using three-dimensional digital imaging correlation techniques to validate tire finite-element model

USING THREE-DIMENSIONAL DIGITAL IMAGINGCORRELATION TECHNIQUES TO VALIDATE TIREFINITE-ELEMENT MODEL

The field of finite-element analysis (FEA) is becomingincreasingly important as a tool for tire design. FEAsupplies the tools necessary to move from a ‘‘build-and-test’’ mentality to a ‘‘predictive’’ approach. In

the past, the tire design procedure was to build different var-iations and perform testing to provide product performancedirection. This process can be both costly and time consuming.By modeling different designs and predicting the perfor-mance, FEA provides the capability to reduce both develop-ment time and costs along with creating increasedunderstanding of the end product. Validation of the FEAresults is a key point that must be performed in order for itto be a useful tool for design engineers.

The optical techniques of digital image correlation (DIC) havebeen around for a number of years. The theory and proceduresinvolved in the digitizing and correlation of images withspeckle patterns before and after deformation is described inliterature.1,2 Applications in rigid-body mechanics, specifi-cally in regard to measurement of in-plane displacementsand strains, can also be found in literature.3–5 These opticaltechniques were used early on for studies such as photograph-ically depositing a set of grid lines on the surface of a photoe-lastic birefringent coating to determine full-field strains.6

These techniques have evolved to the point of having the abil-ity to capture dynamic tire deformations.7 Other techniqueshave been used successfully, such as holography and moire,but these methods are tedious, impractical, and do not providestrains directly.

DIC techniques provide a noncontacting means of measuringdisplacements and resulting strains. The fact that FEA out-puts displacements as a primary variable is another reasonfor making the DICmethod a logical choice for validation. Theideal situation is to validate the FEA with a measurementmethod that produces the same type of output. This allowsfor a direct one-to-one comparison of the two approaches.

Another rationale for using this technique is the relative dif-ficulty of measuring strains in a tire using other methods.Most traditional strain-measuring techniques are not effec-tive on tires. The metal foil strain gages are designed foruse with stiff materials such as hard plastics or metals. Therubber used in tires is so much lower in stiffness that thestrain gages provide local stiffening and mask the true defor-mations. In addition, the magnitude of strains is typically anorder of magnitude larger than that of most structural mate-rials. In the past, these problems were overcome using liquidmetal strain gages.8 While these strain gages were successful,they are delicate, difficult to construct, and do not provide full-field measurements. They also utilize mercury, which

requires added concern regarding safety and environmentalprecautions.

BASIC PRINCIPLE OF DIC MEASUREMENT

DIC is a three-dimensional (3D) full-field optical techniquethat measures the shape deformations of an object. The sys-tem used in the following analyses tracks the random grayvalue pattern in a small neighborhood, subset, during defor-mation.9 These subsets, also known as facets, are used alongwith two cameras and the triangulation principle to obtainthe 3D object shape during different stages of deformation.7

The corresponding surface strains are then calculated fromthese deformations. The DIC method is ideal for deformationand surface strain measurement because it does not requireany instrumentation on the tire itself. The system is robustand repeatable, relying on nothing besides obtaining imagesfrom both cameras that are in focus and not overexposed.

A commercially available system was used for all image col-lection and processing. The theory and equations used to cal-ibrate and translate the displacements from the images tostrain values can be found in the references sited herein.

EXPERIMENTAL SETUP

Figure 1 shows the experimental setup for the DIC method.The random pattern, which is tracked to determine the defor-mations, is shown at the bottom of the tire. Two cameras areshown with a series of support bars that allow flexibility inpositioning the cameras along with a stable mounting base.The small lights shown are used to provide optimum expo-sure. Static loading is applied upward by the plate under-neath the tire.

The base, which is fixed to the floor, is designed to minimizecamera movement and vibration. This is important when tak-ing images at different loading conditions. If the camerasmove, this could cause errors in camera calibration or in defor-mation calculations. Trials were conducted to determine opti-mal camera placement and random speckle pattern.

VERIFICATION OF DIC METHOD

An important step before utilizing any measurement equip-ment is to validate the method and results. Once the accuracyof the DIC method is verified, it can be used to validate thefinite-element (FE) process. It is imperative to be certain thatthe measurement method is accurate before proceeding to theFEA validation. This must occur before presenting FEA vali-dation results to design engineers. These design engineersmust have confidence in the measurement method in orderto have confidence in the FEA validation.

A thin, rectangular rubber test specimen, shown in Figs. 2and 5, was chosen for the verification of the DIC method.

TECHNIQUES by R. Moser and J.G. Lightner III

R. Moser (SEMmember) is an engineer and J.G. Lightner III is a section supervisorCAD/CAE systems with Bridgestone Firestone North American Tire, LLC, Akron,OH.

doi: 10.1111/j.1747-1567.2007.00157.x� 2007, Bridgestone Firestone North American Tire, LLC July/August 2007 EXPERIMENTAL TECHNIQUES 29

A bracket, shown in Fig. 2, was used to deform the samplea measurable amount in the plane of the bracket. Figure 3shows the rotational base that was used to rotate the samplea known number of degrees about the vertical axis. Thebracket was also tilted backward, rotated about a horizontalaxis, a measurable angle as shown in Fig. 4. The verticaldirection is also referred to as the radial direction for thispaper (see Fig. 9).

There were several reasons for choosing this test to verify themeasurement system. One reason was that this would enablean analytical calculation to be performed to check the normalstrain levels. The in-plane normal strain could be easily calcu-lated using the formula for normal engineering strain, Eq. 1:

ðe 5 DL

LÞ ð1Þ

with normal engineering strain5e and the original length5 L(all strains throughout this paper are of this form). This couldthen be compared to the results of the DIC measurement.Also, the rotations about the vertical and horizontal axescould verify that the system correctly processes the 3Dmotions. The sample was rotated and tilted with the normal

strain held constant to verify that the output showed constantnormal strain through the 3D movements. Figure 6 showshow the grid appears to have optical shear and compressionin the picture furthest to the right. The DIC system shouldcompensate for this phenomenon.

The rubber sample was deformed an amount that provideda longitudinal engineering strain of 0.10. No specimen rota-tions were performed at this strain level. All measurementdata were extracted along the solid line shown in Fig. 5.Figure 7 shows all the results, including those of the 0.10longitudinal strain level. The legend in Fig. 7 named themeasurement data in the following way: % longitudinal

Fig. 1: DIC experimental setup

Fig. 2: Bracket to stretch rubber sample a known distance

Fig. 3: Rotational base with fine adjustments to rotate rubbersample a known angle

3D DIGITAL IMAGING CORRELATIONTECHNIQUES

30 EXPERIMENTAL TECHNIQUES July/August 2007

engineering strain_degrees rotated about horizontal axis_de-grees rotated about vertical axis.

As one can see, at the 0.10 level of longitudinal engineeringstrain, the DIC method was within 0.01 engineering strain(between solid horizontal line and 0.10). It is also within0.01 engineering strain when subject to deformations causinga 0.20 longitudinal engineering strain state. There are fivecases of rigid-body rotations up to 308 and tilt angles up to608 with a constant longitudinal engineering strain state of0.284. All DIC results are within 60.02 engineering normalstrain. The results confirm that the DIC method correctlytracked the deformations and rigid-body rotations since itaccurately calculated the engineering strain values, withina limited amount of error. It was observed that some of thepaint speckles were delaminating from the rubber specimenat the higher strains. It is believed that some of the error andstrain fluctuations stem from this speckle delamination. Thedemonstrated level of accuracy was judged as acceptable forthis application.

SURFACE STRAINS

The surface strains on the sidewall of a statically loaded tirewere chosen to validate FEA using DIC measurements. Thistire location was ideal for the DIC method since the tire side-wall region is visible throughout the inflation and radial load-ing sequence. Although full-field results were obtained, theresults on a radial line in the midplane containing the loadaxis (see Fig. 9) are of most interest since this is the region ofhighest sidewall bending strain.

There are several FEA parameters that have a large influenceon in-plane strain results. Mesh refinement is one of these. Itwas determined that having adequate mesh refinement isimperative to obtain accurate in-plane strain results in tire

models (see Fig. 8 for a representative two-dimensionalmesh). Also, it is important to verify that the cross-sectionalgauges of the tire materials are accurate. Another majorparameter is to confirm that the placement of corded compo-nents in the model accurately reflect those in the tire.

Figure 10 shows the radial engineering strain as a function ofradial position in the tire sidewall. The solid curve shows themeasurement results for the DIC system, while the curvewith points shows the predicted results of the FE code. Theportion of the curves near the rim is not in the area of interest,so most of the work went into getting the portion of the curves

Fig. 4: Bracket measured at tilt angle using digital level

Fig. 5: Thin rubber sample with random and grid patterns

Fig. 6: Rubber sample showing optical compression and shear,which DIC method accounts for


July/August 2007 EXPERIMENTAL TECHNIQUES 31

near the tread to match. Strains for this study are caused byradial load only, not inflation pressure.

Figure 11 shows the absolute value of the difference betweenthe DIC measurement and the predicted maximum sidewallsurface engineering strain for 13 different tires. The average

in-plane strain difference between the DIC measurement andthe FE model in peak radial in-plane engineering strain is0.024, shown with solid horizontal line, with a standard devi-ation of 0.012 strain.

The next figure, Fig. 12, illustrates the accuracy of the pre-dicted radial location of the peak radial normal engineeringsurface strain. This figure shows that the average absolutevalue of the difference between the DIC measurement andthe FE model in radial location of peak strain is approxi-mately 0.06 inch (1.5 mm), with a standard deviation of about0.05 inch (1.3 mm).

Figures 11 and 12 show results from a wide range of tire sizesand constructions. The tires had the following ranges for sizeand construction features—section width: 215–255 mm;

0.35

0.3

0.25

0.2

0.15

0.1

0.05

030252015105–30 –25 –20 –15 –10 –5 0

Radial Position (mm)

Radial Engineering Strain vs. Radial Position

Rad

ial E

ng

inee

rin

g S

trai

n

10Per_0Tilt_0Rot28.4Per_30Tilt_0Rot

20Per_0Tilt_0Rot28.4Per_30Tilt_30Rot

28.4Per_0Tilt_0Rot 28.4Per_0Tilt_30Rot28.4Per_60Tilt_0Rot

Grip Effect0.02 strain

0.01 strain

0.01 strain

Fig. 7: DIC method validation results at different normal strain levels and degrees of tilt and rotation

Fig. 8: Representative two-dimensional cross-sectional meshshowing twice as much mesh refinement in the shoulder asin the rest of the cross-section

Fig. 9: Tire showing coordinate system and terminologyused for strains

Radial Engineering Strain vs. Radial Position

0.200.150.100.050.00

–0.05–0.10–0.15–0.20–0.25

–250 –260 –270 –280 –290 –300 –310

Rad

ial E

ng

inee

rin

g S

trai

n

Radial Position (mm)

Tire 1 FEA Tire 1 DIC Measurement

DICNear Rim

FEA

Tension

Compression

Near Tread

Fig. 10: Radial engineering strain in tire sidewall versus radialposition (measurement and FEA)



aspect ratio: 45–55; rim diameter: 16–18 inches; body ply:mono ply, two ply, two ply with high turn up; steel plies:two plies; and nylon reinforcement in tread: with and without.Each of the 13 tires was unique in size and/or constructionand the tires were loaded to 100% of their rated load. Thiswide range of tires brings into account a wide range of sourcesfor error between modeling, measurement, and tire varia-tions. The errors shown were not related to any particularsize or construction.

INTERNAL STRAIN

Determining the internal strains of structures is also impor-tant for FEA validation. However, there is an inherent diffi-culty obtaining in-plane strains that are not on the externalsurfaces of objects. Removing material may change the globalbehavior of the object, namely, stiffness. Instrumenting an

object with internal strain gages may be extremely difficult,if not impossible.

The approach that was used for this study was to removea small ‘‘window’’ of rubbermaterial from the shoulder of a tire(Fig. 13). The window is approximately 2 inches (50.8 mm)wide and is deep enough to expose the edges of both steel plies(Fig. 14). To validate the FE model, a comparison of the in-plane shear strain (see Fig. 13) of the rubber between the twoply edges (Fig. 15) of the DIC measurement and the FEAmodel was made. To ensure a valid comparison, a correspond-ing model was created with a window of material removed inthe shoulder to match the measured tire.

To analyze such a small region, care needed to be taken dur-ing the measurement process. High-zoom lenses were usedalong with a 1-inch2 (25.4 mm) calibration block. A calibration

Absolute Value Difference in Engineering Strain DIC vs. FEA0.050

0.045

0.040

0.035

0.030

0.025

0.020

0.015

0.010

0.005

0.000Tire 1 Tire 2 Tire 3 Tire 4 Tire 5 Tire 6 Tire 7 Tire 8 Tire 9 Tire 10 Tire 11 Tire 12 Tire 13

Dif

fere

nce

of

Pea

k R

adia

l Str

ain Average Difference ~ 0.024

Standard Deviation ~ 0.012

Fig. 11: Difference in radial engineering surface strain between DIC measurement and FEA

Absolute Value Difference in Location of Peak radial Strain DIC vs. FEA

0

1

2

3

4

4.5 35%

25%

15%

5%

–5%

–15%

–25%–220 –230 –240 –250 –260 –270 –280 –290 –300 –310 –320

3.5

2.5

1.5

0.5

Tire 3Tire 2Tire 1 Tire 4 Tire 5 Tire 6 Tire 7 Tire 8 Tire 9 Tire 10 Tire 11 Tire 12 Tire 13

Dif

fere

nce

of

Pea

k R

adia

l Str

ain

Lo

cati

on

(m

m)

Average Difference ~ 1.5 mm ~ 0.06 in

Standard Deviation ~ 1.3 mm ~ 0.05 in

Radial Strain

Y (mm)

eyy

LA152E MeasLA152E FEA FFP

TRPLRim Guard

Fig. 12: Difference in radial location of peak radial surface strain between DIC measurement and FEA



block is a target with a dedicated pattern with known patterndimensions used to calibrate the two cameras. Special pro-cessing was used to manufacture the calibration block toensure the accuracy of such a small piece. Also, trial and errorwas required to create random speckles small enough to workwell in such a magnified region. Another important issue dur-ing the measurement was ensuring that the cameras wereimmobile because even a small amount of movement whenthe images are magnified this much will lead to large errorsin strain calculations.

Figure 16 shows the engineering shear strain in the rubberbetween the two steel plies for a single radial load for the DICmeasurement and the FEA prediction. The solid curve showsthe measurement results for the DIC system, while the curvewith points shows the predicted results of the FE code. Sincethe shear strains calculated using the DIC system are surfacestrains, the FE model shear strains are calculated as an aver-age value of the four integration points that are closest to thesurface in each element. The average difference between theDIC measurement and the FE model comes out to approxi-mately 0.05 shear strain.

An observation has been made in the past while analyzing FEmodels that the shear strain in the center of the footprintbetween the two steel plies at the plies edge seems to reacha maximum value and level off when loaded beyond a certainradial load. The physical explanation is that at the center ofthe footprint, the steel plies edge stops deforming when it is

completely flattened out. Additional load creates no additionaldeformation and therefore no additional strain. This was ver-ified using the same test tire and the DIC system. Figure 17demonstrates this phenomenon using the DIC method andthe FE model. The average error between the DIC measure-ment and the FE model comes out to approximately 0.025shear strain. This provides further evidence to validate theFE prediction within a limited error.

SUMMARY

The DIC system was validated through the testing of a simplethin, rectangular rubber sample. By stretching, rotating, andtilting the sample, the 3D capabilities of the DIC system wereverified. It was proven that the DIC system was able to over-come the optical shear and compression caused by the rota-tions and tilting of the sample. The DIC results were within60.02 normal engineering strain for a normal strain level ofapproximately 0.284. It was shown that the FE predictionsclosely matched the DIC measurements for in-plane normalstrains of the tire sidewall. The average in-plane strain dif-ference between DIC measurement and FE prediction forpeak in-plane normal strains was shown to be approximately0.024. Important parameters for prediction accuracy wereidentified through this process. The FE model was also shownto agree well with the DIC measurements when analyzing in-plane engineering shear strain between the two steel plies.The average error between the DIC measurement and theFE model was approximately 0.05 strain when analyzing

Fig. 13: Test tire with 2-inch-wide window removed from shoulder exposing the edges of two steel plies and sketch showing shearstrain in rubber material (dashed region) between two plies with steel cords

Fig. 14: Close-up view of window cutout, with front view in left picture and top view in right picture



engineering shear strain for this case. The prediction alsoagreed well with the measurement in showing that the engi-neering shear strain approached a limiting value beyond a cer-tain radial load.

Validating the DIC measurement system and the FE predic-tion method were important steps in increasing tire engi-

neers’ confidence in FE model results. The goal is todecrease the time and overall cost of the tire developmentprocess by utilizing FEA modeling effectively.

ACKNOWLEDGMENTS

This paper and the analyses therein were impacted by theefforts of many individuals. John Turner provided knowledgeof DIC techniques for theoretical and practical applications.His contributions were key in developing the DIC measure-ment technique. Robert Asper was a key contributor to thedevelopment of the FE models utilized in this study. Hisexpertise was instrumental in obtaining the most accuratemodeling results possible. The assistance of Karl Neimesand Gene Chen for creating FE models for sidewall surfacestrain validation is appreciated. Karl also contributed in thedevelopment of the FE model for surface strain analysis.Thanks go out to Mike Frank for the development of the FEmodel with the material removed from the shoulder region.He also assisted in the DIC test measurements of the tire withthe material removed from the shoulder. Stan Olesky gave ofhis time to prepare the tires for the DIC measurements. Healso developed the test device used to validate the DIC sys-tem. The technical contributions of the team at CorrelatedSolutions are also greatly appreciated.

Fig. 15: Rubber material with speckle pattern inside of white box between two steel plies

Fig. 16: Engineering shear strain between two steel plies versus window position

Shear Strain vs. Load

% T&RA Load (Ibs)

0.50

0.45

0.40

0.35

0.30

0.2530% 40% 50% 60% 70% 80% 90% 100% 110% 120%

Sh

ear

Str

ain

DIC Experiment FEA Model

Fig. 17: Engineering shear strain between two steel pliesversus percent radial load



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Displacement Measurements Using Digital Image Correlation and

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using three-dimensional digital imaging correlation techniques to validate tire finite-element model

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