Buckle

8/14/2019 Large Sliding Contact Analysis of a Buckle

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Chapter 27: Large Sliding Analysis of a Buckle

27 Large Sliding Contact Analysis

of a Buckle

Summary 463

Introduction 464

Modeling Details 464

Solution Procedure 467

Results 469

Modeling Tips 472

Input File(s) 473

Video 473


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463CHAPTER 27

Large Sliding Contact Analysis of a Buckle

Summary

Title Chapter 27: Large Sliding Contact Analysis of a Buckle

Features Deformable-deformable contact, bilinear, Coulomb friction model, Hookean, isotropic

elastic material, adaptive time stepping, solid elements with assumed strain formulation

Geometry

Material properties ,

Analysis characteristics Quasi-static analysis using: adaptive time stepping and geometric nonlinearity due tolarge displacement

Boundary conditions Sliding, frictional contact with: ends fixed for second contact body and contact between

the two deformable bodies with

Applied loads Prescribed displacements for the end nodes of the first contact body with two load cases:

insertion (clipping) and removal of the buckle

Element type 8-node solid element with assumed strain formulation

FE results 1. History plot of y-displacements for specific nodes

2. Normal and frictional contact force comparison of Nastran and Marc

3. Load displacement curves comparison between the frictional and frictionless cases

HalfSym

metry

X

Y

Z

247mm

168 mm

E 10 G P a= 0.4=

0.1=

0.5 1.0 1.5

-2000

-1500

-1000

-500

0

500

1000

Frictional

Frictionless

Time (s)

F (N)x

Fx Fx

FxFx

Insert Remove


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MD Demonstration Problems

CHAPTER 27

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Introduction

This problem demonstrates the ability of MD Nastran SOL 400 to do a frictional contact problem. An ostensiblysimple geometry poses a substantial challenge for the contact algorithm due to the large sliding involved between the

two deformable bodies. Sudden changes in the motion path pose a challenge to the ability of the contact algorithm to

correctly place the node on the contact surface while respecting the various geometric details in the problem.

Due to large bending stresses in the deformed configuration, assumed strain formulation is used with the 8-node

hexahedral elements. The material is elastic and the original geometry without residual stresses is recovered upon the

complete removal of the loading.

From elementary strength of materials analysis, the tip deflection for beam bending can be written as:

where is the applied load, is the length of the beam, is the moment of inertia and is the Youngs modulus.

The normal stress along the beam cross section varies in the thickness direction as:

where is the moment and is the thickness coordinate. It must be noted that the above solution only holds for small

displacements and uniform cross section.

Modeling DetailsA numerical solution has been obtained with MD Nastrans SOL 400 for a 3-D representation of a belt buckle with a

deformable-to-deformable contact between the two pieces of the buckle. The details of finite element model, contact

simulation, material, load, boundary conditions, and solution procedure are discussed below.

The case control section of the input contains the following options for nonlinear analysis:

SUBCASE 1STEP 1TITLE=Insertion (Clipping)ANALYSIS = NLSTATICNLPARM = 1BCONTACT = 1SPC = 2LOAD = 1DISPLACEMENT(PLOT,SORT1,REAL)=ALLSPCFORCES(PLOT,SORT1,REAL)=ALLSTRESS(PLOT,SORT1,REAL,VONMISES,BILIN)=ALLNLSTRESS(PLOT,SORT1)=ALLSTEP 2TITLE=RemovalANALYSIS = NLSTATICNLPARM = 2BCONTACT = 2SPC = 6LOAD = 2DISPLACEMENT(PLOT,SORT1,REAL)=ALLSPCFORCES(PLOT,SORT1,REAL)=ALLSTRESS(PLOT,SORT1,REAL,VONMISES,BILIN)=ALLNLSTRESS(PLOT,SORT1)=ALL

P L3 3 EI =

P L I E

xx

Mt

I=

M t


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465CHAPTER 27


The analysis contains a single subcase with two steps. The two steps comprise of individual load sequences consisting

of insertion (clipping) and removal of the belt buckle. Each step has a definition of convergence control option via

NLPARM, contact table and parameters via BCONTACT, applied displacements (or single point constraints) via SPCand the displacements and stress results for the .f06 (output) file. A zoomed-in view of the cross section of the model

shown in Figure 27-1 consists of an outer piece modeled as body 2, the buckle, while the inner piece is modeled as

body 1, the insert.

Figure 27-1 Geometry and a Zoomed-in View of a Belt BuckleLarge displacement effects are included in the nonlinear analysis using the option:

PARAM LGDISP 1

While the assumed strain formulation is flagged using the option:

NLMOPTS,ASSM,assumed

The NLMOPTS field triggers the assumed strain formulation which provides a better bending behavior of the

continuum elements. This alleviates the difficulty associated with spuriously large shear stresses induced due tobending moment. The LGDISP field indicated the use of large displacement, large rotation kinematics of the element.

This is adequate when the analysis consists of Hookean elastic material; however, incase of large deformation

plasticity or other inelastic models, the LRGSTRN parameter should be used in the NLMOPTS option (for more details

on its usage, please refer to : Chapter 3: 3-D Sheet Metal Forming of this manual).

Element Modeling

Besides the standard options to define the element connectivity and grid coordinate location, the bulk data section

contains various options which are especially important to do nonlinear analysis. The nonlinear extensions to
http://mdug_03.pdf/http://mdug_03.pdf/


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lower-order solid element, CHEXA can be activated by using the PSLDN1 property option to the regular PSOLID

property option in the manner shown below:

PSOLID 1 1 0PSLDN1 1 1 1 ++ C4 SOLI L +

The PLSLDN1 option allows the element to be used in both large displacement and large strain analysis and has no

restrictions on the kinematics of deformation unlike the regular CHEXA elements with only PSOLID property entry.

The standard CHEXA elements are more suitable for large rotations but small strain analysis due to their linear

formulation in co-rotational system. While the difference may be small or even negligible in elastic analysis, use of

any inelastic material model would certainly require the use of these options.

Modeling Contact

The BCPARA defines the number of bodies in contact with maximum number of contact entities (e.g., patches), nodes

on the periphery of the contact surfaces and contact parameters like friction type (in this case node based, bilinear

Coulomb model), friction coefficient, bias factor, and type of contact procedure used.

BCPARA 0ERROR 0.005BIAS 0.99FTYPE 6

It must be mentioned that the contact procedure being used (flagged via ISPLIT flag) is iterative penetration checking

procedure and must always be used for robustness in a quasi-static analysis.

Friction has been flagged via the FTYPE field where a 6 denotes the bilinear, Coulomb model. The friction coefficient

is 0.1 and is included in contact body definition with BCBODY option or the contact tables using the BCTABLE option.

Another significant point is the use ofBIAS in frictional problems. The bias factor measures the non-dimensionalized

distance on both sides of the contact surface which is used to make a decision if the node is in contact or not, based on

whether the node falls within this band defined by contact zone tolerance. Ideally, it should be 1.0 or as close to it.

However, due to the possibility of excessive iterations in case of even very slight penetration, the bias is kept as zeroor, in other words, a slight penetration is accepted. While a bias of zero works well for nonfrictional problems, it can

be a detriment for frictional problems which require the bias to be set as close to one as possible in order to avoid a

fictitious tangential force on the node which can cause non convergence of the solution. Finally, the ERROR parameter

denotes the contact zone tolerance. The default value is about 1/20th of the smallest element size for a solid element.

In this case, it has been chosen to be an even smaller value of 0.005.

To identify how the contact bodies can touch each other, the BCTABLE option is used. BCTABLE with ID 0 is used to

define the touching conditions at the start of the analysis. This is a mandatory option required in SOL 400 for contactanalysis and it is flagged in the case control section through the optional BCONTACT = 0 option. The BCTABLE with

ID 1 is used to define the touching conditions for later increments in the analysis, and it is flagged using BCONTACT

= 1 in the case control section. Also, the SLAVE-MASTER combination defines that the nodes for body 1 are nodes

belonging to the slave body. This, in literature, is referred by various terminologies as either contacting body nodes or

tied nodes (imagining the situation of multi-point constraints). The nodes belonging to body 2 are said to belong to the

master body which are also referred to as the contacted body nodes or the retained nodes (imagining the situation of

multi-point constraints)

BCTABLE 0 1SLAVE 2 0. 0. .1 0. 0

0 0 0MASTERS 1


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467CHAPTER 27


BCTABLE 1 1SLAVE 2 0. 0. .1 0. 0

0 0 0

MASTERS 1

The definition of the contact bodies (defined as body 1 and 2 in Figure 27-1) consists of the bulk data entries. The

BCBODY option defines the deformable body including the body ID, dimensionality, type of body, type of contact

constraints and friction etc. while the BSURF identifies the elements forming a part of the deformable body as:

BCBODY 2 3D DEFORM 2 2BSURF 2 50000 50001 50002 50003 50004 50005 50006

50007 50008 50009 50010 50011 50012 50013 5001450015 50016 50017 50018 50019 50020 50021 5002250023 50024 50025 50026 50027 50028 50029 50030

(list of element forming this body)

Material Modeling

The isotropic, Hookean elastic material properties of the deformable body are defined using the following MAT1

option as follows:

MAT1 1 10000. 0.4 Isotropi

The Youngs modulus is taken to be 10 GPa with a Poissons ratio of 0.4.

Loading and Boundary Conditions

The displacements for body 2 are fixed at the end in the following manner:

$ Displacement Constraints of Load Set : right_fixed_xyzSPC1 5 123 100056 THRU 100074SPC1 5 123 100446 THRU 100464

The loading involves application of displacement controlled boundary conditions as follows:

SPCADD 2 1 8 5$ Enforced Displacements for Load Set : case1_left_xyz$ Dummy Force Required to Activate the Following Enforced DisplacementsFORCE 1 50084 0. .57735 .57735 .57735SPCD 1 50084 1 85. 50085 1 85.

A total X displacement of 85 mm is applied to body 1. The application of the loads or displacements is such that the

total load applied at the end of the loading sequence is given in the input.

Solution ProcedureThe nonlinear procedure used is defined through the following NLPARM entry:

NLPARM 1 20 FNT 50 UV ALL0.01

NLAUTO 1 .01 1. .1 1.2 1.-5 .5 0

10 0

FNT represents Full Newton-Raphson technique wherein the stiffness is reformed at every iteration; KSTEP (field

after FNT) is left blank and in conjunction with FNT, it indicates that the program will determine if the stiffness needs


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to be reformed between the end of the load step and the start of next load increment. Fifty (50) is the maximum number

of allowed recycles for every increment and, if this were to be exceeded, the load step would be cut-back and the

increment repeated. UV indicates that the maximum norm of vector component of the incremental displacements willbe checked for convergence. ALL indicates that intermediate output will be produced after every increment. The

second line ofNLPARM indicates that a tolerance of 0.01 will be used for displacement based convergence checking.

NLAUTO defines the parameters in the adaptive load stepping scheme. The initial load step is 1% of the total load. It

must be noted that, for many problems including plasticity of complicated contact conditions in the early stages of the

analysis, this must be a very small percentage (typically 0.5%). The smallest and largest ratio between the steps is 0.1

and 1.2, respectively, while the minimum value of the step is . Finally, the desired number of recycles is kept at

ten which is the default in SOL 400. If this number is chosen to be very small, then the step size is cut to a smaller sizefor convergence to be achieved and there will be larger number of steps. If this number is very large, then the load step

will allow more iterations for convergence in the same step.

The number of increments is provided in the third field of the NLPARM option. It is also worth noting that removing

the NLAUTO option results in a constant load step procedure with a total of 20 load increments per step (thus, a total

of 40 for the analysis).

Alternately another nonlinear procedure used is defined through the following NLSTEP entry like:

NLSTEP 1 1. ++ ADAPT 1.00E-2 1.E-5 0.10 1.2 0 999999 ++ 0 0.0002 ++ MECH PV 0.1 PFNT

Adaptive time procedure with total time of 1 is used. Initial time step of 0.01 is used as fraction of total time. It means

the initial load step is 1% of the total load. It must be noted that, for many problems including plasticity of complicated

contact conditions in the early stages of the analysis, this must be a very small percentage (typically 0.5%). The

maximum number of recycles allowed for each increment are 10 and minimum is 1. The desired number of recycles

per increment is 4. If this number is chosen to be very small, then the step size is cut to a smaller size for convergence

to be achieved and there will be larger number of steps. If this number is very large, then the load step will allow more

iterations for convergence in the same step.The smallest and largest ratio between the steps is 0.1 and 1.2, respectively,

while the minimum value of the step is 1E-5. Output is written to result file for every single increment.

10 5


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469CHAPTER 27


Results

Figure 27-2 shows the sequence of the analysis with a close-up view of the buckle. It can be seen that the clip slideson top of the protrusion of the static frame without any penetration. It is quite remarkable that even with the large

motion as well as large sliding contact per load increment between the two deformable contact bodies, the analysis

shows a robust behavior.

A vector plot of the comparison of normal and frictional contact forces with the Marc results is presented in

Figure 27-3 and Figure 27-4, respectively. The contact forces for SOL 400 and Marc agree very well in both

magnitude and direction.

Figure 27-2 Various Stages of Insertion of the Clip


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Figure 27-3 Comparison of Contact Normal Forces

Figure 27-4 Comparison of Contact Frictional Forces

Next, the load displacement for the frictional and frictionless cases are compared in Figure 27-5. Only the X direction

forces are plotted versus time. It is always recommended to perform a frictionless analysis (nug_27f.dat)

whenever possible to aid in the understanding of the affect of adding friction. As expected, for the frictionless case,

the load displacement curve is symmetric about the center line (between the insertion and removal steps). Deformed

geometry is shown at various peaks of the curve and, as intuition would suggest, the peak forces correspond to the

point of maximum bending. Addition of the non-conservative friction forces destroys the symmetry and the peak

insertion force increases compared to the peak force in removal. The removal of the clip generates less pull-out force

compared to the push-in force. Also, the insertion force starts reducing due to frictional forces aiding the motion as

opposed to resisting the motion as the sliding switches from the convex part to the concave part of the contact surface.

(a) SOL 400 (b) Marc

(a) SOL 400 (b) Marc


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471CHAPTER 27


Figure 27-5 Load Displacement Curve for the Frictional and Frictionless Cases

Checking the finite element analysis with a hand calculation assists both in understanding the FEM as well as the

physics of the simulation. Solving elementary equations mentioned earlier for the bending stress yields,

where is the tip displacement shown in Figure 27-6 during the insertion of the clip.

Figure 27-6 Verify FEM with Simple Calculation

Performing the calculation of the bending stress at the outer fibers of the thinnest section gives,

. The value of

agrees closely to the corresponding bending stresses in Figure 27-6 of . As expected, the linear solution

presents an upper-bound to the actual stresses.

0.5 1.0 1.5

-2000

-1500

-1000

-500

0

500

1000

Frictional

Frictionless

Time (s)

F (N)x

Fx Fx

FxFx

Insert Remove

3

2---

Et

L2------------=

lcase1

Comp 11 of Stress

X

Y

Z

-4.232e+002

-3.388e+002

-2.543e+002

-1.699e+002

-8.542e+001

-9.664e-001

8.349e+001

1.679e+002

2.524e+002

3.368e+002

4.213e+002

Inc: 17Time: 4.250e-001

1

L=80

mm

= 20 mm

2 = 6 mmt

32---

E 2t

L2

--------------------3

2--- 10x10

9 N m2 20mm 6m m

80mm 2------------------------------------------------------------------------------------ 4.69 x 108

N

m2

------m

103 m m------------------

2469

N

m m2

-----------= = = = 469 N m m2

423 N m m2


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Modeling Tips

The two most important aspects in the analysis comprise of the inclusion of assumed strain enhancements to thestandard element formulation and the choice of contact and time stepping scheme parameters use of adaptive load

stepping scheme, and its associated parameters. The former is important due to presence of bending stresses in the

structure which can manifest themselves as (sometimes large) spurious shear stresses. This is a purely numerical

artifact due to the standard, displacement based finite element chosen which can be ameliorated by the use of an

assumed strain enhancement to the standard element.

Among the numerical parameters affecting the convergence of the job, the two most important parameters for this kind

of analysis are the contact bias and maximum number of recycles for the adaptive stepping scheme.

In contact analysis with friction, it is important to use a high bias (preferably 0.99) for frictional problems for improved

convergent results. In many cases (although, not in this problem, nug_27b.dat), it can decrease the number of

iterations as well.

Next is the contact zone tolerance. Typically, a default value is 1/20th the smallest length of solid element. If the

contact zone is too big, then there could be a loss of accuracy due to acceptance of penetrated nodes or large amount

of recycling due to contact nodes separating. However, reducing the contact zone tolerance may not always yield the

reduction in the number of iterations. In fact, in certain problems where there are not many separations expected,reducing to a very small number can even increase the number of iterations due to contact detection and scaling of

incremental displacements in the iterative penetration checking algorithm in contact.

It is also worth noting that the adaptive load stepping improves the speed and accuracy of the analysis quite

significantly for this problem due to its intelligent choice of time steps based on the convergence parameters. This

adequately demonstrates the strength of the adaptive stepping in tough problems where the smart algorithm adjusts the

increment size based on the kinematics of deformation, contact constraints, and convergence rates rather than the fixed

time stepping where the only alternative is to cut down the existing increment size in case of non convergence in the

specified number of recycles.

It is also noted that a very high or very low number of desired number of recycles can either invoke an excessive

number of iterations or induce cutbacks during the analysis. For example, decreasing the desired number of recycles

to may increase the number of increments. Due to a large amount of sliding and significant contact nonlinearity, a large

number of recycles, in general, are expected for most increments. Therefore, a high number of desired recycles proved

to be useful in this particular example. However, in problems with milder material and/or contact nonlinearities where

only a few iterations per increment are expected, a smaller number of desired recycles can yield faster results. This

difference can result in notable savings of the computing time for large jobs.

Flat rigid surfaces can be glued to the ends of the buckle and insert to control the insertion and extraction of the insert

in and out of the buckle. The advantage of this modeling technique is that the total insertion and extraction force

component, Fx, can be easily determined as shown in Figure 27-5, since all of the forces acting on rigid bodies are

resolved to a single force and moment vector acting at the position of the rigid bodies.

Finally, since the buckle has a plane of symmetry, it is cost effective to only model the half of the model say above this

plane of symmetry.

Note: For contact problems, artificial damping can improve the speed of convergence and stability of the

analysis as seen in nug_27c.dat.

473CHAPTER 27


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473CHAPTER 27


Input File(s)

VideoClick on the image or caption below to view a streaming video of this problem; it lasts approximately 47 minutes and

explains how the steps are performed.

Figure 27-7 Video of the Above Steps

File Descriptionmug_27.dat Marc input for fixed time

nug_27.dat MD Nastran input for fixed time stepping

nug_27a.datMD Nastran input with adaptive time stepping with bias = 0.99, contact zone tolerance = 0.0

(default), desired number of recycles = 20 (default = 10)

nug_27b.datMD Nastran input with adaptive time stepping bias = 0.0 (default), contact zone tolerance =

0.005, desired number of recycles = 20 (default = 10)

nug_27c.datMD Nastran input with adaptive time stepping bias = 0.99, contact zone tolerance = 0.005,

desired number of recycles = 20

nug_27b.bdf Input file similar to nug_27b.dat above with half symmetry use in the video

nug_27_star

t.SimXpert

MD Nastran input with adaptive time stepping bias = 0.99, contact zone tolerance = 0.005,

desired number of recycles = 20

HalfSym

metry

X

Y

Z

247mm

168 mm
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Large Sliding Contact Analysis of a Buckle

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