Master's Project

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University of Miami Master’s Project (MAE 751) – Micromechanical Analysis of Hybrid Composites Dr. Karkainnen Omar Kashkash 12/14/2015

Transcript of Master's Project

Page 1: Master's Project

University of Miami

Master’s Project (MAE 751) – Micromechanical

Analysis of Hybrid Composites

Dr. Karkainnen

Omar Kashkash

12/14/2015

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Abstract

A micromechanical analysis has been done for a hybrid composite model with

carbon and dyneema SK-60 fibers for military applications. The finite element

analysis was done using ABAQUS software to obtain stiffness and strength

properties. Different fiber combinations were studied for comparison.

Introduction

Hybrid composites have increased in popularity due to their unique features

that can be used to meet various design requirements in a more economical way

than conventional composites. For example, expensive fibers such as graphite and

boron can partially be replaced by less expensive fibers such as glass and Kevlar.

Hybrid composites can contain several different fiber types in a single matrix,

however, it has been found that a combination of only two types of fibers would

be most beneficial. Some of the specific advantages of hybrid composites over

conventional composites include balanced strength and stiffness, balanced

bending and membrane mechanical properties, balanced thermal distortion

stability, reduced weight and/or cost, improved fatigue resistance, reduced notch

sensitivity, improved fracture toughness and/or crack arresting properties, and

improved impact resistance.

A computational model is created using ABAQUS software that can easily be

modified to model hybrid composites of different volume fractions of

constituents. This saves the designer valuable time and resource as opposed to

experimental techniques that require fabrication of various composites with

various fibers, their volume fractions and matrix properties in hybrid composites

which are time consuming and cost prohibitive.

In this paper, a computational model is presented in which finite element based

micromechanics is used to obtain results of strength and stiffness properties.

Direct Micromechanics Method (DMM) is used for predicting strength, which is

based on first element failure method; although conservative, it provides a good

estimate for failure initiation [1 & 2].

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Carbon Dyneema Hybrid Composites

Dyneema fibers are made from ultrahigh molecular weight polyethylene

(UHMWPE). In the process called gel spinning the very long molecules are

dissolved in a volatile solvent and spun through a spinnerette. In the solution the

molecules get disentangled and remain so after cooling in gel-like filaments (See

Figure 1). As the fiber is drawn, a very high level of macromolecular orientation is

attained and a high fiber with a very high tenacity and modulus is obtained (See

Figure 2). This fiber is now available as Dyneema SK60. It is characterised by a

parallel orientation greater than 95% and a high level of crystallinity (up to 85%).

This gives Dyneema SK60 its specific properties. A comparison with other fibers is

given below (See Table 1). On a weight-for-weight basis Dyneema is the strongest

fiber on the market. Its tensile strength is 2.7 GPa, which combined with a density

less than 1, gives a tenacity, or specific strength, of 30 g/den. Modulus is also very

high: 87 GPa and on a specific basis 1.000 g/den. Even higher values may be

expected in the future as research continues. A comparison of Dyneema with

other high performance fibrers is given below (See Figures 3 & 4). Figure 3 gives

specific strength versus specific modulus while Figure 4 is the stress/strain

diagram. Dyneema SK60 is advantageous in composites where weight saving is

important. Dyneema composites can be strong and stiff in tension and that light

weight composites can be made using this fiber. However, compression and shear

modulus will often be limiting when using only Dyneema fibers in a composite. So,

in general, hybrids will be used in which the strong points of the Dyneema fiber in

the construction will lower the weight and give high stiffness and high tensile

strength with a good dimensional stability. Composites made from carbon fibers

are extremely strong, stiff and lightweight structural materials. Therefore, such

composites are very suitable for application as aircraft skin material. However,

sheets from carbon composite skins are somewhat sensitive to the out of plane

loads caused by impact. Hybridizing with gel-spun polyethylene fibers is a well-

known way to improve the resistance against impact [3, 4, and 5]

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Figure.1 Dyneema Gel Spinning Process

Figure.2 Macromolecular orientation of Dyneema SK60

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The low compressive strength of Dyneema SK60 makes it unsuitable for structural

aerospace composites as a sole fiber ingredient. Compression resistant fibers like

glass or carbon are needed for such applications. However, Dyneema® fibers are

excellent for armor applications [6]. This is due to the combination of high tensile

strength, low density and intrinsic fiber toughness. This fiber toughness is

illustrated below (See Figures 5 & 6). Figure 5 shows a knotted filament. The

curvatures in the knot and the transverse deformation are impossible for other

high strength fiber types like glass, carbon or aramid fibers. Figure 6 shows

filaments that are tensioned over the edge of a sharp razor blade. Again, a sharp

curvature and extensive transverse deformation occur, allowing pressure re-

distribution over a larger distance along the blade edge. Thus the excellent cutting

resistance is explained. Both pictures illustrate the damage tolerance of

Dyneema® on micro-scale. Hybridization with a carbon fiber composite may add

damage tolerance to the composite on macro scale.

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Results from [7] show that hybridizing the carbon composite with Dyneema®

fibers improves the resistance to impact considerably. The impact resistance

increases with increasing amount of Dyneema® fibers. Figure 7 shows a Scanning

Electron Microscope (SEM) picture indicating deformed, but unbroken Dyneema®

fibers together with broken carbon fibers, thus illustrating the contribution of the

damage tolerant Dyneema® fibers to the impact resistance of the hybrid

composite

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Methodology

After a plain weave hybrid composite model has been created (See Figures 8 and

9), the following steps were done to run 6 unit strain cases in ABAQUS software

[8]:

Figure 8. Location and definition in RVE

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Figure 9. Warp and Weft yarns

- In property module, define material properties of fiber, matrix, and

interface (See Table 2). Also, define local material coordinates to easily

interpret longitudinal stresses for both Carbon (Warp) and Dyneema (Weft)

fibers by setting the primary axis 1 along the direction of fibers (See Figure

10).

Table.2 Mechanical Properties of UD laminates (approx. 55% fiber in epoxy

laminates)

Engineering constants Carbon IM7 fiber Dyneema SK60 fiber

E1 (GPa) 136 46.6 E2 (GPa) 11.5 3.6

E3 (GPa) 11.5 3.6

V12 0.31 0.32 V13 0.31 0.32

V23 0.35 0.35 G12 (GPa) 5.19 1.1

G13 (GPa) 5.19 1.1

G23 (GPa) 4.26 1.374045802

Density of fibers 0.002 0.002

Matrix data

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Young’s modulus (GPa) 3.5

Poisson’s ratio 0.35

Density 0.00125

Interface data

Density 0.00125

Young’s modulus (GPa) 3.5

Poisons ratio 0.35

Figure.10 Local Material Coordinates of fibers

- In mesh module, 3-D continuum elements can be hexahedral (bricks),

wedges, or tetrahedral. Whenever possible, hexahedral elements or

second- order tetrahedral elements should be used in ABAQUS (See Figures

11, 12, and 13). First-order tetrahedral (C3D4) have a simple, constant-

strain formulation, and very fine meshes are required for an accurate

solution.

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Figure.11 Meshed yarns

Figure.12 Meshed Interface

Figure.13 Meshed Representative Volume Element (RVE)

- In load module, boundary conditions are defined for each unit strain case

with unit normal strain cases having four boundary conditions and unit

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shear strain cases having three boundary conditions (See Figures 14 & 15,

Table 3, and Appendices).

Figure.14 Definition of each side in RVE

Figure.15 Degrees of freedom

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Table.3 Boundary conditions for both unit normal strain and unit shear

strain cases

Unit normal strain cases

front back right left top bottom

Case1 U*1=6 U1=0 U3=0 U3=0 U2=0 U2=0 Case2 U1=0 U1=0 U3=0 U3=0 U2=1.38 U2=0

Case3 U1=0 U1=0 U3=0 U3=6 U2=0 U2=0 Unit shear strain cases

Case1 U1=0 ; U2=1.38

U1=0 ; U2=0

U3=0 U3=0

Case2 U1=0 U1=0 U3=0 ; U2=0

U3=0 ; U2=1.38

Case3 U1=0 ; U3=6

U1=0 ; U3=0

U2=0 U2=0

*Boundary conditions are in units of mm and only displacement degrees of

freedom were used in the simulation

- In job module, a job is made for each unit strain case.

- In visualization module, a representative volume element (RVE) analysis is

done to obtain forces at every node on a surface. The summation of these

forces divided by the area of the surface outputs stress on that surface. This

analysis is put into an EXCEL file to invert stiffness [C] matrix into

compliance [S] matrix from which elastic constants(stiffness properties) can

be found [9, 10, 11, 12, & 13].

Results

A comparison of stress strain graphs highlighting the first fiber to fail

longitudinally in each unit strain case while highlighting matrix failure if it occurs

before it. For both RVE’s, all the elements experience failure due to the full unit

strain case applied except for a very few that will be noted below. The five modes

of failure are fiber (longitudinal, transverse, and shear) and matrix (normal and

shear). Highlighting the first longitudinal failure for the fiber in either warp (x dir.)

or weft (z dir.) doesn’t represent composite failure because the other fiber have

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not failed longitudinally yet. This method is called the first element failure

method which is conservative and important as a first step. Note in the graphs

that a single asterisk is for matrix failure and a double asterisk is for first

longitudinal fiber failure.

0.00749255, 107.8706198CF, x dir. Longitudinal

Failure **

0.001659329, 23.88945026

Epoxy Normal Failure*

0.006382979, 91.89606593Epoxy Shear

Failure*

-500

0

500

1000

1500

2000

2500

3000

3500

4000

4500

-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3

Stre

ss (

σfc

ell a

nd

τfc

ell (

Mp

a))

Failure Strain in the Material (ϵf and γf)

Hybrid Unit Strain Case 1:ϵx=1

0.007398066, 118.5163775

CF, x dir. Longitudinal Failure**

0.00163606, 26.20953984

Epoxy Normal Failure*

0.006435986, 103.1039359

Epoxy Shear Failure*

-1000

-500

0

500

1000

1500

2000

2500

3000

3500

4000

4500

-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3Stre

ss (

σfc

ell a

nd

τfc

ell (

Mp

a))

Failure Strain in the Material (ϵf and γf)

Unit Strain Case 1:ϵx=1

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0.281060364, 1326.310722

CF, x dir. Longitudinal

0.003257979, 15.37424933

Epoxy Normal Failure*

0.022169249, 104.6156504Epoxy Shear

-400

-200

0

200

400

600

800

1000

1200

1400

1600

1800

-0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4Stre

ss (

σfc

ell a

nd

τfc

ell (

Mp

a))

Failure Strain in the Material (ϵf and γf)

HybridUnit Strain Case 2:ϵy=1

0.000325745, 1.887087512CF, x dir. Longitudinal failure with

CF, x&z dir. Shear failure occuring before it

-500

0

500

1000

1500

2000

2500

-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35Stre

ss (

σfc

ell a

nd

τfc

ell (

Mp

a))

Failure Strain in the Material (ϵf and γf)

Unit Strain Case 2:ϵy=1

0.016589003, 146.1145424

DF, z dir. Longitudinal Failure**

0.00251411, 22.14406781

Epoxy Normal Failure*

0.010334482, 91.02524542

Epoxy Shear Failure*

-500

0

500

1000

1500

2000

-0.05 0 0.05 0.1 0.15 0.2 0.25

Stre

ss (

σfc

ell a

nd

τfc

ell (

Mp

a))

Failure Strain in the Material (ϵf and γf)

Hybrid Unit Strain Case 3:ϵz=1

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0.007398066, 118.5163775

CF, x dir. Longitudinal Failure**

0.00163606, 26.20953984

Epoxy Normal Failure*

0.006435986, 103.1039359

Epoxy Shear Failure*

-1000

-500

0

500

1000

1500

2000

2500

3000

3500

4000

4500

-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3

Stre

ss (

σfc

ell a

nd

τfc

ell (

Mp

a))

Failure Strain in the Material (ϵf and γf)

Unit Strain Case 3:ϵz=1

0.215422277, 14.62795312

CF, x dir. Longitudinal Failure**

0.044343891, 3.011110897

Epoxy Normal Failure*0.209176788, 14.20386182

Epoxy Shear Failure*

0

2

4

6

8

10

12

14

16

0 0.05 0.1 0.15 0.2 0.25

Stre

ss (

σfc

ell a

nd

τfc

ell (

Mp

a))

Failure Strain in the Material (ϵf and γf)

Hybrid Unit Strain Case 4:γxy=1

0.209498869, 1153.121065

CF, x dir. Longitudinal Failure**

and CF, z dir. Longitudinal doesn't

fail

0.043324492, 238.4661268

Epoxy Normal Failure*

0.203323131, 1119.128643

Epoxy Shear Failure*

-200

0

200

400

600

800

1000

1200

1400

-0.05 0 0.05 0.1 0.15 0.2 0.25

Stre

ss (

σfc

ell a

nd

τfc

ell (

Mp

a))

Failure Strain in the Material (ϵf and γf)

Unit Strain Case 4:γxy=1

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0.579489962, 31.95328161

DF, z dir. Longitudinal Failure**

0.050107373, 2.762938279

Epoxy Normal Failure*

0.289629399, 15.97026757

Epoxy Shear Failure*

-5

0

5

10

15

20

25

30

35

-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Stre

ss (

σfc

ell a

nd

τfc

ell (

Mp

a))

Failure Strain in the Material (ϵf and γf)

Hybrid Unit Strain Case 5:γyz=1

0.209498869, 1153.121065CF, x dir. Longitudinal

Failure**and CF, z dir. Longitudinal

doesn't fail

0.043324492, 238.4661268

Epoxy Normal Failure*

0.203323131, 1119.128643

Epoxy Shear Failure*

-200

0

200

400

600

800

1000

1200

1400

-0.05 0 0.05 0.1 0.15 0.2 0.25

Stre

ss (

σfc

ell a

nd

τfc

ell (

Mp

a))

Failure Strain in the Material (ϵf and γf)

Unit Strain Case 5:γyz=1

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Table.4 Allowable Composite and Matrix Strength Properties

Fibers -> Dyneema SK60 Carbon IM7

Longitudinal Stress 1068 1760

Transverse Stress 7.2 81.3 Shear Stress 15.9 0.48

Matrix -> Epoxy Longitudinal Stress 49

Shear Stress 93 *units are in MPa

This table is used for comparing the stress values obtained from Abaqus as

a result of each of the unit strain cases with those from the literature and

0.031333452, 41.67619244

CF, x dir. Longitudinal Failure

0.006344685, 8.438977635

Epoxy Normal Failure*

0.023111332, 30.74006399

Epoxy Shear Failure*

-100

0

100

200

300

400

500

600

-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

Stre

ss (

σfc

ell a

nd

τfc

ell (

Mp

a))

Failure Strain in the Material (ϵf and γf)

Hybrid Unit Strain Case 6:γzx=1

0.027056111, 1.965828857

CF, x dir. Longitudinal Failure**

0.005675237 , 0.412348458

Epoxy Normal Failure*

0.017247774, 1.253179853

Epoxy Shear Failure*

-5

0

5

10

15

20

25

30

-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Stre

ss (

σfc

ell a

nd

τfc

ell (

Mp

a))

Failure Strain in the Material (ϵf and γf)

Unit Strain Case 6:γzx=1

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plotting the stress strain graphs.

The uniaxial failure points for the warp(x dir.) and weft (z dir.) are defined

as the longitudinal far field stress that causes fiber failure in the warp from

unit strain case 1 and weft from unit strain case 3 for both RVE’s [14 & 15].

Table.5 Stiffness properties for both RVE’s

Engineering Constants C,C C,Dyneema

Ex (GPa) 16.01991262 14.39705033

Ey (GPa) 5.793144219 4.718953262

Ez (GPa) 16.02313277 8.807915952

Vxy 0.455247679 0.455636536

Vyx 0.455247709 0.149344901

0, 146.1145424Hybrid

-107.8706198, 0Hybrid

0, 118.5163775Non-hybrid

118.5163775, 0Non-hybrid

-200

-150

-100

-50

0

50

100

150

200

-150 -100 -50 0 50 100 150

War

p M

Pa

Weft MPa

Uniaxial Failure Points

Hybrid

Non-hybrid

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Vyz 0.164650914 0.235034449

Vzy 0.164650774 0.438690752

Vzx 0.109435236 0.100312805

Vxz 0.109413166 0.163966889

Gxy (GPa) 5.504187539 0.067903623

Gyz (GPa) 0.072619677 0.055140354

Gxz (GPa) 0.072657481 1.33008621

Discussion

From table.5 and the stress strain graphs the first unit strain

comparison between RVE’s has values of Ex= 16 and 14.4 GPa’s, for the

non-hybrid and hybrid, respectively. The hybrid experiences first

longitudinal fiber failure perhaps because the dyneema allows the

carbon fibers to strain faster and thus fail faster due to the RVE plain

weave geometry.

Conclusion

In general, the amount of Dyneema® fibers will not be higher than 50%, usually

even lower. Very high amounts of Dyneema® fibers are reserved for composites

with armor functionality only. Such composites utilize the tensile strength and

damage resistance of Dyneema® fibers to a full extent, but exhibit hardly the

balance of properties of structural materials. Combination with carbon fibers

provides more balanced structural properties.

Composites allow trading of property directions by choosing relative amounts of

fibers in different orientations. The amounts of choices are increased, considering

that replacing carbon fibers by Dyneema® fibers allow trading of compression

strength and ILSS against impact resistance. Hybrid composites with carbon fibers

and Dyneema® fibers show considerably improved impact resistance over

composites with carbon fibers only .

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Moreover, application of carbon Dyneema® hybrid composites can be considered

as an improvement option over pure carbon composites if the situations below

apply:

1. The structure is critical on impact resistance

2. The structure is mainly designed for tension load, and/or

3. The structure is a thin skin Consequently, it is concluded that Carbon Dyneema® hybrid composites may be

attractive for structures where impact resistance is the limiting load case and

flexural resistance is important as well [16, 17, & 18].

References

[1] Tsai SW, Hahn HT. Introduction to composite materials. Lancaster (PA):

Technomic Publishing Co; 1980

[2] S. Banerjee and B. V. Sankar. “Mechanical Properties of Hybrid Composites

using Finite Element Method Based Micromechanics.” Science Direct, Composites

part B: Engineering Vol.58 March 2014

[3] Peijs T. High-performance polyethylene fibres in structural composites?.

Promises, reality and applications in hybrid composites. PH.D Thesis, Eindhoven

University of Technology, The Netherlands, Dec. 1993.

[4] Feraboli P., Kedward K. T., Enhanced Evaluation of the Low-Velocity Impact

Response of Composite Plates. AIAA Journal , Vol. 42, No. 10, pp. 2143- 2152,

2004

[5] Marissen R., Smit L. and Snijder C., Dyneema® Fibers in Composites, the

Addition of Special Mechanical Functionalities. Proceedings, Advancing with

composites 2005, Naples, Italy, October 11-14, 2005

[6] Jacobs M.J.N., van Dingenen J.L.J., Ballistic protection mechanisms in personal

armour, Journal of Materials Science 36, pp. 3137-3142, 2001

[7] J. G. H. Bouwmeester, R. Marissen and O. K. Bergsma, “Carbon/Dyneema®

Intralaminar Hybrids: New Strategy to Increase Impact Resistance or Decrease

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Mass of Carbon Fiber Composites,” ICAS2008 Conference Anchorage, Alaska,

September 2008

[8] Gurit, David Cripps. "Woven Fabrics." NetComposites Now. David Cripps, Gurit,

2015. Web. 20 Oct. 2015

[9] Sankar BV, Lee BW, Karkkainen RL. Evaluation of failure criteria for plain weave

textile composites using finite element micromechanics. In: Proceedings of the

35th international SAMPE technical conference, Dayton, OH; September 2003

[10] Marrey RV, Sankar BV. Micromechanical models for textile structural

composites. NASA CR-198229; 1995.

[11] Lomov SE et al. Textile composites: modelling strategies. Composites: Part A

2001;32:1379–94.

[12] Karkkainen, Ryan L., and Bhavani V. Sankar. "A Direct Micromechanics

Method for Analysis of Failure Initiation of Plain Weave Textile Composites."

Www.elsevier.com/locate/compscitech A Direct Micromechanics Method for

Analysis of Failure Initiation of Plain Weave Textile Composites (n.d.): n. pag. Web.

25 Sept. 2015.

[13] Whitcomb JD. Three-dimensional stress analysis of plain weave composites.

Composite materials fatigue and fracture (third volume), ASTM STP 1110; 1991. p.

417–38

[14] Zhu, H., Sankar, B. V., Marrey, R. V., “Evaluation of Failure Criteria for Fiber

Composites using Finite Element Micromechanics”, Journal of Composite

Materials, Vol 32, No. 8/1998

[15] Choi, Sukjoo, Sankar, B. V., “Micromechanical Analysis of Composite

Laminates at Cryogenic Temperatures”, Journal of Composite Materials, Vol. 00,

No. 00/2005

[16] Chamis, C. C., Lark, R. F.,”Hybrid composites – State-of-the-art review:

Analysis, Design, Application and Fabrication”, NASA Technical Memorandum,

NASA, TM X-73545

[17] Hearle, J. W. S High-peformance Fibres, Boca Raton: CRC, 2001. PDF.

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[18] Gibson, Ronald. F., “Principles of Composite Material Mechanics”, Third

Edition, CRC Press

Appendices

Unit Normal Strain cases

Case 1:𝜀𝑥 = 1

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Case 2: 𝜀𝑦 = 1

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Case 3: 𝜀𝑧 = 1

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Unit Shear strain cases

Case 1: 𝜀𝑥𝑦 = 1

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Case 2: 𝜀𝑦𝑧 = 1

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Case 3: 𝜀𝑥𝑧 = 1

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Representative Volume Element (RVE)

Warp and Weft Yarns

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Matrix

Matrix with Interface

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Interface

Assemblage of yarns, interface, and matrix

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Meshed yarns

Meshed Interface

Meshed RVE

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Local Material Coordinates in Yarns

Skin material version of RVE