Engineering Design of Textiles Extrel1le Textiles Strength Of
Indian Journalof Fibre & Textile Research
Vol. 31, March 2006, pp. 134- 141
Engineering design of textiles
J W S Hearle" Department ofTcxtiles and Paper. Univcrsity of Manchester, Manchester. UK
The engineering design of textiles continues to follow the traditional empirical methods and for technical as distinct from aesthetic design has not adopted computer-aided design as used in other industries. The reasons for this and the need for change have been discussed. This paper reviews the state-of-the-art in the structural mechanics of yarns and fabrics. The major challenge is to develop programs that industry will use and hence open up a creative interchange between academic researchers and industrial users. A description of key features of TexEng software, which includes an easy-to-use program aimed at meeting this challenge, is given. Keywords: Computer-aided design. Fabric. Yarn.Strucl Ural mechanics IPC Code: Int. CI.8 G06G
1 Old and New Design Cultures The combination of strength and flexibility in· What is engineering design? And to what extent is unbonded fibre assemblies held together by frictional forces makes wonderful products. From ancient times, it practised in the textile industry? Until about 100 years ago, engineering was an empirical skill. the needs for clothing of the proletariat and fashion Bridges, bui Idings. machines, vehicles and all the for the aristocrats were provided by woven and other constructs needed by mankind were designed on knitted fabrics. A range of technical uses from sails the basis of experience and practical trials - with and tents to conveyor belts and tyre fabrics was also disastrous errors often leading to advances. Geometry met by textiles. The current Extrel1le Textiles linked to drawing was backed up by empirical rules of exhibition at the Cooper-Hewitt National Design thumb on what loads could be carried and what might Museum in New York shows how this tradition has be needed to meet other performance requirements. been exploited in new materials for space, medicine, The wealth of practical knowledge and skills sport, buildings and transportation, as well as developed over thousands of years enabled the advances in more traditional applications such as ' production of textile materials to be an outstanding ropes and nets. However, a conversation with a example of this form of engineering design. manufacturer of materials for medical implants Experience and trial-and-error formed the design confirmed the preference for working through protocol; intuition led to advances. Point paper and traditional practical trials and eschewing mechanical weaving plans were the design tools. The flowering of modelling. textile research in research institutes and universities In most other branches of engineering, design after the first world war led to an exploration of the procedures changed. The growth of the science of academic science of fibres and textiles. In a applied mechanics, starting with Galileo and Newton commercial and industrial context, this led to and augmented by giants like Euler and Hamilton as advances through a growth of qualitative well as others who worked on the details. made understanding, but the empirical design tradition quantitative predictions possible. In the education of remained as it was. Even the exploitation of the new mechanical and civil engineers, the design tools were manufactured fibres followed an empirical path of provided ,in the first half of the 20lh century by such development. The possible quantitative performance classic works as Love's Treatise Oil the Mathematical predictions of the academic work were not taken up Th eory of Elasticity, Timoshenko's several books and, by industry. as a simpler textbook, Den Hartog's Strength of Materials, with Roark and Young's Fonnulas fo r Stress and Strain being a vade meculll of the "Emcritus Professor Present address: The Old Vicarage, Mellor. Stockport, UK equations that design engineers evaluated on their E-mail: [email protected] slide rules. Other scientific advances led to HEARLE: ENGINEERING DESIGN OF TEXTILES 135 quantitative design in aerodynamic, electrical and needed for safety and to optImIse cost benef:�. In chemical engineering. In the second half of the 20th contrast to this, most textile products are small scale: century, computers replaced slide rules and computer individual costs are low; failure in a trial is a nuisance aided design (CAD) made more elaborate calculations but not a disaster; design times are short. and modelling possible. The application of this new There is a more fundamental reason. The science of form of quantitative engineering design, which flexible fibre assemblies is an extremely challenging replaced empiricism and augmented the qualitative subject and is little related to the mainstream 20th insights, led to enhanced performance in traditional century development of applied mechanics. As I uses, such as bridges, and made possible the wrote in 1979: Textiles are solid lIlaterials. but lillIe technological transformation of the 20th century. of direct relevance to textile behaviour will be fo und In most respects, the changing design culture in any textbook on the lIlechanics of materials. Ta ble passed by the textile industry. There are some I shows some fe atures which distinguish textile exceptions. The machinery spawned the academic materials ji-Ol11 those usually studied in engineering subject of lIlechanics of machines, covering gears, materials. In ordinary engineering, the developlllents levers and drives. The textile machinery industry has of discon.tilluities, porosity. buckling. long-range embraced CAD but this is almost entirely in the displacemellt. surfa ce roughness. or a soft elastic machine actions independently of the fibres and yarns yieldillg under transverse pressure are ojien taken as passing through the machines. For example, a signs of fa ilure of the materials. and the need fo r conversation with company engineers indicated that meclwnical analysis ceases with the onset of these there was no attempt to model the movement of fibres phelloll1ena but in textiles their manifestation signals in air streams in the outstanding development of air the value (4 these materials. alld the beginning of the jet spinning by Murata; intuition and practical trials region where the mechanical analysis is of //lost led to the commercial success. Modern engineering interest.2 The convenient assumptions of small strains design is used for fi bre-reinforced composites, which in an isotropic continuum are not applicable to notably are included as Extreme Textiles in the flexible fibre assemblies, and fibre materials are not exhibition, but these were developed in the elastically governed by Hooke's law with two elastic mechanical engineering sector and have an affinity constants or ideal elastic-plastic, but are anisotropic with rigid materials, subject only to small strains. and visco-elastic. Rope engineering is a particular example discussed The above causes lead to another. There has been below. no creative interchange between those doing the basic In the application of science, there is a major research and engineers using it. The best academic difference between the two halves of the textile work has opened up the fundamentals of the subject; processing industry. The chemical part, wet the worst has concentrated on mathematical processing, has embraced science. The manager of a sophistication, which is of little practical value. dyehouse or a finishing plant would regard himself as Texti Ie engineers have not found methodology that a chemist. Not so in the mechanical part. The manager they could apply. of a spinning plant or a weaving shed would not There are several reasons why this is bound to regard himself as a member of the applied mechanics change in the 21st century. The general development community, even though his work is overseeing of IT culture means that young people entering mechanical actions and the mechanical performance industry expect to use computers to help solve their of the textile products. problems. The wealth of practical experience. which
2 Conditions for a Cultural Change Table I-Important distinctions Why has the textile industry not adopted a modern Common engineering Textile engineering design culture'?There are several reasons. material material One is conservatism. Another is that it is not absolutely necessary. Bridges must be built so that Rigid Flexible they do not fall down; aircraft must fly. The structures Homogeneous Disconlinuous Hard Soft are large; the costs are high; performance continually Impervious Porous needs to be increased; the design process for new Smooth Textures models is long. Quantitative engineering design is Strong Strong 136 INDIAN 1. FIBRE TEXT. RES .. MARCH 2006 was available when a textile technologist worked in [strand] [rope). The inputs to the computer --+ the same area throughout a career, is dissipating with program, Fibre Rope Modeller (FRM), are the changing employee patterns. The diversity of fibres dimensions and tensile properties of the component and textile manufacturing methods is increasing yarns and the twist inserted at each manufacturing greatly, opening up more choices and more problems. stage. The predictions agree well with measured rope Textiles are finding uses in more demanding load-elongation properties, except that typically break applications where the project engineers expect loads of well-made ropes are about 10% less than engineering data on the performance of the material. computed due to lack of optimum load sharing. The If the techniques are available, the modelling geometric modelling enabled relative fibre motions in predictions are cheaper than time-consuming pilot various slip modes to be computed and, applying the studies, and are welcomed by the engineering principle of virtual work, the internal transverse community. pressures between rope components to be determined. The fundamental reason is in Moore's law. The FRM is now being used by the leading UK rope huge increase in computer power and reduction in manufacturer to design high strength ropes, such as cost mean that the difficult problems can be tackled. the 2000 tonne break load polyester rope used to moor The history of computing is that advances are first an oil-rig in 1400 meters of water in the Gulf of used by specialists and then taken up by the majority. Mexico. This is one of the first examples of a textile Once started. the changes occur rapidly. In the design calculation being used in a modern engineering aesthetic aspects of the industry. designing for pattern design sense. and colour, CAD went from almost nowhere in 1975 FRM was extended to compute responses under to common practice by 2000. cyclic loading conditions.5 The modelling takes Although research has elucidated only a few of the account of fibre creep and hysteresis heating. Slip and problems in textile mechanics to a level for industrial pressure are determinants of inter-fibre abrasion. performance prediction, the more urgent priority is to Buckling of some components at low rope tensions introduce programs that are easy to use and truly help leads to axial compression fatigue; modelling was the engineer in industry. adapted from previous studies of buckling of heated pipelines.6 This part of FRM gives useful guidance Current State-of-the-Art 3 but is limited in predictive power by lack of 3.1 Yarnsand Ropes experimental values for rates of fibre abrasion and The mechanics of twisted continuous filament axial compression fatigue. yarns had been effectively worked out by the 1960s. An energy method led to one integral and four Collaboration between marine engineering algebraic non-linear equations, which are easily consultants, Noble Denton, and fibre rope consultants, ) solved numerically. The inputs are the fibre stress Tension Technology International (TTl) supported by strain curve, yarn linear density and twist. Although a consortium of rope makers, rope users and there are some approximations in the model, the certifying authorities, led to the production of Deep predictions are good, except that the stresses at low water Fibre Moorings. an engineers ' design guide.7 strain are slightly less than expected because of some The main criteria to be met in use are peak loads buckling of filaments at the centre of yarns. The safely below the rope break load, rig offsets less than reason for success is that twisted continuous filament an acceptable distance, and long enough life. Mooring yarns can be modelled by a well-defined geometry, analysis programs existed to predict the response of which consists of superimposed layers of helices with steel wire and cable moorings. However, these constant twist period, and consequently there is a moorings are controlled by the weight of the rope and direct relation between yarn extension and extension changes in the catenary, whereas fibre rope moorings of the filaments. In real yarns, the filaments migrate in are controlled by the tension due to the extension of a radial position but over short lengths, the idealised taut rope. In principle, tension is given by (modulus x model is a good approximation. extension). The problem is that viscoelasticity means The same methodology has been applied to the that fibre modulus is not a well-defined property. It multiple twist levels of ropes.4 A hierarchical depends on the nature of the loading and the previous procedure is followed. Typically the sequence of twist loading history. There is further complication that levels is: [yarn as produced] [rope yarn] rope constructions tighten up under cyclic loading. --+ --+ HEARLE: ENGINEERING DESIGN OF TEXTILES 137
The collaboration made it possible to specify test Now it would be possible to apply the same procedures to give a minimum value of post principles to an individual fibre computational model installation stiffness which relates to offsets, and a to give improved predictions. The major limitation maximum value for storm stiffness which relates to would be to define the migration paths of the fibres. A peak load. Limits were given for the number of cycles full theoretical computation would require treatment at low tension to avoid axial compression fatigue (e.g. of the more difficult problem of modelling the process <100,000 cycles at < I 0% of break load for polyester; of yarn formation. An alternative design methodology <2,000 cycles at <5% of break load for aramids). A would be to create a database of values of the number of Joint Industry Projects, carried out by TTl empirical factor K and use a neural network or other and the National Engineering Laboratory, of cyclic soft procedure to give values for particular cases. loading on large test-rigs have provided data on The several forms of open-end spun yarns require moduli and effects of long-term testing (with the right modelling in terms of their structures. Bulky wool products, no failure after millions of cycles). Polyester yarns have proved more difficult to model, because ropes have the best combination of properties for deep the structure changes as the fibres move closer water moorings and their long-term life is better than together. Modelling of false-twist textured yarns with the steel ropes under similar conditions. alternating fibre helices and pig-tails, and air-jet The combination of modelling and testing has textured yarns with projecting loops, needs to be given oil companies the confidence to moor oil-rigs in advanced to take account of modern computer power.l) deep water. A typical installation would consist of 20 km of 50 Mtex polyester rope with break load of 2000 3.3 Woven Fabrics tonne and, in total, weighing 1000 tonnes. The mechanics of woven fabrics raises more Collaboration between textile experts and application difficulties. One problem is that the zero-stress state is engineers is the way forward for engineering design not well defined. Agreement is needed on the of textiles for demanding uses. Combinations of definition of a reference state under low biaxial theoretical modelling and practical testing are needed loading. Another difficulty is that there is no direct to meet performance and safety requirements and to geometrical relation between the fabric deformation optimise cost benefits. Experience in use must also be and the component yarn deformation, since the latter taken into account. Unexpected problems cannot be depends on a balance among yarn extension, yarn avoided. For example, in an early deep water mooring bending and yarn flattening. One consequence of this off the coast of Brazil, a rope section removed for is that fabric geometry as specified will not, in testing showed a reduced break load due to minute general, be in equilibrium. The first stage of a i crustaceans penetrating the rope and abrading the mechanical am lysis is to determine the zero-stress fibres. Once recognised, this problem could be state. In practice, this is complicated by the ways in eliminated by protecting the rope or substituting a which fabrics can become set in different states as a steel section at the relevant depth, but it had not been result of relaxation. Furthermore, the yarns go through anticipated despite extensive design studies. different states as they go from contact regions at crossovers to free regions between crossovers, with 3.2 Other Yarns more complicated forms in non-plain weaves. The treatment of continuous filament yarns can be The majority of the many papers on woven fabric modified to take account of slip at fibre ends in mechanics is based on equilibrium of forces and compact ring-twisted staple fibre yarns. An elaborate moments. Most of them are limited to plain weaves theoretical analysis, which took account of fibre and simplifying assumptions, such as Kawabata's migration but was limited to small strains, was s saw-tooth model, are necessary. In my opinion, this reduced to the following semi-empirical equation : approach will not lead to engineering design methods. Yarn strength or modulus / Fibre strength or modulus The alternative is the energy-based approach of lo cos"a [1-(2 cosec / 2 fl)112] Hearle and Shanahan. This is now being more = a / 3L) (0 Q cos2a (l-K cosec a) strongly developed in a graphical computing mode in = a research project at the University of Manchester. where a is the surface twist angle; L, the fibre length; The fabric geometry is flexibly formulated by a, the fibre radius; Q, the migration period; and fl, the defining yarn paths by spline-fitting through specified coefficient of friction. points and by defining yarn cross-section by the 138 INDIAN J. FIBRE TEXT. RES., MARCH 2006
lengths of a set of radial vectors. The mechanics is fabrics, there are six fundamental directions to be
treated by minimisation of [yarn extension energy + modelled: in-plane (two tensile and one shear); and yarn bending energy + yarn flattening energy] through out-of-plane (two bending and one twisting); the adjustments of the geometry when the fabric is held to latter, which is related to bending on the bias, being given dimensions. Determination of strain energy at frequently ignored. Solution of these problems covers small increments of deformation means that tensile fabric micromechanics and gives the constitutive forces can be found from conservation of energy. relations for yarns and fabrics. The hierarchy is: Yarn extension energy is well defined. Yarn bending Fibre properties Yarn structure energy is fairly well understood. The neglected + t feature of yarn flattening energy, which depends on Yarn properties Fabric structure change of volume and shape, needs more research. + t Progress can be helped in other ways. One is to Fabric properties. concentrate on control points. Three primary control Macromechanics covers more complex points, given by the fabric repeat, are needed to deformations and modes of behaviour, which are specify the fabric's biaxial deformation. Additional relevant to a totality of engineering design. These primary control points are needed for fabric shearing include features, such as pilling and bagging of and bending. For a plain weave, the primary control fabrics where modelling has been limited, and heat points also define the internal displacements, but and moisture transmission where modelling is additional secondary control poi nts are needed for advanced. Two examples illustrate ways to approach non-plain weaves. Another is to identify special cases. the problems. For monofilament and highly twisted yarns, yarn Many attempts at modelling of drape by finite flattening can be ignored, except for a Poisson's ratio element programs have been reported in the literature. effect usually at constant volume. For very soft yarns, However, these include unjustified simplifications the free zone between crossovers disappears. and demand excessive computer time. In my view, it Simplifications of this sort, although lacking in is not a useful approach to apply software developed academic rigour and generality, offer better prospects for other systems. Programs adapted to the particular of developing useful engineering design software. features of textiles are needed. Drape is just one 3.4 Other Fabrics manifestation of complex buckling of fabrics. I In mechanical terms, braided fabrics are simply a believe that progress will come from a fundamental variant of woven fabrics. Simple plain knits have been study of the mechanics of buckling, elaborating the modelled by equilibrium of forces and moments with study of symmetrical threefold buckling of a linear limitations similar to those for woven fabrics. The elastic sheet to cover more realistic and complicated energy method should be developed for the various forms. I I knit fabric structures. Bulk and compressibility of fibre assemblies are Modelling of bonded, needled and stitch-bonded another important problems. Here, the pioneering nonwovens has followed the familiar pattern of aiding individual fibre computational modelling of Bell and 2 qualitative understanding but not quantitative Roberts 1 shows the way forward. Again this is based engineering desigll predictions. Random networks on energy minimisation of the forms of fibre could be modelled by individual fibre computations, segments between contact points. but the problem, as with staple yarns, is to define yarn paths. In the absence of detailed process modelling, 4 Useful Software semi-empirical procedures are needed for engineering How can we make the increasing knowledge of the design. structural mechanics of textiles into engineering design procedures that will be used in industry? This 3.5 Other Mechanical Properties is necessary, not only for its inherent value, but as a The above discussion has been primarily concerned means of developing a creative interchange between with tensile properties, but others are also important academic research and practical utility. The critical for textile perf ormance. The transverse need is for programs that are easy to use and answer compressibility of yarns has been mentioned in the questions that engineers and managers want to connection with flattening energy in fabrics. For ask. HEARLE: ENGINEERING DESIGN OF TEXTILES 139
TexEng Ltd offers programs developed by the inputs are yarn tensile properties, specified by break Textiles and Paper Group, School of Materials, load, break extension and shape of stress-strain curve University of Manchester in association with TTl Ltd, through polynomial coefficients, bending stiffness in the forms which run in a familiar Windows mode and flattening stiffness. The predictions agree well on a Pc. The entry screen is shown in Fig. 1. with experimental data on plain weave cotton fabrics Yarn Modeller covers the established model for from Kawabata et al.14 and monofilament nylon twisted continuous filament yarns and will include fabrics from Dastoor et al.. 15 However, as indicated empirical rules for other yarns. Weave GeoModeller above, more theoretical research and validation is covers the structure of single-layer woven fabrics. needed for more complicated woven fabric problems. Fig. 2 shows montages from several windows. A file Fibre database and yarn database, which can also is created in three stages (i) weave can be input by store results from Yarn Modeller, are sources of traditional point paper/mesh, which is easy for inputs to the modelling programs. Fabric database computer usage and more illustrative or for the stores the files of models that have been run. It can mathematically inclined by formula; (ii) yarn also be used to store experimental data on fabrics; dimensions are input; circular, lenticular and racetrack ways of using this data to give empirical predictions cross-sections are current options; and (iii) warp and will be developed. weft spacings and one crimp value complete the Conversion tool derives from a pioneering fabric specification. If needed, conversion tool development of a question-answer program by transforms input values for other parameters to those Konopasek. Formulation of a great many textile required for the program. Three-dimensional views of problems involves a multiplicity of relevant variables. a the fabric can be manipulated in various ways. For few of which are independent and more are dependent. example, slice allows the viewer to see how pore sizes change through the thickness of the material, which is OTHER WEAVESCAN BE CREATEDBY FORMULA relevant to transmission properties. Weave [e.g. 3/3 ".p 1). POINT PAPER OR MESH GeoModeller is the basic program that allows particular applications to be developed. For example, in one project in the University of Manchester, a fi ltration module is being developed. Knit GeoModeller is similar to Weave GeoModeller but is currently limited to plain, rib and purl single-layer and interlock rib double-layer weft knits. The currently available application in TexEng is weave mechanics. which is based on an energy method described by Sagar et al.. 13 The additional
IN 3D GRAPHICS. t.loduIes J!eiD MOnlpulote Models ALLOWS VARIOUSMAN/PULA CHANGES. TE Fibre Database Be�tore ENLARGES PICTURE �__ •.g. ZOOM IN ______,"oom In --� ZQom Out GOES TO GeoModelier Yarn Database r RESTORE �-"-,---' ���l______END-ON VIEW OF FABRIC � Weave �� ·I L ... I ' Ironslote Rot�te by An Angle Weave MeChani � Rotots: mouse Fabric Database ""th � e Knit GeoModelier �Iite THROUGH GIVES A B S!lrl l:!l:' ::::. __a l� �· ROTATEANGLE GIVES SLICESECTION THROUGH I ------� ANOTHER VIEW FABRIC Weav: Conversion Too_� • Engin�er J :;� J of fer'!!. textil� 1 -1��'[;1-9-SOf�tllre t�ol' tOf techni�ol design-of fabrics. . ClIck the bunon tn launch the spDcitic app'cation. I.' . I· I· ! I, I,I ; " "-'
Fig. I-Entry screen for TexEng programs Fig. 2-Montages from Weave GeoModeller 140 INDIAN FIBRE TEXT. RES., MARCH 2006 1.
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Weave Engineer is a program developed by 2 Hearle J W S, in Mechallics (IF FII'Xihle Fibre Asselllblies. Xiaogang Chen and Isaac Porat for 3-D fabrics, which edited by J W S Hearle. J J Thwaites and J Amirbayat (Sijthoff & Noordhoff. Alphen dcn Rijn, Netherlands). ,I; " are important for composite preforms. It covers the . 1980. weave specification and a view of the topology of the 3 Hearle J W S, On the theory of the mechanics of twisted 4. yarns. J lilSI. 60 (1969) 95- 1 fabric, as illustrated in Fig. The information can be Tnl OJ. transmitted to the electronic Jacquards or other 4 Leech C M, Hearle J W S. Overington M S & Banfield S J. control means of weaving machines; this part of the Modelling tension and torque properties of ropes and splices. Proceedillgs. ISOPE COIIFerellce. II. 3"" Singapore. Vol. program can also be used with Weave GeoModeller 1993. 370-376, for single layer fabrics. 5 Hearle J W S. Parsey M R. OveringlOn M S & Banfield S J. Proceedillgs. ISOPE COI(Ferellce. 3r.1 Singapore. Vol. [I. Conclusions 1993, 377-383. 5 6 Hobbs R E, Overington M S, Heal'le J W S & Banfield S J. The last three-quarters of the 20111 century showed a Buckling of fi bres and yarns in ropes and other IIbre great flowering of fibre and textile research, including assemblies, J Text IlIst, 91 (2000) 335-358. the structural mechanics of fabrics. This increased 7 TTl & Noble Denton. Deepwater Fibre Moorillgs: All understanding and stimulated invention, but it was not Engilleers ' Design GlIide ( Oilfield Publications. Ledbury, adapted to quantitative engineering design in the way UK), 1999. 8 Hearle J W S. Theoretical analysis of the mechanics of that happened in other industries. Partly, this was due twisted staple fibre yarns. Text Res J, 35 (1965) 1060- I 071. to the difficulty of the problems. Great simplifications Texlilrillg 9 Hearle J W S. Hollick L & Wilson D K. Ya rn were needed in models to be treated by hand Techll% gv (Woodhead Publishing. Camhridge. UK). 200 I. calculations and even by early computing facilities. 10 Hearle J W S & Shanahan W J, An energy method for calculations in fabric mechanics: Part I-Principles of the Most research gave generic results, or just a few method and Part 11- Examples of the application of the examples, and did not give ways of taking account of method to woven fabrics, J Text li1Sl, 69(1978) 8 I -9 1, 92- the options in the choice of design parameters. The 100, challenge for the s century is for the technical I I Amirbayat J & Hearle J W S, The complex huckling of 2 I l textile materials: Part Theoretical analysis and Part 11- aspects of textiles. A creative interchange between 1- Experimental study of threefold buckling, lilt J Mech Sci, 28 academic researchers and industrial users will (1986) 339-358. 359-370, transform how the industry operates in the design of 12 Bell N B & Roberts W W, Modeling and computcr textiles to optimise performance and cost benefit and simulation of the compressional behavior of fibre assemblies: will open up new markets for fibre assemblies in Part I-Comparison to van Wyk's theory and Part 11- common and extreme applications. Hysteresis, crimp and orientation effects, Text Res J, 72 (2002) 341-351. 375-382. 13 Sagar T V, Potluri P & Hearle J W S, Energy approach to Acknowledgement predict uniaxial/biaxial load-deformation of woven preforms. The author is thankful to Dr Xiaogang Chen, Dr Proceedillgs, 10th Europe(1II COlllerence 011 Composite Prasad Potluri, Dr Yong Jiang and Dr Raj Ramgulam Malerials (ECCMIO), ComposiTes fo r Fllture. Brugge. for their contribution in the development of modelling Belgium. 2002. 14 Kawabata S. Niwa M & Kawai H, The finite-deformation and software for woven fabric structure and theory of plain weave fabrics: Part II-The uniaxial mechanics. deformation theory, J Text /lIst, 64( 1973) 47-61, 15 Dastoor PH. Ghosh T K. Batra S K & Hersh S P, Computer References assisted structural design of industrial woven fabrics. Part 1 Extrellle TeXT iles, edited by M McQuaid (Princeton III-Modelling of fabric uniaxial/biaxial load-deformation. J Architectural Press. New York, USA), 2005. Text Illsl. 85 (1994) 135-157,