Mechanics of Electronic Textiles”Literature Study”

M.J.M. FeronReport number MT08.19

Supervisors:Dr. P. BoutenDr. Ir. R.H.J. PeerlingsProf. Dr. Ir. M.G.D. Geers

Philips Research LaboratoriesPhotonic Materials and Devices

Eindhoven University of TechnologyDepartment of Mechanical EngineeringMechanics of Materials

May, 2008

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Abstract

Electronic textiles incorporate flexibility as a feature to functional applications such as elec-tronically addressed LED matrices. The robustness of such a device is essential to its successwhen introduced into the market. The textile substrate’s material behavior has to be readilyunderstood in order to improve robustness. Modeling of the substrate is crucial in order topredict material behavior. An extensive literature study categorizes modeling and experi-mental possibilities, which are subsequently presented and discussed.

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iv

Contents

Abstract iii

Contents v

1 Introduction 1

2 Vision on electronic textiles 22.1 Overall background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.2 Mechanical background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

3 Continuum macroscopic approach 63.1 Elastic behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63.2 Plane stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.3 Experimental identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

4 Continuum mesoscopic approach 104.1 Geometrical and mechanical coupling . . . . . . . . . . . . . . . . . . . . . . . 114.2 WiseTex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114.3 Alternative mesoscopic models . . . . . . . . . . . . . . . . . . . . . . . . . . 12

5 Microscopic approach 135.1 Micromechanics analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135.2 Multi-chain digital element analysis . . . . . . . . . . . . . . . . . . . . . . . . 13

6 Conclusions 15

References 16

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Chapter 1

Introduction

The applicability and marketability of electronic (e.g. photonic) textiles seems extremelypromising [1]. Not surprisingly, significant investments are made in research and start-upcompanies to anticipate a future demand of applications within this field of technology. Ap-plications embrace a multitude of sectors, e.g. healthcare and lifestyle. Before customers arewilling to spend their money on electronic textile products, quality, lifetime and flexibilitymust be drastically improved. In order to predict failure modes and optimize product design,a profound understanding of the mechanics behind this technology is of primary importance.The demands on the flexibility of the products imply application of large strains. The mate-rial behavior subject to these strains and consequent stresses has to be readily understood inorder to solve design and quality issues.

Textile mechanics research is a relatively old field of research, where the first publicationsgo back to the early twentieth century. Our main interest lies in the mechanics of the textilesand ultimately the mechanical effect of stiff islands on the compliant textile substrates. Sincethe mechanics of textiles have been of interest for many years, important work has alreadybeen performed on analytical solutions to simple textile structures, subject to mechanicalloading. During the past few years, due to the increased computing power available, multi-scale modeling has matured as a method with great possibilities. Through the use of unitcells or RVE’s (representative volume elements) a coupling can be made between mechanicsat different scales of spatial resolution.

In the following chapter some general thoughts on photonic or electronic textiles are pre-sented, in order to justify and introduce the mechanical aspects. The next three chaptersdescribe possible mechanical analyses on three different levels, macroscopic [2–5], mesoscopicand microscopic, where the former contains the least detail on material structure, assuminghomogeneity, and the latter takes the heterogeneous properties of the fibres into account.

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Chapter 2

Vision on electronic textiles

Electronic textiles have an important application within the field of the wearable electronicsand photonics. Numerous examples exist, e.g. information and communication, healthcareand medical applications, fashion/leisure and home applications, as well as military and in-dustrial applications [1]. As stated in the introduction, applicability and marketability seempromising. As can be concluded from Table 2.1, estimations are promising and investments

Table 2.1: Market estimation for smart fabrics and intelligent clothing (Venture Development Cor-poration, 2003)

Market$US x 1000

2003 2008 Annual increase rate (%)Consumer sector 122 205 251 691 15.5Professional/Industrial sector 150 884 388 086 20.8Government 30 751 80 223 21.1Total 303 840 720 000 18.8

should be made by companies interested in taking their market share. As always time-to-market will be of vital importance to success in gaining market share. Maturing this technol-ogy, i.e. improving lifetime and robustness, is essential for a successful market introduction.

2.1 Overall background

Several fields of expertise come together within the technology of electronic textiles. In orderto create ”wannahaves” the designers play an important role in the design stage, whereaselectrical engineers should work closely together with computer scientists and system archi-tects. However, without a profound understanding of the mechanics within these textiles, therobustness cannot be optimized.

Within Philips (LumaLive) [6], the first generation of electronic textiles has already beenlaunched, displaying the possibilities and impact of this technology. In this generation somedegree of flexibility has been introduced, which is still far from the flexibility desired in a

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fashion, leisure or commercial application, Fig. 2.1. However, progress within Philips Re-search shows promising results with LED-packages attached to fully flexible plain weave cloth,interlaced with conductive yarns. Robustness is an important issue, which has not yet beensolved. Fig. 2.1 clearly shows some fashion and leisure applications, however flexibility ofthese examples is still limited unfortunately.

Figure 2.1: Examples of current electronic textile prototypes and first generation products. Courtesyof (LumaLive) [6].

For ’smart textiles’ integrated functions are present within the textile environment, preferablyembedded within the textile itself, [7]. Depending on the complexity of the product, thesystem configuration may look like Fig. 2.2.

Wearable electronics or

photonics product

Interface Communication Energy supplyData

managementIntegrated

circuits

Figure 2.2: General system configuration for a wearable electronics or photonics product [1].

Accordingly, not only the ”interface”, e.g. LED matrix is interesting as a flexible component.However, the other components are not within the scope of this research.

2.2 Mechanical background

Many classes of textiles can be distinguished, but most important are:

• Woven textiles

• Non-woven textiles

• Knitted textiles

In the present study, only woven structures are considered.

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The mechanical properties of woven textiles have been studied extensively, and numericalapproximations as well as analytical solutions to stress states within textiles are readily avail-able. Effective models should include the anisotropy, which is inherently connected to thisclass of materials, differing significantly from the traditional two-dimensionally reinforcedlaminates. Reference [2] provides a comprehensive overview of the necessary anisotropic elas-tic theory to support the modeling phase.

The number of weave structures that can be produced is practically unlimited. Typically,two main classes of weave techniques can be distinguished, namely orthogonally and non-orthogonally woven structures. In current research within the Photonic Textiles group, or-thogonally woven structures have the main focus. The plain weave structure represents thesimplest orthogonal example, which is depicted in Fig. 2.3(a), while Fig. 2.3(b) shows anon-orthogonal fibre configuration, i.e. a braided structure [8–12]. The plain weave structureis produced by alternatively lifting and lowering one warp thread across one weft thread.

weft

warp

2

1

plain weave

RVE

(a) orthogonal plain weave structure

braided

RVE

(b) non-orthogonal braided structure

Figure 2.3: Two examples of woven structures, where the dashed areas represent an arbitrary Rep-resentative Volume Element (RVE) and the weft and warp direction are indicated.

When regarding textiles as a material with a specific material behavior, one can imagine thatthe material behavior is determined by

• Structure of weaving (e.g. plain weave, braided weave)

• Yarn properties

• Settings of the weaving process (e.g. tension in weft and warp direction)

• Textile treatment (e.g. resin addition)

• Environment

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• Material history (e.g. pre-loads)

Several possible approaches exist in textile composite mechanics. These approaches differ inaccuracy, but most importantly, also in complexity.

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Chapter 3

Continuum macroscopic approach

The continuum macroscopic approach regards the textile composite, schematically representedin Fig. 3.1, at a continuum level [13–15]. In other words, the fact that this specific type of solidis made of fibres and that it has a heterogeneous microstructure is ignored and it is insteadregarded as a uniform material, which has the homogenized fabric properties. For smallstresses or strains, problems can already be described with the simplest form of continuumbehavior, namely linear elastic behavior.

Figure 3.1: Schematic representation of a textile structure interpreted as a continuum

3.1 Elastic behavior

The simplest behavior to be assumed is fully elastic behavior, which can be completely de-scribed by 21 independent parameters for a generally anisotropic material.

If textile is taken to be a woven structure, a given strain in one direction will result in acertain stress in at least that direction. However, this effect or constitutive response is notnecessarily similar in all directions, i.e. anisotropy. A composite material shows anisotropicbehavior, where anisotropy refers to the directional dependency of the material properties,as opposed to isotropic material properties. Due to the anisotropic behavior, the Young’smodulus is not the same in all directions, i.e. Ex 6= Ey. From a textile point of view this is

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readily understood.

Simplifications can be made systematically in order to account for material symmetries, reduc-ing the number of independent material parameters significantly. A special case of anisotropicbehavior is orthotropic behavior. An orthotropic material has two mutually orthogonal sym-metry planes so that the mechanical properties are, in general, different along the directionsof each of these axes.

The fully elastic constitutive relation, with twelve elastic engineering constants or mater-ial parameters, is given by

εx

εy

εz

γyz

γxz

γxy

=

1Ex

−νyx

Ey−νzx

Ez0 0 0

−νxy

Ex

1Ey

−νzy

Ez0 0 0

−νxzEx

−νyz

Ey

1Ez

0 0 00 0 0 1

Gyz0 0

0 0 0 0 1Gxz

00 0 0 0 0 1

Gxy

σx

σy

σz

σyz

σxz

σxy

(3.1)

Because the following relation holds for orthotropic materials, only nine of the constants areindependent

νyx

Ey=

νxy

Ex,

νzx

Ez=

νxz

Ex,

νzy

Ez=

νyz

Ey(3.2)

Where Ei is the Young’s modulus along axis i, and νjk is Poisson’s ratio in plane jk, wherei, j, and k can be x, y, and z. In this case the properties can be described by the nine elasticengineering constants (Ex, Ey, Ez, νxy, νyz, νxz, Gxy, Gyz, Gxz) , with E Young’s modulus, νPoisson’s ratio, and G shear modulus. However, for some commonly woven structures moresimplifications can be made.

Symmetric lay-ups of orthogonal balanced woven fabric composites are depicted in Fig. 2.3(a).The assumption is made that the directional dependency of the material behavior (e.g. onmanufacturing process) is chosen in such a way, that the behavior is simplified. The equiva-lence between the ’x’ and ’y’ direction leads to three identity relations, Ex = Ey , νxz = νyz,Gxz = Gyz. The three-dimensional constitutive model takes the form

εx

εy

εz

γyz

γxz

γxy

=

1Ex

−νxy

Ex−νxz

Ex0 0 0

−νxy

Ex

1Ex

−νxzEx

0 0 0−νxz

Ex−νxz

Ex

1Ez

0 0 00 0 0 1

Gxz0 0

0 0 0 0 1Gxz

00 0 0 0 0 1

Gxy

σx

σy

σz

σyz

σxz

σxy

(3.3)

3.2 Plane stress

If one of the problem dimensions is significantly smaller than the other two, the stress in thisdirection can be neglected, resulting in a planar stress state. This stress state is known as

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plane stress, because of the fact that the normal stress σz as well as the two shear stresses σxz

and σyz vanish. This assumption is only valid in the macroscopic approach as large piecesof cloth are examined. The out of plane stresses are negligible because the stresses are notable to develop within the small material thickness and are therefore small compared to thein-plane stresses.

The column representation of the stress state as shown in (3.1) takes the form

σ =[

σx σy 0 0 0 σxy

]T (3.4)

Accordingly, the strain state is of the form

ε =[

εx εy εz 0 0 γxy

]T (3.5)

Now, only four of the initial nine engineering constants are needed to describe the elasticproperties. This is concluded from substituting the plane stress condition in (3.1) and as-suming orthotropic behavior. The strain component in the out-of-plane direction, εz, can beexcluded from the system of equations and solved separately. For in-plane elastic orthotropicmaterial behavior the following holds.

εx

εy

γxy

=

1Ex

−νxy

Ex0

−νxy

Ex

1Ey

00 0 1

Gxy

σx

σy

σxy

(3.6)

3.3 Experimental identification

Experimental determination of the material properties of the textile is essential in the case ofthe macroscopic approach, simply because the model should respond in the same way as the’real’ material. This can be achieved without modeling the substructures, responsible for themechanical behavior. Four parameters are determined: two Young’s moduli, one Poisson’sratio, and a shear modulus.

The determination of the Young’s modulus is readily understood and common practice withsupport of tensile testing equipment. Adding imaging techniques yields a possibility to mea-sure the Poisson’s ratio. An elaboration is presented in a note on the experimental setup [16].

Textile fabrics can shear up to 50◦. Three main methods for measuring shear propertiesof fabrics can be distinguished. All are depicted in Fig. 3.2. In the biaxial shear test, thefabric sample is held between a fixed clamp and a movable clamp. Shear force and shear angleare measured, while maintaining a constant normal force. More background can be found in[3, 15, 17]. The Bias extension test is addressed in the work of Potluri and Zhu [11, 18]. Thepicture frame test has been performed by different groups [10, 15].

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Figure 3.2: Three shear deformation test methods are depicted. From left to right: Biaxial sheartest, Bias extension test, Picture frame test(hinges at the corners), where the gray areas representrigid bodies

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Chapter 4

Continuum mesoscopic approach

Mesoscopic analyses consider repetitive units of homogenized fibre bundles. This type ofanalysis identifies and analyzes ’repetitive unit cells’ or ’representative volume elements’ on amesoscopic level, i.e. at the level of a few interacting fibres. The first models were developedrelating geometrical and mechanical equilibrium between the yarns [19–22]. A schematicrepresentation is depicted in Fig. 4.1.

A-A B-B

A A

B

B

Figure 4.1: Peirce model; Schematic orthogonal unit cell showing interlacing geometry for plainweaving structure [1, 19]

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4.1 Geometrical and mechanical coupling

The Peirce geometrical model, for circular cross-sectional yarns, assumes a uniform structureand isotropic yarn properties. An orthogonal interlace cell consisting of straight and circularportions has been selected to undergo both geometrical and mechanical analyses, where themodel and the corresponding parameters of the unit cell are shown in Fig. 4.1.

The analytical background can be found in [19]. The model is designed to obtain a force equi-librium within the woven structure and accordingly derives geometric parameters. Newton-Raphson is used as a numerical solution algorithm. Eventually, bending forces and crimp canbe calculated.

Crimp, or waviness of a yarn in a fabric, is caused during weaving and may be modifiedin finishing. It is due to the yarns being forced to bend around each other during the weavingprocess. Crimp is measured by the relation between the length of the fabric sample and thecorresponding length of the yarn, when it has been straightened after being removed fromthe textile structure [8].

4.2 WiseTex

One tool from the group of Lomov et al. [23], called WiseTex, deserves extra attention. Thistool is a model of the internal geometry of textiles and takes full advantage of the hierarchicalprinciple of textile modeling. The simulation algorithm uses extensively the minimum energyprinciple, calculating the equilibrium of yarn interactions. The models cover wide range oftextile structures, either relaxed or after compression (out-of-plane), shear or tensile deforma-tion. As input the tool takes yarn properties, e.g. geometry of the cross-section, compression,

Figure 4.2: A graphical representation of interlaced yarns with different properties, WiseTex

bending, frictional and tensile behavior. It is even possible to account for fibrous content,therefore WiseTex can even be considered as a micromechanics tool (5). A graphical editoris provided to virtually create the topology of the yarn interlacing pattern within the fab-ric repeat. A graphical representation of the yarn interlacing geometry is presented by Fig. 4.2

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Unit cell dimensions, areal density, average porosity/fibrous content and yarn lengths inthe unit cell are direct outcome of the energetic analysis. For any point within the unit cell,the fibrous content, the average orientation and an identification of the fibre material in thevicinity of the point are obtained. Furthermore, yarn path, position and size of the yarncross-sections are obtained as well as fibre density and orientation distribution over the yarncross-section.

However, this model has not yet been validated for multilayered structures. Applicabilityto multilayered textile might therefore still be limited in the near future.

4.3 Alternative mesoscopic models

Instead of an analytical approach, more complex models map the geometric description of thetextile meso-structure into a 3D grid of finite elements. These models are discussed in Refs.[24–32].

Another approach to approximate homogenization of elastic properties on meso-level exploitsaveraging of properties of differently oriented yarns in the reinforcement, based on expres-sions for transformation of the stiffness tensor with the reference coordinate system [2]. Thisapproach allows calculations for complex 3D braided, woven and knitted composites, [33–42].The inclusion-based model [43–45] can be considered as a generalization of this approach.

Table 4.1 below groups the different meso-level analysis methods into several categories andrepresents a literature overview on meso-level analysis. It should be noted that some of theliterature references focus on textile composites, where a resin and a textile are combined.However, in essence this does not change the methods applied and hence they are incorporatedin this overview.

Table 4.1: Meso-level literature overview

Investigations on proper boundary conditions [10, 46–49]Meso-FE modeling of textile composites in theelastic deformation regime and with damage

[10, 46–48, 50–76]

Multi-scale modeling [1, 10, 23, 27, 28, 77–83]Geometrical modeling and meshing of the unitcell structure of textile fabrics

[11, 84, 85]

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Chapter 5

Microscopic approach

The microscopic approach takes into account the heterogeneities at the fibre level in order topredict material behavior. This approach is also referred to as the micromechanics approach[5].

A major advantage this technique has, is the great level of detail and the ability to analyzestructures at a small scale. However, this advantage already implies that it is numericallycostly. The decision on whether to use this method should strongly depend on the purposeof the analysis.

5.1 Micromechanics analysis

Techniques of this kind typically start from a geometric model of a relaxed fibre geometry,which may be based on energy considerations. Bundle properties are predicted using classicalmicromechanics equations such as a composite cylinder assemblage model [86], with the fibrecontent and the constituent properties as the input parameters. These bundle properties aretransformed to the properties in a laminate coordinate system by the appropriate rotationmatrices, according to the undulation of the bundles. Finally, the fabric composite propertiesare found by averaging the properties of the separate bundle, for instance by assuming auniform state of strain in all regions. Various software applications are currently available onthe internet, such as [17, 87, 88].

5.2 Multi-chain digital element analysis

Another microscopic approach, founded by Wang and Sun [89], is described by Zhou [9]. Thismulti-chain digital element method models each separate yarn in a bundle as a frictionlesspin-connected truss element chain. These truss elements are modeled as ”digital elements”and contact is modeled by contact elements. Zhou tackles the original weakness of the un-changed cross-section by carefully conforming to fibre, yarn and fabric physics.

In multi-chain digital element analysis, each fibre, rather than each yarn in the mesoscopic ap-proach, is modeled as a flexible one-dimensional physical entity with a circular cross-section.Each yarn is modeled as an assembly of fibres, simulating both yarn movement and cross-section deformation during fabric deformation. Figs. 5.1 and 5.2 depict illustrations of this

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Figure 5.1: Yarn under single side compression, results of the multi-chain digital element method by(Zhou, 2004, [9])

microscopic approach.

Figure 5.2: woven fabric generated by the multi-chain digital element model by (Zhou, 2004, [9])

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Chapter 6

Conclusions

Plain textiles have been subject to an extensive period of research, leading to a solid mechani-cal background. Analytical studies coupling geometrical properties with mechanical behaviorcover the most important woven textile structures, where mechanical models present solutionsto more complicated problems or whenever simplification is desired.

A literature overview is presented and acts as a guideline for mechanical analysis of tex-tile woven structures. Characteristics are discussed and a potential direction is presented onhow to continue mechanical research of photonic textiles within Philips Research.

Analyses can be split into three main categories: Macroscopic, mesoscopic and microscopicanalyses. Each of these analysis levels has specific advantages and disadvantages, whereadvantages generally refer to applicational difficulty, level of detail, accuracy, whereas thedisadvantages predominantly refer to computational cost or difficulty concerning materialcharacterization.

The research intention lies within the field of textile characterization and modeling in or-der to predict and improve material behavior. A continuum macroscopic approach is to beused as the observation scope of a first generation solution.

Ultimately, the research goal is to describe the effect of stiff islands mounted, either chemi-cally or mechanically, on the textile substrate. A first generation model will act as a tool topredict product robustness and quality [90].

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