Experimental Measurement and Computational Simulation 

of the Strains on a Single Yarn in a Kevlar Fabric 

During Stretching

by Jian H. Yu, Brandon McWilliams, 

Peter G. Dehmer, and Chian-Fong Yen

ARL-TR-5224 June 2010

Approved for public release; distribution unlimited.
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Army Research Laboratory

Aberdeen Proving Ground, MD 21005-5066

ARL-TR-5224 June 2010

Experimental Measurement and Computational Simulation 

of the Strains on a Single Yarn in a Kevlar Fabric 

During Stretching

Jian H. Yu, Brandon McWilliams,

Peter G. Dehmer, and Chian-Fong Yen

Weapons and Materials Research Directorate, ARL

Approved for public release; distribution unlimited. 
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Experimental Measurement and Computational Simulation of the Strains on a 

Single Yarn in a Kevlar Fabric During Stretching 

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Jian H. Yu, Brandon McWilliams, Peter G. Dehmer, and Chian-Fong Yen 

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14. ABSTRACT 

The ability to measure the strain on an individual yarn is essential for the understanding of mechanical properties of fabrics. 

Using a non-contact technique called photogrammetry, we investigate the deformation of a single yarn in a Kevlar® fabric as it 

undergoes stretching. Photogrammetry uses two charge-coupled device (CCD) cameras fitted with macro lenses to record 

stereo images of the fabric during stretching. We tracked the change in the arc length between a set of points and calculated the 

strain from the arc length at various locations. We used a finite element method (FEM) model to simulate the experiment, 

optimizing the material parameters in the FEM model by comparing the experimental data to the computational results. After 

optimization, the simulated displacement and strain time histories matched reasonably well with the experimental data. 

15. SUBJECT TERMS

Photogrammetry strain measurements optical technique Kevlar fabric yarn 

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Contents

List of Figures iv

1. Introduction 1

2. Experimental Method 1

3. Experimental Results 3

4. Finite Element Modeling 5

5. Comparison of Experimental and Modeling Results 7

6. Conclusions 9

7. References 10

Distribution List 11
iv

List of Figures 

Figure 1. The push-rod assembly and the steel frame. ................................................................... 2

Figure 2. The field-of-view of the fabric in the steel frame, showing the three sets of points 

on the yarn for tracking the displacement on yarn crossover #2. .............................................. 3

Figure 3. The x-,y-, and z-displacements at applied forces of 0, 110, and 438 N, 

respectively. ............................................................................................................................... 4

Figure 4. Average strains along the principal yarn at the crossovers; the error bar is the 

standard deviation from the mean strain. ................................................................................. 5

Figure 5. (a) FEM mesh of the fabric and (b) the yarn dimensions. .............................................. 6

Figure 6. Comparison of experimental and modeling results: E11 modulus sensitivity 

(frictionless case). ...................................................................................................................... 8

Figure 7. Comparison of experimental and modeling results: strains at the principal yarn 

crossovers (friction coefficient = 0.25). .................................................................................... 9
1

1. Introduction

The use of woven Kevlar fabric is prevalent in many applications, such as body armor, helmets,

and composite structures. The performance of these fabrics is influenced by yarn material 

properties, yarn geometry, yarn architecture, boundary conditions, crimping, friction, etc. The 

ability to measure the strain on an individual yarn can provide insight into the yarn-to-yarn 

interactions within a fabric. Photogrammetric analysis has been used to measure the 

deformability of fabrics and textile composites. For instance, Lomov et al. (1, 2) studied the 

in-plane deformation of yarns in a fabric that underwent shearing using two-dimensional (2-D) 

photogrammetry. Non-optical techniques have also been used to measure the strain in yarns. In 

one case, Chocron et al. (3) wove a nickel-chromium wire that can measure strain into a fabric. 

In this report, we present a three-dimensional (3-D) photogrammetric analysis of a Kevlar fabric 

that has been subjected to a push-rod stretching test. 

Computational (or finite element method [FEM]) models have been used to analyze ballistic 

impact on fabrics. Cheeseman (4), Duan (5, 6), Lim (7), and Talebi (8) used 3-D FEM solid 

elements to simulated fabrics impacted by projectiles of various geometries and confined under 

different boundary conditions. A fabric membrane model was developed by Yen (9) to lower 

the computation cost with a minimal reduction in accuracy. Most the aforementioned models 

need to be validated and the input parameters need to be optimized. We present an approach to 

optimize a constitutive model of a Kevlar fabric. We use experimental results to validate the 

FEM model and identify the sensitivity of the friction coefficient between yarns under a static 

stretching condition. 

2. Experimental Method

We used a 5x5 plain-weave Kevlar fabric in the stretching test (5 warp yarns per inch and 5 

weft yarns per inch, 12105 denier yarn, areal density = 530 g/m2). The fabric was clamped to a 

steel frame that had a circular opening diameter of 5.08 cm (figure 1). The push rod had a 

1.905-cm-diameter brass ball attached to the end of the rod. We measured the applied force 

with an in-line load cell and used a screw rod to provide the forward movement (in the zdirection) of the push rod. To track displacement, we painted the surface of the fabric facing the 

cameras with a random dot pattern using black pen ink. Two charge-coupled device (CCD)

cameras (Photron SA1, Photron USA, Inc.) were employed to generate stereo images of the 

deforming fabric. The cameras were placed behind the target fixture along the z-direction and 

the angle between of the cameras was set at 20°. The images were recorded at a 512×512 pixel 

resolution with a 1/60 s exposure on each frame. Each camera used a macro lens (Nikon AF-
2

Nikkor) with a focal length of 85 mm and a f-stop of f/8. The field of view was about 5 x 5 cm,

centered on the location of the push-rod ball point. We saved the images as 8-bit TIFF files and 

analyzed them using a commercially available photogrammetric software program called 

ARAMIS (GOM GmbH, Germany, distributed by Trilion Quality Systems in the United States). 

ARAMIS has a built-in algorithm for calculating the displacement (the ARAMIS default 

settings are 15×13 facets × step, which is a standard calculation). The displacement sensitivity 

was at least 1.7 microns (10). 

Figure 1. The push-rod assembly and the steel frame.

The displacement on a particular yarn crossover was tracked based on a set of points. The strain 

was calculated using the arc length across a set of four points (equation 1): 

) l

l ln(

o

ε =

(1)

where ε is the strain, l is the deformed arc length, and lo is the undeformed arc length. The 

deformed arc length is calculated using equation 2:

2 2 2 1/ 2 l =∑ (∆x + ∆y + ∆z ) (2)

where ∆x, ∆y, and ∆z are the displacements between the tracking points. The average strain on 

the yarn crossover is an average from three sets of tracking points (figure 2). The initial arc 

length is about 3.5 mm. The axes shown are the global coordinates. The tracking points are 

along the yarn axis, which is not necessarily parallel to the global x-axis.
3

Figure 2. The field-of-view of the fabric in the steel frame, 

showing the three sets of points on the yarn for 

tracking the displacement on yarn crossover #2. 

3. Experimental Results

We collected photogrammetric data to determine the fabric deflection as a function of the 

applied force. Figure 3 shows a full-field measurement of the x-, y-, and z-displacements of the 

fabric during stretching. The displacement plots indicate that the principal warp and weft, the 

yarns that were directly engaged by the push rod, experienced a higher stretching ratio than the 

secondary yarns. The contour lines illustrate that the fabric response is not isotropic; the 

greatest displacement gradients are along the weft and warp directions. The deformed fabric 

takes on a shape of a square pyramid with its corners along the warp and weft directions. This 

shape is similar to the shape of a deformed fabric that has been impacted by a high-speed 

projectile. Under static stretching conditions, the corners of the pyramid extend to the boundary 

of the circular clamp. However, during an impact event, the corners of the pyramid move 

toward the boundary.

A full-field strain tensor cannot be evaluated using the deformation gradient derived from the

displacement vectors in this experiment. Fabric is not a rigid body. There are crimps in the 

yarn that can straighten out before the yarn is actually strained. Also, one yarn can slip past 

other yarns creating a false indication of strain. The best method for calculating strain is to 

track the changes in the arc length at the yarn’s crossovers.
4

Figure 3. The x-, y-, and z-displacements at applied forces of 0, 110, and 438 N, respectively.

Figure 4 shows the calculated average strain along the principal yarn at various locations. At 

low applied forces, the calculated strain values are very noisy. This effect is due to the 

displacement sensitivity limit of the instrument. According to the ARAMIS manufacturer, the 

instrument’s sensitivity is ~0.002 mm for a field of view of 50 mm2 (10). 
5

Figure 4. Average strains along the principal yarn at the crossovers; the error bar is the standard 

deviation from the mean strain.

The strain plots indicate that the strains along the yarn are not uniform. The highest strain is 

located near the contact point between the push rod and the fabric; the lowest strain is near the 

clamp boundary. The loads are not transmitted uniformly along the yarn. The yarn is pinned 

between the crossovers and the frictional force that interlocks the crossovers constricts the 

movement of the weft yarn, preventing strain relief from the relaxed section to the location 

where the yarn is already under strain. Once the applied force overcomes the frictional force at 

the crossovers, yarns can slip past each other, allowing the principal yarn to uncrimp and 

provide strain relief. The crossover near the push rod on the principal weft yarn experiences the 

highest strain among the crossovers. The loading is attenuated from the point of contact with 

the push rod to the boundary of the clamp, which indicates that some of the loading is being 

borne by the secondary yarns between the crossovers.

4. Finite Element Modeling

The fabric model used here is a yarn-level FEM model based on a ballistic model from an 

earlier work (9). Computations were performed using the ABAQUS/Explicit software package. 

The yarns are represented by membrane (no bending stiffness) elements to reduce computation 

time, and the yarns in the fabric are simplified to plane segments (figure 5). 
6

Figure 5. (a) FEM mesh of the fabric and (b) the yarn dimensions. 

An orthotropic elastic constitutive model is used to describe the yarns: 

 (3) 

where  is the strain,  is the stress, E is the Young’s modulus, G is the shear modulus, and is 

the Poisson ratio. The yarns are oriented such that the fiber axis is the 11 direction. In 

actuality, each yarn consists of a bundle of fibers, which could be considered transversely 

isotropic. However, since we are using a continuum model at the yarn level, the moduli in all 

other directions, including the shear moduli, are assumed to be two orders of magnitude smaller 

than the principal yarn direction (9). Note: The modulus used here is an effective modulus, 

E11*

, where E11* < Efiber. This is due to the density of the yarn being less than the density of the 

base material due to the packing of the fibers. Poisson effects are assumed to be negligible and 

a small Poisson ratio of 0.001 is used. 

A fixed boundary condition is applied to the yarn at the edge of the circular frame. The push 

rod is modeled as a rigid body. The value for the dynamic and static friction coefficients 

between the push rod and the fabric is 0.36 (11) and the friction coefficient, s, between the 

yarns is set to 0.25. Since there is uncertainty in E11*

, due to difficulties in measuring the actual 

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7

density of the yarn and local variations in the fiber packing, a parametric study of for E11* was 

used to determine this effect on the fabric’s response. An optimized effective modulus, E11*, 

was determined by comparing the experimental data to the modeling results. 

5. Comparison of Experimental and Modeling Results

Figure 6 compares the experimental and modeling results of the applied force as a function of 

fabric displacement for the frictionless case. If the value of E11 is set too high, the fabric is too 

rigid. On the other hand, if E11 is set too low, the fabric is too compliant. There is an optimum 

value for E11 in which the modeling results are in reasonable agreement with the experimental 

results. Root mean square errors (RMSEs) were computed between the modeling values and 

the experimental curves for E11 = 35, 30, and 25 GPa. The RMSEs were 0.114, 0.048, and

0.106, respectively. E11 = 30 GPa yielded the lowest RMSE; the force versus displacement 

profile was closely matched to the experiment data, especially in the low applied force (low 

displacement) region. RMSEs were also computed for μs = 0, 0.25, 0.50, and 0.75 while setting 

E11 = 30 GPa. The RMSEs were 0.048, 0.046, 0.046, and 0.048, respectively, indicating that 

the displacement was insensitive to the fiction coefficient between the yarns. Unlike the case in 

dynamic impact, the yarns have time to redistribute their loads by slipping pass each other at the 

crossovers during the static stretching. 
8

0

50

100

150

200

250

300

350

400

450

500

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Maximum displacement in the z-direction (mm)

Applied force (N)

Experiment

E = 70 GPa

E = 35 GPa

E = 30GPa

E = 25 GPa

Figure 6. Comparison of experimental and modeling results: E11 modulus sensitivity (frictionless 

case). 

There was a small discrepancy at the high applied force region where the modeled fabric 

showed more compliance than the actual fabric in the experiment. Instead of having a 

continuous curvature, the modeled yarns actually had a large crimping angle of 154.5°, which 

allowed the modeled yarns to have more yarn length to uncrimp than the actual yarn has. So, 

the modeled fabric had a higher deflection than the actual fabric at a given applied force. 

The yarn strains at the crossovers are compared in figure 7 for E11 = 30 GPa. Although the 

strain values are not exactly matched, the trend of increasing strain as a function of increasing 

applied force is in close agreement. The strain as function of the yarn crossover location also 

follows a similar trend: the strain increases from the fabric boundary to the area where the 

fabric is in direct contact with the push rod.
9

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0 100 200 300 400 500

Applied Force (N)

Principal yarn strain

exp: #2

exp: #3

exp: #4

sim: #2

sim: #3

sim: #4

Figure 7. Comparison of experimental and modeling results: strains at the principal yarn crossovers 

(friction coefficient = 0.25). 

6. Conclusions

In this study, we used photogrammetry to measure fabric stretching under static conditions. We 

successfully measured the local strain along a yarn in a fabric as it underwent stretching. The 

ability to measure the local strain on an individual yarn is a valuable tool for examining the 

mechanical behaviors of a fabric. We implemented a FEM model to simulate the experiment. 

The moduli in the FEM model were optimized by comparing the modeling results with the 

experimental data. After the optimization, the simulated displacement and strain time histories

agreed reasonably well with the experimental data. 

E11 = 30 GPa
10

7. References

1. Lomov S. V.; et al. Full-field Strain Measurement for Validation of Meso-FE Analysis of 

Textile Composites. Composites: Part A 2008, 39, 1218–1231.

2. Lomov S. V.;et al. Full-field Strain Measurements in Textile Deformability Studies. 

Composites: Part A 2008, 39, 1232–1244.

3. Chocron, S.; et al. Measurement of Strain in Fabrics Under Ballistic Impact Using 

Embedded Nichrome Wires. Part I: Technique. International J. of Impact Engineering

2009, 36, 1296–1302. 

4. Cheeseman, B. A.; Bogetti, T. A. Ballistic Impact Into Fabric and Compliant Composite 

Laminates. Composite Structures 2003, 61, 161–173.

5. Duan, Y.; et al. A Numerical Investigation of the Influence of Friction on Energy 

Absorption by a High-strength Fabric Subjected to Ballistic Impact. International J. of 

Impact Engineering 2006, 32.

6 Duan, Y.; et al. Finite Element Modeling of Transverse Impact on a Ballistic Fabric. 

International Journal of Mechanical Sciences 2006, 48, 33–43.

7 Lim, C. T.; Ng, Y. H.; Shim, V.P.W. Finite Element Modeling of the Ballistic Impact Into 

Fabric Armor. International Journal of Impact Engineering 2003, 28, 13–31.

8. Talebi, H.; Wong, S. V.; Hamouda, A.M.S. Finite Element Evaluation of Projectile Nose 

Angle Effects in Ballistic Perforation of High Strength Fabric. Composite Structures 2009, 

87, 314–320.

9. Yen, C. F.; et al. Experimental Validation of a Kevlar Fabric Model for Ballistic Impact. 

Proceedings of the 24th International Symposium on Ballistics, New Orleans, LA, 2008, 

51–58.

10. Schmidt, T.; et al. Full-field Dynamic Displacement and Strain Measurement Using 

Advanced 3D Image Correlation Photogrammetry: Part I. Experimental Techniques

May/June, 2003, 47–50.

11. Orthwein, C. W. Clutches and Brakes: Design and Selection Edition: 2, Illustrated; CRC 

Press, ISBN 082474876X, 2004, p 9
11

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