1-s2.0-S1359835X11001059-main

Modelling approach for the prediction of stitch influence during woven fabric drapingM.Duhovic a ,⇑,P.Mitschang a ,D.Bhattacharyya ba Institute for Composite Materials (IVW GmbH)Erwin-Schrödinger-Straße,Geb.5867663Kaiserslautern,GermanybCentre for Advanced Composites Materials,The University of Auckland Building 740,Tamaki Campus,Morrin Rd Glen Innes Private Bag 92019,Auckland,New Zealanda r t i c l e i n f o Article history:Received 26November 2010Received in revised form 28March 2011Accepted 29March 2011Available online 1April 2011Keywords:A.Fabrics/textilesC.Finite element analysis (FEA)E.Stitching E.Forminga b s t r a c tThe following paper focuses on the development of an accurate and efficient modelling approach for the prediction of fibre angles in woven reinforcements resulting from the influence of localised stitching pat-terns.The modelling procedure involves a process of calibration valid for both dry and wet woven fabric preform materials and has been carried out using the explicit finite element analysis code LS-DYNA.The details and capabilities of the model are discussed and comparisons are made with real fibre angle mea-surements taken from dry fabric hemispherical dome and three dimensional test shape forming experi-ments,under the influence of different stitch patterns.The current model demonstrates a high level of functionality allowing accurate prediction of yarn and stitch pattern movement as well as stresses and strains.Full-scale forming simulations for any desired sheet forming scenario can be performed within reasonable timeframes.Ó2011Elsevier Ltd.All rights reserved.1.IntroductionWoven fabrics are one of the most widely used of all textile reinforcement structures in polymer based fibre reinforced com-posite materials.The effective modelling of the forming properties of woven fabric polymer composite materials has been the focus of research for more than a decade.Perhaps the most important pre-diction for these materials is their resulting fibre orientations.This is because it is very important to be able to predict the drapability or the formation of wrinkling defects during the manufacture of components.The resulting fibre orientations also influence a whole host of other properties including fabric permeability and final component strength.Stitching is the most common method of joining or creating localised areas of reinforcement in dry composite prepregs.In par-ticular,stitching can be used to solve a number of important com-posite manufacturing issues such as the connection of layers of reinforcement fabric in the thickness direction,the creation of three dimensional reinforcement structures from two dimensional forms,and to provide a tailored connection medium between com-posite and non-composite elements in multi-material components.The flexibility of stitching can also lend itself to in-plane localised reinforcement.In the case of woven reinforcements,in-plane local-ised stitching at the manufacturing stage can help control yarn fi-bre angles and distribute strains in order to help avoid wrinkling.The placement of in-plane localised reinforcement for the control of yarn fibre angles during manufacturing is currently a costly trial and error process.The component is first formed without any stitch-ing at all and patterns are then trialled and tweaked based on obser-vations and measurements.Even for simple geometries it becomes less than intuitive to guess the appropriate pattern and placement position of the in-plane stitching to achieve the desired result.The current work is an attempt to devise the methodologies and tools required to eliminate the trial and error process and to make the process of pattern selection and placement faster and easier.The simulation of woven textile composite sheet forming contin-ues to be an intensely researched topic.Key research groups around the world include most prominently those in France led by Boisee [1–8]and Cherouat et al.[6,9–11];Belgium,Lomov and Verpoest et al.[12–15];as well as the UK and China,Clifford,Long,Harrison and Peng [16–19].These research groups continue to support the development of material modelling techniques for composites forming simulation software such as ESI’s PAMFORM,LSTC’s LS-Dyna and Simulia’s Abaqus/Explicit,amongst other leading FEA codes.Other notable efforts in the field include works by ten Thije,Sutcliffe,Pickett and Ramakrishna [20–23].In a recent article by Sar-gent et al.[24]several of the aforementioned groups,including two more from the US have been brought together in a collaboration which compares results of outputs such as fabric draw-in and result-ing shear angles following the simulated stamping of prescribed test geometry.Until now however,an efficient model which can incor-porate the influence of stitching on fabric behaviour has to the best of the authors’knowledge not yet been explored.1359-835X/$-see front matter Ó2011Elsevier Ltd.All rights reserved.doi:10.1016/positesa.2011.03.025Corresponding author.Tel.:+496312017363;fax:+496312017199.E-mail address:miro.duhovic@ivw.uni-kl.de (M.Duhovic).Various approaches to the modelling of woven fabric deforma-within reasonable timeframes.Models are also being developed at thefibre/filament level(microscale)[38],but currently require enormous amounts of computing power to consider anything other than the material on a unit cell basis.In the study carried out by Sidhu et al.[28],afinite element model which gives very accurate predictions of the resultingfibre orientations is developed using a well thought-out arrangement of beam and shell elements.A good review of the modelling ap-proaches taken by various researchers up to the date of their pub-lication is also given.Their review is clear to highlight that no model to date has considered inter-tow sliding and that very few models have takenfibre jamming into account[28].A similar ap-proach is taken by Yu et al.[29]where a‘‘restrained membrane model’’is proposed.This also utilises a combination of beam and shell(membrane)elements implemented byfinite element model-ling(FEM)simulation.The model provides a very good description of the experimental results,both tensile forces and shear angles, using empirical inputs,however,the model does not consider in-ter-tow sliding.In more recent work[34–36],the focus moves to-wards mesoscale models which provide greater detail with regards to the fabric geometry as the yarns here are modelled explicitly. However,it becomes difficult to model non-symmetric stitch con-figurations efficiently on a unit cell basis as the stitches can occur at any location and orientation.The examination of macroscale properties using a mesoscale model which includes the influence of stitches is currently considered too demanding with respect to model setup and solving time.2.Model descriptionThe current macroscale modelling approach builds on the ideas of Sidhu et al.[28].The FEM model uses a combination of shell and truss elements connected together at common nodal points in or-der to represent the behaviour of the woven fabric material.In thisTable1Fictitious material/matrix properties.Property Valuea Tensile modulus,EA,B,C(compression behaviour)5.2083eÀ04GPaPoisson’s ratio,P r BA,CA,CB0.20a Shear modulus,GAB,BC,CA1.4356eÀ02GPaa Simplified stress–straincurve(tension behaviour)r(GPa)e(mm/mm)0.000.007.8125eÀ050.15(initial jamming)7.3438eÀ040.23(final jamming)8.4863eÀ030.50b Thickness offictitiousmaterial(calibrated)0.32mm(0.0115mm)a Value calculated from fabric only specimen tensile tests.b Initial value for the thickness of thefictitious layer set to actual fabric thickness.Table2Yarn characteristic properties.Yarn property ValueYarn size:E-glass,Kevlar49204tex,127texDensity:E-glass,Kevlar49 2.54eÀ06kg/mm3,1.44eÀ06kg/mm3a Tensile modulus,E of crimped yarn in fabric forboth E-glass and Kevlar492Â2twill17.5GPa(Fibre112GPa,72GPa)b Cross sectional area,A:E-glass,Kevlar49(calibrated for both)0.08mm2,0.09mm2(0.00288mm2)Poisson’s ratio,P r0.30a Value calculated from fabric only specimen tensile tests.b Initial value for yarn cross sectional area set to actual yarn cross sectional area.M.Duhovic et al./Composites:Part A42(2011)968–978969approach,the truss elements are used to model the properties of the yarns or tows,while the shell elements represent afictitious medium that takes into account the stiffness due to interyarn scis-soring,sliding,andfibre jamming.Thefictitious medium can also be used to describe the effects a surrounding molten polymer ma-trix has on the yarn movement when dealing with thermoforming of preimpregnated materials.This is made possible by assuming that in both the cases of dry fabric draping and organosheet form-ing,the material behaviour is governed by the in-plane movement of the yarns,primarily in the form of yarn rotation(scissoring), yarn slippage and yarn jamming.For dry fabric draping it is as-sumed that the restriction to this movement comes from a combi-nation of the friction forces between individualfilaments and yarns coupled with yarn compression(fibre jamming).For an organosheet material during forming,where the yarns andfibres and Harrison[39–42]is not taken here.Rather,the input for this aspect of the material’s behaviour takes on the form of a stress–strain curve which is assigned to the shell elements present in thefinite element model.In this way,the movement of the yarns can be simulated whether they are restricted only by friction or by the presence of a molten polymer at different temperatures. In addition,the specific material models[43]assigned to the shell and truss elements account for the overall behaviour of the woven fabric material without the need to consider contact definitions within the fabric itself.For the efficient consideration of stitches,simple elements are again used together with a material model which considers the key parameters of stitch behaviour(e.g.stiffness,breaking strength,slack,and initial tension)[43].The stitching elements interact with the fabric through special contact definitions[43] so as to remain independent of the fabric mesh density and there-fore do not require connection to common nodal points.A form of tied contact offered by the LS-DYNA code,usually used to model spot welds and to tie shell edges to surfaces has been used.This type of contact interface uses a kinematic constraint method to tie the slave nodes on the ends of the stitch elements to the master segments on the shell elements representing the scissoring,sliding and jamming behaviour of the fabric in the directions as indicated in Fig.1.The formulation considers both translational and rota-tional degrees-of-freedom.During the actual simulation,the tied interface constraint is applied byfirst distributing the nodal forces and nodal mass of each stitch element slave node,n s to the four master nodes,n m defining the shell segment containing the contact point as shown in Fig.1.Note once again as described in Section2, that the master nodes,n m on the shell and beam elements defining the fabric are shared.Mathematically this can be expressed as shown in the following equation.D f im¼/iðn c;g cÞf sð1Þwhere f s is the force vector of the slave node and/i(n c,g c)is a weighting function based on the location of the contact point.A similar equation holds for the mass.For each time step,the incre-ments of mass and force for each stitch are added to the mass and force vectors of the master surface.After summation of all the stitch nodes is complete,the acceleration of the master surface is computed and the acceleration of the slave node on the stitch is then interpolated from the master segment containing the stitch contact as shown in the following equation.a iðsÞ¼X4j¼1/jðn c;g cÞa j ið2ÞNodal velocities and displacements are then updated in the nor-mal way.The interpolated contact point(n c,g c)for each stitch slave node is computed only once since its relative position on the mas-ter segment remains constant for the duration of the simulation.Coordinate data for the desired stitch patterns can be generated in any CAD software and imported automatically into the simula-tion through the spot weld generation interface.This creates zero-length stitching elements which are then adjusted to the cor-rect length by operating on the simulation inputfile using an auto-mated spreadsheet created in Microsoft Excel containing the desired stitch length and stitch direction vectors.3.Defining physical parameters3.1.Fictitious material/matrixThe implicit simulation of yarn interactions is made possible by considering the stiffness response of the fabric(initially without any stitching)due to a combination of yarn scissoring,sliding,Fig.3.Cable material model parameters used to describe lock stitch behaviour.Fig.4.Experimental stitched and unstitched dry fabric tensile test curves.970M.Duhovic et al./Composites:Part A42(2011)968–978and jamming.The material law can be simplified into a tri-linear stress–strain curve as shown in Fig.2.The dominant mechanisms are identified up to key values of strain which are based on the ini-tial andfinal yarn jamming angle.The information required to de-fine the material law can be obtained by performing tensile tests on single layer±45°fabric or composite specimens.The initial jam-ming angle can also be calculated analytically as shown by Sidhu et al.[28],using parameters derived from the fabric geometry.This information was then implemented using shell membrane ele-ments and the airbag fabric material model available in LS-DYNA [43].The material behaviour can be assigned in one(ICOMP=0) or both directions(ICOMP=1)of the shell elements,also shown schematically in Fig.2.The key parameters extracted from the shear deformation tensile test are summarised in Table1.Note that the modulus for the compression behaviour has been taken as the smallest stiffness measured in tension while the shear modulus has been calculated as half of the largest stiffness value measured in tension.Due to the nature of the shell and beam element con-nectivity the Poisson’s ratio has a negligible effect on the materialbehaviour and should be set to a typical value to ensure stability.3.2.YarnsA beam element truss formulation together with a simple linear elastic material model was used to represent the longitudinal behaviour of the yarns in the fabric.The material properties as-signed are given in Table2.Following tensile tests of fabric speci-mens in the0–90configuration,a straight line approximation to the linear portion of the curve was made and this value then used as the tensile modulus of the crimped yarn.3.3.Stitches loading.The actual values used for the aforementioned parame-ters are a function of the type and size of the yarn used for the stitches as well as the stitching machine parameters.To obtain the correct quantitative values,the force displacement response of fabric specimens with and without stitching were compared and the data for only the stitching was then isolated.Parameters for the various stages of stitch deformation were then obtained from these curves.These parameters can be compared to the ac-tual stiffness,strength,and elongation at break of the yarns used for the stitching which would in fact represent the limits of the properties that can be achieved by the stitch.For example,if the elongation at break of thefibre(Nomex)used to create the stitch is17.8%,then we would expect the stitch itself to exhibit an overall elongation greater than this value.Likewise,the tensile modulus and strength of the stitch are expected to be much lower than that of the yarn orfibre.4.Material characterisation and model verificationBefore simulations of complex three dimensional parts could be considered,a number of calibration and verification simulations were performed using simple geometries.Firstly,physical tensile tests on single-layered two dimensional fabric strip specimens with and without centreline stitching were carried out.Force displace-ment data,centrefibre angle,stitch elongation,and the overall gen-eral deformation pattern for both types of specimens were measured and recorded.Once the two dimensional properties were satisfied,three dimensional verification in the form of dome forming tests were carried out.This was performed on square sheet speci-mens,again made from a single layer of fabric,cut to two different fibre orientations(0/90°and±45°).Specimens in the0/90°configu-ration were tested in the presence of several stitch patterns which showed the most significant influence on the deformation behaviour of the fabric.For these specimens,both the fabric and stitch defor-mation behaviour were compared.Following the successful calibra-tion,tool geometry,blank size,and stitch pattern type and placement were modified to test any desired sheet forming scenario.4.1.Two dimensional forming4.1.1.Physical experimentsSpecimens taken from2Â2twill weave material comprised of a mixture of glassfibre and Kevlar49yarns with a yarn ratio of2:1 respectively,were cut to a±45°orientation and tested in tension to obtain the stress–strain data which was then used to define the parameters of the material model applied to the shell elements.Fig.5.Force displacement curves of stitch behaviour for single and double layer specimens.Table3Stitch characteristic properties.Stitch property ValueStitch material Amann Nomex70/3(Gray) Stitch type301lock stitchLinear density160Â3dtexa Material density 1.38eÀ06kg/mm3b Average elongation at break27.20%(Fibre17.80%)b Tensile modulus,E93MPa(Fibre17GPa)Stitch size3mmTensile strength of stitching yarn496MPa(1737cN)b Initial tensile force(pretension),F00kNVolume,VOL0.105mm3b Offset,(slack)19.00%(À0.57mm)Cross sectional area,CA0.035mm2Note:All other values taken from Nomex70yarn datasheet provided by Amann Nähgarne GmbH&Co.a Value retrieved from DuPont’s Nomexfibre technical guide and Matweb.b Value calculated from stitched fabric specimen tensile tests.M.Duhovic et al./Composites:Part A42(2011)968–978971The distinct difference in colour between the two yarns (yellow forglass)allowed for much easier measure-shear angles in the specimens Aver-three different sets of dry fabric tests temperature were generated and are shown average of the unstitched single layer stitched single and stitched double layer that the shapes of the curves follow one shown in Fig.2.The curves sug-of the fabric is extended by the pres-approximately 3%,while the maximum failure same increase in strain was also ob-specimens.The parameters required for the stitching elements were ob-tained by considering the difference of each type of sample with and without The force displacement curves showing are presented in Fig.5.In the current parameters to be extracted are the offset sile force (pretension),elongation stitch (tensile modulus).It can be seen in Fig.5that for both the single and imens,very little load take-up is developed also indicates the absence of any pretension types of specimens then exhibit linear failure strain of approximately 27%.The Fig.6.Experimental and numerical tensile test curves for plain and 2Â2twill weaves.the curve are summarised in Table3.For describing more complex types of stitch behaviour,the assignment of a stress–strain curve is also possible.4.1.2.Numerical simulationThefirst set of simulationstensile tests carried out for thedata obtained from the physicalPrior to this,force displacementusing the dry fabric data given inallowed the concurrentphysical experiments on anyalso provided the data todifferent characteristics could beinput parameters.Thement curves for the twotogether in Fig.6.It can be seental curves for both are in goodthe parameters taken from therial behaviour wasfirst(ICOMP=0).It is shown in Fig.6iour to both(perpendicular)(ICOMP=1)further improvedall simulations thereafter.Thisscenarios could also beThe compression behaviourand investigated.This was takenculated from the simplifieda sensitivity study on thisany significant influence on theunless very large unrealisticbehaviour of the material in thepath taken by the loadingthe unloading stress–strainnot required to follow the sameway hysteresis of the materialThe second way to ensurefor the two dimensionalangle versus the strain ofimen.Fig.7shows the change incentre of the specimen,againmeasurements taken from theplied material models.Thenumerical and physical tensileother in Fig.8a–d.For clarity ofKevlar49yarns have beenmation pattern of the simulatededge effects of the specimento slide apart severely.4.2.Three dimensional forming4.2.1.Physical experimentsTo provide a basis for three250mm square sheet specimenssingle layer specimens wereforming a70mm diameterproduced incorporating asigned to influence the shearrial.Details of the physicaltogether with stitch patternment techniques are discussed innar and Mitschang[44,45].Thisinformation for verifying thedimensional forming numerical 4.2.2.Numerical simulationFollowing on from the material model development presented in Section4.1,a comparison of the three dimensional deformation behaviour of a selection of dry fabric specimens with and without8.Image overlay of overall deformation pattern of experimental and simulatedfabric tensile specimen(a)0%strain,(b)10%strain,(c)20%strain and(d) strain.(For interpretation of the references to colour in thisfigure legend,the reader referred to the web version of this article.)M.Duhovic et al./Composites:Part A42(2011)968–978973Fig.10.Dome forming measurement template[44,45].have been placed on them by the stitching.However,due to the variations that exist in the experimental angle measurements in the different stitched specimens shown in Figs.11and12(between 5–10%),it is difficult to verify whether the shape of the scissoring dome specimen between points1and6is approximately16% and28%respectively.While it is unreasonable to ever expect an exact prediction of the yarn crossover angle in such a complex 3D forming case,it is believed that a more detailed treatment ofFig.11.Dome formingfibre angle measurements.Fig.12.Dome forming stitch slack studyfibre angle measurements.M.Duhovic et al./Composites:Part A42(2011)968–978975Fig.13.Bias extension force-strain curves over a range of forming temperatures.Fig.14.Actual thermoformed multicavity test geometry showing yarn crossover angle measurement locations.(For interpretation of the references to colour in thisfigure legend,the reader is referred to the web version of this article.)Fig.15.Simulated stitch influence on the deformation behaviour of the thermoformed legend,the reader is referred to the web version of this article.)tests and used to measure and comparefibre angles at certain locations.A complete mapping comparison was also performed in the same way as shown in Fig.8a–d.A camera system linked to the tensile testing machinery again allowed the force dis-placement data to be correlated with the recorded images of specimen deformation.Fig.14shows the yarn crossover angle measurement template ferent regions could yet be another way of controlling the yarn crossover angles during forming.The possibility of such a simula-tion is however left for future work.5.Conclusionsparison of experimental and simulated shear angle measurements170°C.M.Duhovic et al./Composites:Part A42(2011)968–978977measurements of the shear angle versus strain and force versus strain.Three dimensional verifications can then be carried out using the basic hemispherical dome geometry.Once the behaviour of the given material has been verified,simulations can be per-formed on more complex geometries of up to0.25m2in size with-in reasonable timeframes on standard level computing resources. Different types of stitch patterns can then be trialled in regions where shear deformation is most prominent and pattern shape and location can be selected based on these results.The present work has demonstrated the feasibility of such an FEA model for the efficient prediction of stitch pattern influence.Furtherfine tun-ing of the modelled stitch behaviour and the establishment of a material model database is expected to give useful information for composite parts produced in this way.AcknowledgmentsThe authors would like to thank the German Research Founda-tion(DFG)for supporting the project‘‘Drapierung’’(MI647/14–2) and in addition,the Foundation for Research Science and Technol-ogy(FRST)New Zealand for theirfinancial support during the course of the project.References[1]Boisse P,Zouari B,Gasser A.A mesoscopic approach for the simulation ofwovenfibre composite pos Sci Technol2005;65:429–36.[2]Zouari B,Daniel JL,Boisse P.A woven reinforcement forming simulationmethod influence of the shear put Struct2006;84:351–63. [3]Boisse P,Hamila N,Vidal-SalléE,Dumont F.Simulation of wrinkling duringtextile composite reinforcement forming influence of tensile,in-plane shear and bending pos Sci Technol2011;71:683–92.[4]Boisse P,Gasser A,Hivet G.Analyses of fabric tensile behaviour:determinationof the biaxial tension–strain surfaces and their use in forming simulations.Composites Part A2001;32(10):1395–414.[5]Allaoui S,Boisse P,Chatel S,Hamila N,Hivet G,Soulat D,Vidal-Salle E.Experimental and numerical analyses of textile reinforcement forming of a tetrahedral posites Part A2011;42(6):612–22.[6]Soulat D,Cherouet A,Boisse P.Simulation of continuousfibre reinforcedthermoplastic forming using a shellfinite element with transverse stress.Comput Struct2006;84:888–903.[7]Hamila N,Boisse P.Simulations of textile composite reinforcement drapingusing a new semi-discrete three nodefinite posites Part B 2008;39:999–1010.[8]Vidal-SalléE,Nguyen QT,Charmetant A,Bréard J,Maire E,Boisse e ofnumerical simulation of woven reinforcement forming at mesoscale:influence of transverse compression on the global response.Int J Mater Form 2010;3(1):699–702.[9]Giraud-Moreau L,Cherouat A,Borouchaki H.Adaptive remeshing of compositefabrics during the forming process.Int J Mater Form2010;3(1):659–62. [10]Cherouat A,Borouchaki H,Giraud-Moreau L.Mechanical and geometricalapproaches applied to composite fabric forming.Int J Mater Form 2010;3(2):1189–204.[11]Cherouat A,Radi B,El Hami A.The frictional contact of the composite fabric’sshaping.Acta Mech2008;199:29–41.[12]Willems A,Lomov SV,Verpoest I,Vandepitte D,Harrison P,Yu WR.Formingsimulation of thermoplastic commingled woven textile on a double dome.Int J Mater Form2008;1(1):965–8.[13]Vanclooster K,Lomov SV,Verpoest I.Simulating and validating the draping ofwovenfiber reinforced polymers.Int J Mater Form2008;1(1):961–4.[14]Vanclooster K,Lomov SV,Verpoest I.Simulation of multi-layered compositesforming.Int J Mater Form2010;3(1):695–8.[15]Lomov SV,Verpoest I.Model of shear of woven fabric and parametricdescription of shear resistance of glass woven pos Sci Technol2006;66:919–33.[16]Peng XQ,Guo ZY,Rehman Zia-Ur,Harrison P.A simple anisotropicfiberreinforced hyperelastic constitutive model for woven composite fabrics.Int J Mater Form2010;3(1):723–6.[17]Lin H,Wang J,Long AC,Clifford MJ,Harrison P.Predictive modelling foroptimization of textile composite pos Sci Technol 2007;67:3242–52.[18]Cao J,Xue P,Peng X,Krishnan N.An approach in modeling the temperature effectin thermo-stamping of woven put Struct2003;61:413–20. [19]Peng X,Ding F.Validation of a non-orthogonal constitutive model for wovencomposite fabrics via hemispherical stamping posites Part A 2011;42:400–7.[20]ten Thije RHW,Akkerman R.Finite element simulations of laminatedcomposites forming processes.Int J Mater Form2010;3(1):715–8.[21]Skordos AA,Sutcliffe MPF.Stochastic simulation of woven composites forming.Compos Sci Technol2008;68:283–96.[22]Pickett AK.Review offinite element simulation methods applied tomanufacturing and failure prediction in composites structures.Appl Compos Mater2002;9:43–58.[23]Lim TC,Ramakrishna S.Modelling of composite sheet forming:A review.Composites Part A2002;33(4):515–37.[24]Sargent J,Chen J,Sherwood J,Cao J,Boisse P,Willem A,et al.Benchmark studyoffinite element models for simulating the thermostamping of woven-fabric reinforced composites.Int J Mater Form2010;3(1):683–6.[25]Robertson RE,Hsiue ES,Sickafus EN,Yeh GSY.Fiber rearrangements during themolding of continuousfiber composites.I.Flat cloth to a hemisphere.Polym Composite1981;2:126–31.[26]Bickerton S,Simacek P,Guglielmi SE,Advani SG.Investigation of draping andits effects on the moldfilling process during manufacturing of a compound curved composite posites Part A1997;28A:801–16.[27]Rudd CD,Middleton V,Owen MJ,Long AC,McGeehin P,Bulmer LJ.Modelingthe processing and performance of preforms for liquid molding processes.Compos Manuf1994;5:177–86.[28]Sidhu RMJS,Averill RC,Riaz M,Pourboghrat F.Finite element analysis of textilecomposite preform pos Struct2001;52:483–97.[29]Yu X,Zhang L,Mai Y-W.Modelling andfinite element treatment of intra-plyshearing of woven fabric.J Mater Process Tech2003;138:47–52.[30]Yu X,Cartwright B,McGuckin D,Ye L,Mai Y-W.Intra-ply shear locking infiniteelement analyses of woven fabric forming posites Part A 2006;37:790–803.[31]Sharma SB,Sutcliffe MPF.A simplifiedfinite element model for draping ofwoven posites Part A2004;35:637–43.[32]Skordos AA,Monroy Aceves C,Sutcliffe MPF.A simplified rate dependentmodel of forming and wrinkling of pre-impregnated woven composites.Composites Part A2007;38:1318–30.[33]Yua X,Zhanga L,Mai Y-W.A mesoscopic approach for the simulation of wovenfibre composite pos Sci Technol2005;65:429–36.[34]Lin H,Clifford MJ,Long AC,Sherburn M.Finite element modelling of fabricshear.Modell Simul Mater Sci Eng2009;17:1–16.[35]Creech G,Pickett AK.Meso-modelling of non-crimp fabric composites forcoupled drape and failure analysis.J Mater Sci2006;41:6725–36.[36]Loix F,Badel P,Orgéas L,Geindreau C,Boisse P.Woven fabric permeability:From textile deformation tofluidflow mesoscale pos Sci Technol2008;68:1624–30.[37]Miao Y,Zhou E,Wang Y,Cheeseman BA.Mechanics of textile composites:pos Sci Technol2008;68:1671–8.[38]Hermann F.Numerische simulation der mechanischen Eigenschaften textilerFlächengebilde–Gewebeherstellung.Bamberg:LS-DYNA Anwenderforum;2004. [39]Spencer AJM.Deformation offibre-reinforced materials.Oxford:ClarendonPress;1972.[40]Rogers TG.Rheological characterisation of anisotropic posites1989;20(1):21–7.[41]Christensen RM.Effective viscousflow properties forfibre suspensions underconcentrated conditions.J Rheology1993;37(1):103–21.[42]Harrison P,Clifford MJ,Long AC,Rudd CD.A constituent-based predictiveapproach to modelling the rheology of viscous textile posites Part A2004;35:915–31.[43]Livermore Software Technology Corporation,Hallquist,John O.LS-DYNATheory Manual,March2006;/.[44]Molnar P,Ogale A,Lahr R,Mitschang P.Influence of drapability by usingstitching technology to reduce fabric deformation and shear during pos Sci Technol2007;67:3386–93.[45]Mitschang P,Molnar P.Influencing the drapability of organic sheets duringthermoforming.8th International conference on textile composites (TEXCOMP-8),Nottingham,UK,16–18Oct2006.978M.Duhovic et al./Composites:Part A42(2011)968–978。