Numerical modeling and buckling analysis of inflatable structures

93 3.7 Critical loads for a simply supported inflatable beam under a compressive concentrated load in the case of materials 1 and 2.. 95 3.8 Fundamental buckling modes on a simply suppor

University Claude Bernard Lyon 1 Ecole Doctorale MEGA, INSA de Lyon´Thesis reference number : 123 − 2012

Numerical modeling and buckling

analysis of inflatable structures

PhD THESIS

Presented and defended publicly on August, 31th

2012 at 10:30 in the Lecture hall 2− Building A,IUT Lyon 1 − Site Gratte-Ciel

A Dissertation submitted in partial fulfilment of the requirements for the degree of

Doctor of University Claude Bernard – Lyon 1

(Department of Mechanical Engineering)

During my time in Lyon, there are a number of people who have supported me both insideand outside the lab From my early days at IUT Lyon 1, I had many difficulties to adapt

a new life in French, which is different deeply from Vietnam At that time, I received

a tremendous amount of help and support from the personnels of IUT Lyon 1 - GratteCiel, specially Professor Christian Jardin, Mrs Bettina Fenet and Mr Benoit Thomas

I would like to thank them for all their kindness during my time here

Although being a Ph.D student at UCBL has not always been easy and ward to me, there has been so much help and support around

straightfor-First, I would like to thank my supervisors, Sylvie Ronel and Michel Massenzio forproviding me the opportunity to work with them It is a superb experience to have them

as supervisors and learn how to face, think, approach and evaluate problems directlyfrom them Sylvie Ronel with her keen insight into science of structures has alwaysamazed me She has a wonderful ability to see and find beautiful things from what lookssomewhat boring and unimportant I would like to thank her for her consistent supportand encouragement in the middle of failures and sometimes slow progresses Also, MichelMassenzio, who just makes everything in our group much simpler, is also thanked forcareful reading and helpful advices throughout this thesis

In particular, I would like to thank Professor Eric Jacquelin for giving me lots ofvaluable suggestions in research He has always inspired me to see how to research ineach paper with challenging questions that I had never thought of Those questionsalways have guided and helped me gain a solid understanding of my research projectswith new insights

Special thanks are due to Professor Le Van Anh and Professor Frédéric Lebon for theirinput, for reviewing this thesis, and for being members of the graduate committee

I would also like to thank Professor Phan Dinh Huan for being an examiner of thisthesis and a member of the graduate committee I owe him many thanks for teaching me

acknowledged in the same way for their advices and encouragement.

Komla Lolonyo Apedo has been much more than a colleague and a friend to me overthe first two years Komla and I were on the same research theme at LBMC and workedbeside together in a same office My work is a development based on his work Komla’sinfectious friendliness, his passion for science and his obsession with understanding havebeen instrumental in making my life at LBMC joyful and productive We spent manymemorable time wrestling the formulations, explained me to understand how an inflatablebeam is In addition, Komla’s deep understanding of inflatable structures provided afantastic resource to bounce ideas back and forth several times a day

I want to single out and thank the people I have worked most closely at LaboratoryDDS of GMP, IUT Lyon 1, especially Abdelkrim Bennani and Lagarde Gérard for theiravailability

I am also grateful for the financial support from the Vietnamese government for thisthesis and from LBMC-IFSTTAR/UCBL for my first European Conference in Austria.Losberger Company and specially Mr Robert Dartois are acknowledged for havingprovided the material samples and inflatable beams which were very useful for the exper-iments in this thesis

Parents, to whom I have dedicated this work, have supported and encouraged me as

I worked toward this degree Finally, I would like to thank my girlfriend for all her loveand support over the years and for her encouragement and faith in my ability to finishthe degree program Let anyone who has contributed directly or indirectly to the success

of this project, finds here my acknowledgments

à mes parents

List of Figures ix

1 Textile fabric composites 2

2 Inflatable structures 3

3 Stability of inflatable structures 3

4 Objectives 4

5 Thesis Outline 4

Chapter 1 BACKGROUND 7 1.1 Textile structures and textile preforms 9

1.1.1 Context 9

1.1.2 Classification of textile preforms 9

1.2 Microscopic observation 16

1.2.1 Unit cell and geometric parameter 16

1.2.2 Stress transfer and characteristics lengths 20

1.2.3 Damage due to tensile loading 21

1.3 Prediction of engineering properties using micro-mechanics 24

1.4 Prediction of engineering properties using numerical approach 26

1.5 Experimental measurement of engineering properties 29

1.6 The role of experiments in structural stability 39

Chapter 2 EXPERIMENTAL STUDIES 41

2.1 Introduction 43

2.2 Mechanical behavior of the fabric 44

2.2.1 Engineering constants 44

2.2.2 Strain measurement 47

2.3 Fabric tensile testing at our laboratory: Biaxial beam inflation test on fabric beam 48

2.3.1 Analysis of elastic moduli 48

2.3.2 Determination of shear modulus of HOWF composite 51

2.4 Experimental buckling of an inflatable beam 53

2.4.1 Introduction 53

2.4.2 Experimental buckling test on a simply supported HOWF beam 54

2.4.2.1 Test set-up and instrumentation 54

2.4.2.2 Boundary conditions 56

2.4.2.3 Measurement of displacements 59

2.5 Conclusion 65

Chapter 3 ANALYTICAL BUCKLING ANALYSIS OF AN HOWF INFLA-TABLE BEAM 67 3.1 Introduction 69

3.2 Theoretical background 71

3.2.1 Kinematics 73

3.2.2 Constitutive equations 75

3.2.3 Virtual work principle 77

3.2.4 Theoretical buckling loads 85

3.2.5 Previous works on the critical load 89

3.3 Examples: in-plane buckling for linearized problems 90

3.3.1 Simply supported inflatable beam under compressive concentrated load 92

3.3.2 Cantilever inflatable beam under compressive axial load at the free end 99

3.3.3 Clamped-clamped inflatable beam under compressive axial load 101

3.4 Influence of the slenderness ratio on the critical load of an inflatable beam 106 3.5 Wrinkling load for an inflatable beam under a compressive concentrated load109 3.6 Conclusion 111

4.1 Literature review 115

4.2 Finite element formulations 118

4.2.1 Linear eigen buckling 118

4.2.2 Nonlinear buckling 121

4.2.3 Implementation of an iterative algorithm for solving the NLIBFE model 122

4.3 Applications and results 124

4.3.1 Linear eigen buckling 128

4.3.2 Nonlinear buckling of a simply supported NLIBFE model 132

4.3.2.1 Wrinkling loads and maximum deflections: Limit of valid-ity for numerical solutions 135

4.3.2.2 Validation of the NLIBFE model: the reference model 137

4.3.2.3 Comparison with the experimental results 140

4.3.2.4 Parametric studies of NLIBFE model 142

4.4 Conclusion 145

GENERAL CONCLUSION AND FUTURE WORK 149 Appendices 155 Appendix A Reminders in mechanics and material science 155 A.1 Mechanical properties of composite materials 155

A.2 Hyperelasticity: theoretical basis 157

A.3 Hyperelasticity and orthotropic materials 160

A.3.1 Orthotropic materials 160

A.3.2 St Venant-Kirchhoff orthotropic material 162

A.4 Thin-walled structures : thin-shells and membranes 164

1 Woven fabrics 2

1.1 Classification of textile preforms in the YTF processes (Cox and Flanagan (1996a)) 11

1.2 Different woven fabric (Source: TexGen) 14

1.3 Schematic diagrams of (a) warp knitted and (b) weft knitted fabrics 14

1.4 Basic weave constructions: (a) plain, (b) twill and (c) 5HS satin weave 15

1.5 Schematics of performing and resin injection molding processes 16

1.6 Cross-section of an orthogonal 2-D woven fabric along the warp direction 18

1.7 Specimens for microscopic observation 19

1.8 Fabric pattern and a unit cell of plain woven fabrics 19

1.9 Fiber breakage 20

1.10 Failure of tensile specimens 21

1.11 Schematic of damage evolution due to tensile loading 23

1.12 Fibrous medium and equivalent continuum 30

1.13 Experimental set-ups used to evaluate intra-ply shear properties: (a) Bias-extension set-up and (b) Picture-frame set-up 31

1.14 Schematics showing the undeformed (left) and deformed (right) shapes of the specimen in the bias-extension test 32

1.15 A bias-extension test apparatus (Cao et al (2008)) 32

1.16 Biaxial testing machine layout (Quaglini et al (2008)) 35

1.17 Shear frame loaded with fabric specimen (King et al (2005)) 35

1.18 Trellising-shear test apparatus fabricated and used by the research groups (Cao et al (2008)) 38

2.1 Plain weave fabric structure 44

2.2 Stress components referred to specimen and material axes 46

2.3 Longitudinal stress distribution in thin-walled cylinder 48

2.4 Transversal stress distribution in thin-walled cylinder 49

2.5 Inflation test layout 50

2.6 Schematic diagram of simply supported HOWF inflatable beam and in-strumentation for buckling test 55

2.7 Digital Manometer KELLER LEO 1 56

2.8 Mounting load cell type ZFA to the structure 57

2.9 Simply supported HOWF inflatable beam and VDAS 5000 57

2.10 Experimental apparatus of HOWF simply supported inflatable beam for measuring the critical load 58

2.11 Inflatable beam with alphabet labels 59

2.12 Tachometer LEICA TPS 300 60

2.13 The formation of the first wrinkles 62

2.14 Crushing test: Experimental curves of axial load versus time 62

2.15 Quasi-static axial compression test: Deflections of simply supported HOWF beam for various pressures 64

2.16 Progression of first buckling mode of the beam with pressure of 30 kPa 64

3.1 HOWF inflatable beam: (a) in natural state and (b) in the reference configuration (inflated state) 71

3.3 Uniform pressure on the cylindrical surface 82

3.4 Definition of the curvilinear coordinate system 83

3.5 Definition of the curvilinear basis at the beam ends 84

3.6 Simply supported inflatable beam 93

3.7 Critical loads for a simply supported inflatable beam under a compressive concentrated load in the case of materials 1 and 2 95

3.8 Fundamental buckling modes on a simply supported inflatable beam under a compressive concentrated load in the case of material 1 96

3.9 Fundamental buckling modes on a simply supported inflatable beam under a compressive concentrated load in the case of material 2 97

3.10 First three buckling modes on a simply supported HOWF inflatable beam under compressive concentrated load 98

3.11 Cantilever inflatable beam 99

3.12 Critical loads for a cantilever inflatable beam under a compressive concen-trated load in the case of materials 1 and 2 102

3.13 Fundamental buckling modes on a cantilever inflatable beam under a com-pressive concentrated load in the case of material 1 103

3.14 Fundamental buckling modes on a cantilever inflatable beam under a com-pressive concentrated load in the case of material 2 104

3.15 First three buckling modes on a cantilever inflatable beam under a com-pressive concentrated load 105

3.16 Clamped-clamped inflatable beam under a compressive axial load 105

3.17 Critical load versus the slenderness ratio of a cantilever inflatable beam under compressive concentrated load in the case of material 1 107

3.18 Critical load versus the slenderness ratio of a cantilever inflatable beam under compressive concentrated load in the case of material 2 108

4.1 Linear eigen buckling: mesh convergence test of normalized linear bucklingload coefficient (Kl

c = 105× σcr/Eeq) for a simply supported LFEIB model 1294.2 Linear eigen buckling: normalized buckling load coefficient (Kl

c = 105 ×

σcr/Eeq) versus radius-to-thickness ratio (Rrt = R0/t0) for a simply ported LFEIB model 1314.3 Linear eigen buckling: normalized buckling load coefficient (Kl

sup-c = 105 ×

σcr/Eeq) versus slenderness ratio (λs = L/ρ) for a simply supported LFEIBmodel 1324.4 Linear eigen buckling: normalized buckling load coefficient (Kl

c = 105 ×

σcr/Eeq) versus bending radius ratio (Rbr = R b B

2R 0) for a simply supportedLFEIB model 1334.5 (a) Inflatable beam subjected to compressive axial load F (b) The effect

of an initial imperfection 1344.6 Wrinkling load: limit of validity of numerical solutions 1354.7 Global beam axes and local material orientation assigned for a orthotropicfabric 1384.8 (a) Inflatable beam with constrained ends, (b) Applied loads on the beamand (c) Beam meshing using S4R shell elements 1394.9 Numerical and experimental mid-span deflection curves of a simply sup-ported NLIBFE model with pn=324 1424.10 Numerical and experimental mid-span deflection curves of a simply sup-ported NLIBFE model with pn=648 1434.11 Numerical and experimental mid-span deflection curves of a simply sup-ported NLIBFE model with pn=972 1434.12 Nonlinear buckling: variation of flexion-to-radius ratio (Rf r = Dv/R0)withincreasing normalized nonlinear load parameter (Knl

c = 106× Fi/(EeqA0))for a simply supported NLIBFE model 144

with increasing incremental load ratio (Kf = Fi/Fp)for a simply supported

NLIBFE model 146

4.14 Nonlinear buckling: variation of the flexion-to-radius ratio (Rf r = Dv/R0) with with increasing incremental load ratio (Kf = Fi/Fp) for a simply supported NLIBFE model 146

A.1 Woven fabric structure with in plane vectors li (l1 = l, l2 = t) 161

A.2 Curvilinear coordinates for a surface 166

A.3 Covariant base vectors associated with a tangent plane 167

1.1 Fiber architecture for composites (Vandeurzen et al (1999)) 101.2 A comparison of yarn-to-fabric formation techniques (Vandeurzen et al.(1999)) 101.3 Classification of the geometric parameters 172.1 Geometrical parameters of HOWF inflatable beam 492.2 Micro-deformations versus internal pressure obtained from two strain gagesRosettes 512.3 Young’s modulus and Poisson’s ratio of the test beam fabric 512.4 Geometrical parameters of HOWF inflatable beam in pressurized configu-ration under various internal pressures 553.1 Data set for inflatable beam 923.2 Critical loads Fcr of inflatable beam models with various boundary conditions100

4.1 Input parameters for modeling NLIBFE model 1244.2 Data set for inflatable beam 1274.3 Normalized pressure (pn) for different values of internal pressure (p) used

in the study 127

4.4 Buckling coefficient (Kl

c) comparison between LFEIB results and analyticalsolutions 130

and the NLSFE model with various slenderness ratios 141A.1 Stiffness matrix of different materials 157

• Abbreviations

• Plain weave fabric testing

which are assumed to represent the axes of material symmetry(L: warp direction; T : weft direction)

G∗ = Gto Membrane shear modulus of the isotropic fabric

Internal forces

Beam geometry

Ro Reference radius of the inflatable beam

Loads

Fcrushing Crushing load

Pressure, pressure forces

v, w Deflections along Y and Z axes

Functions and constants

Matrices and tensors for finite element formulations

{d} Nodal d.o.f

Aspect ratios

Linear eigen buckling

“ Success is never found Failure is never fatal Courage is the only thing ”

Winston Churchill

Motivations and objectives

"The field of composite materials is both old and new" It is old in the sense thatmost natural objects, including the human body, plants, and animals, are composites It

is new in the sense that only since the early 1960s has engineers and scientists exploitedserious the vast potential of fabricated fibrous composite materials Development of newcomposites and new applications of composites is now accelerating The textile structuralcomposite cited in this study should be considered as typical of modern materials.Advanced lightweight laminated composite structural elements are increasingly beingintroduced to new designs of modern aerospace structures for enhancing their structuralefficiency and performance The introduction of new fiber materials, such as glass, carbon

or aramid fibers with orthotropic material behavior have motivated a deep study of suchelements which are used to build membrane and thin shell structures

1 Textile fabric composites

As a well-known definition, a composite is a material which is composed of two or moredistinct phases Thus a composite is heterogeneous The fibrous composites are materials

in which one phase acts as a reinforcement of a second one The second phase is called thematrix The challenge is to combine the fibers and the matrix to form the most efficientmaterial for the extended application

Textile preforms are fibrous assemblies with prearranged fiber orientation preshapedand often preimpregnated with matrix for composite formation The microstructural or-ganization of fibers within a preform, or fiber architecture, determines the pore geometry,pore distribution and tortuosity of the fiber paths within a composite Textile preformsnot only play a key role in translating fiber properties to composite performance butalso influence the ease or difficulty in matrix infiltration and consolidation Textile pre-forms are the structural backbone for the toughening and net shape manufacturing ofcomposites

Figure 1: Woven fabricsThe flexible fibers, such as glass, carbon, and aramid, can be woven into textile fabric,which can then be impregnated with a matrix material A wide variety of weave patternsare available Plain woven composites or homogeneous orthotropic woven fabric (HOWF)

composites are orthotropic materials which can be classified into two patterns, depicted

in (Fig 1): a plain weave (every fiber over and under every other perpendicular fiber)and a two-harness satin weave (under only every two fibers) Woven fabrics naturallyhave better in-plane transverse effective properties than unidirectional lamina They laybetter in structural configurations with substantial curvature and are more durable duringhandling

Due to the nature of coated woven fabrics, these inflatable structures will have complexdeformations and both the stress fields from the fluid-structure interaction during reentryand the mechanics of these materials must be understood

In order to provide a motivation for the use of inflatable structures, engineering perties as well as structural behaviors are compared with those of monolithic structures.Applications where inflatable structures have proven advantages over monolithics are pre-sented in this study

The pattern of research in structural stability for many years has been one of extensivetheoretical studies combined at the most corroborating experiments

Inflatable structures, application of plain woven composites, can be considered asshell or membrane elements which are developed for isotropic and orthotropic material

behavior The popularity of shells is due to the fact that they are very efficient loadcarrying structures However, often they are prone to "catastrophic" elastic instabilities.Thus a thorough understanding of the stability behavior of thin-walled shell is a mustfor all those who employ them Unfortunately, very little relevant references have beenfound on buckling of inflatable structures made of plain woven composites, especially inexperiments.

The main goal of this thesis is to investigate the stability analysis of an inflatable beammade of modern textile materials in analytical and numerical approach which takes intoaccount the material orthotropy as well as the structural geometrical nonlinearities and thefollower force effect induced by the inflation pressure Experiments for characterizing themechanical properties of HOWF composite and buckling behaviors of a HOWF inflatablebeam are also focused

The thesis presented is organized as follows:

• Chapter 1 The first chapter is devoted to the general description of the textilestructures and the plain woven fabrics for composite materials The typologiesavailable will be described and the manufacturing techniques are also summarized.Since this work deals with different topics, a detailed review of the state-of-the-art

is presented A bibliographical research on textile composite and the approaches topredict their engineering properties are given This chapter also reserves a specialattention on the plain woven fabric for orthotropic material behavior and the role

of experiments in structural stability

• Chapter 2 This chapter has two parts The test methods that are commonly used

to characterize the mechanical response of fibrous composite materials known as thebias extension test and the picture-frame test are introduced in the first part of thischapter Then we presented an original biaxial extension test adopted at our labo-ratory to determine the elastic modulus of HOWF The inflation tests, to determinethe elastic modulus of the HOWF composites, performed at our laboratory are alsoincluded In the second part, a buckling test on a simply supported inflatable beammade of HOWF composite, under a compressive axial load is performed in order todetermine the buckling load and monitor the formation of the first wrinkles of thebeam The chapter closes with the results that will be used as the material inputs

• Chapter 3 An analytical approach to approximate the critical load for a HOWF 3DTimoshenko beam is proposed in this chapter This critical buckling load is investi-gated through several load cases with several boundary conditions The discrepancydue to the orthotropic character between the present model and the isotropic mo-dels found in the literature is evaluated, as well as the influence of the inflationpressure and the fabric characteristics on the value of critical load The bucklingmode shapes are also determined To check the limit of validity of the results, thewrinkling load is also presented

• Chapter 4 In this last chapter, the linear eigen and nonlinear buckling analysis

of simply supported inflatable beam made of orthotropic technical textiles are formed The finite element model established here uses a three-noded Timoshenko

the inflation pressure on the stability behavior of inflatable beam are assessed: asimply supported beam is studied The influence of the beam aspect ratios on thebuckling load coefficient are also pointed out The results obtained using the nu-

merical model are compared with the experimental results and those using a 3Dthin-shell finite element model.

CHAPTER 1

BACKGROUND

“ It is not length of life, but depth of life ”

Ralph Waldo Emerson

1.1 Textile structures and textile preforms 91.1.1 Context 91.1.2 Classification of textile preforms 91.2 Microscopic observation 161.2.1 Unit cell and geometric parameter 161.2.2 Stress transfer and characteristics lengths 201.2.3 Damage due to tensile loading 211.3 Prediction of engineering properties using micro-mechanics 241.4 Prediction of engineering properties using numerical approach 261.5 Experimental measurement of engineering properties 291.6 The role of experiments in structural stability 39

1.1 Textile structures and textile preforms

Textile preforms are fibrous assemblies with prearranged fiber orientation pre-shapedand often pre-impregnated with matrix for composite formation The micro-structural or-ganization of fibers within a preform, or fiber architecture, determines the pore geometry,pore distribution and tortuosity of the fiber paths within a composite Textile preformsnot only play a key role in translating fiber properties to composite performance but alsoinfluence the ease or difficulty in matrix infiltration and consolidation Textile preformsare the structural backbone for the toughening and net shape manufacturing of compo-

Vandeurzen et al (1999); Long (2005)

There is a large family of textile preforming methods suitable for composite manufacturing(Ko (1989)) The key criteria for the selection of textile preforms for structural compo-sites are: (a) the capability for in-plane multi-axial reinforcement, (b) through-thicknessreinforcement and (c) the capability for formed shape and/or net shape manufacturing.Depending on the processing and end use requirements some or all of these features are

lin-earity and continuity, fiber architecture can be classified into four categories: discrete,

nature of the various levels of fiber architecture is summarized (Scardino (1989)).

Table 1.2 shows another way of classifying textile preforms based on the fabric tion techniques: the "yarn to fabric" (YTF) The YTF processes are popular means forpreform fabrication wherein the linear fiber assemblies (continuous filament) or twistedshort fiber (staple) assemblies are interlaced, inter-looped or intertwined to form 2D or 3D

"fiber to fabric" (FTF) process and the combination of FTF and YTF processes

yarn introduction

(machine direction)

loops of yarns over previous loops)

(orthogonal)Woven fibers have been in use for centuries for products made from fibrous materials

Layer-to-Layer Through-Thickness

2-D

3-D

Bias Triaxial Tubular Cartesian

2-Step 4-Step Multi-Step

orthogonal woven, non-crimp, triaxial braid and knit

• 2D orthogonal woven fabric In general, a 2D orthogonal woven fabric is made

strand of textile fibers and made of continuous or stretchable fibers with diameterstypically in the order of micron meters (µm) The fabric is produced on a loom

lengthwise yarns are called warps, while the yarns that are shuttled across the loomare called wefts or warps The individual yarns in the warp and weft directionsare also called an end and a pick, respectively The interlacing of the yarns causesyarn undulation or yarn crimp The weave type is determined by the method of

interlacing both sets of yarns.

2D orthogonal woven fabric exhibits unique behaviors while under loading, including

In the past decade, a variety of micro-mechanical models have been employed tostudy the overall thermo-elastic behavior of 2D orthogonal woven fabric compositesbased on the properties of the constituents and the fabric architecture Some ofthese models also provide the opportunity to address strength properties

• 3D orthogonal woven fabric Advances in textile manufacturing technology arerapidly expanding the number and complexity of 3D woven preforms By changingthe traditional weaving technique to produce 2D fabrics, it is now possible to achieve

a much higher degree of integration in the thickness direction of the textile Thetwo major classes of solid 3D weaving are through-thickness angle interlock weaving

Chou (1992); Cox and Flanagan (1996b)) Angle interlock 3D woven fabrics can beproduced on a dobby loom or a jacquard loom The warp yarns can now enter more

yarns are also possible By changing the number of layers, the pattern of repeat andthe position of the laid-in yarns, an almost infinite number of geometric variationsbecomes possible In an orthogonal interlock 3D weave, the yarns are placed inthree mutually orthogonal directions These fabrics are produced principally bythe multiple warp weaving method Matrix-rich regions are created in compositesreinforced with a 3D woven orthogonal preform

• Non-crimp fabric Also known as reinforcing textiles with high resilience, crimp fabrics are distinguished by their stretched fibers inside the individual layers(Fig 1.2c), which optimally absorb mechanical forces such as pressure and tension.Non-crimp fabrics combine unidirectional crimp-free fiber layers by assembling them

non-together by stitching - sewing or knitting - and/or bonding by chemical agents.

• Triaxial braid fabric Braid is one of the most widely used reinforcement fortextile composites In braiding, three or more threads interlace with one another

Such fabrics can often be used directly as net-shape preforms for liquid moldingprocesses such as resin transfer molding

• Knit fabric Knitted fabrics are basically categorized into two types, namely warpknit fabrics and weft knit fabrics, based on the knitting direction In a knit fabric, avertical column of stitches is called a wale, and a horizontal row, a course Schematic

a single yarn looped horizontally to form a row, or course, with each row building

fabric is a weft knit A warp knit is made with numerous parallel yarns that are

of knitted fabrics are used in the garment industry for fashion purposes However,only a limited number of knit structures are being investigated for composites inengineering applications

In this thesis, particular attention should be paid to the 2D orthogonal weave fabrics

review will assist in defining possible modeling strategies for this type of woven fabriccomposite

Fig 1.4 shows three basic constructions: plain, twill and satin weave Even in rathersimple woven fabrics, there are important geometric differences between the warp and theweft direction Those differences are the result of numerous constructional and processparameters such as weaving density, warp tension, weft tension and beating motion.The manufacture of components from woven fabrics involves a forming stage in which

(b) 3d orthogonal woven fabric (a) 2d orthogonal woven fabric

(c) Non-crimp fabric (d) Triaxial braid fabric

Figure 1.2: Different woven fabric (Source: TexGen)

Wale

Course

Figure 1.3: Schematic diagrams of (a) warp knitted and (b) weft knitted fabrics