Modelling of the geometry of weft-knitted fabrics · • Knitting scheme Leicester notation...
Transcript of Modelling of the geometry of weft-knitted fabrics · • Knitting scheme Leicester notation...
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Modelling of the geometry of weft-knitted fabrics
Maarten Moesen, Stepan Lomov, Ignaas VerpoestDepartment MTM, Katholieke Universiteit Leuven
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Content
• WiseTex textile modelling• Model of the weft-knit geometry• Examples and discussion• Applications to micro-mechanical modelling of
composites• Conclusions
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ANSYS
I-DEAS
“WiseTex ” software family
Predictive models of composites mechanics
Models of textile geometry and deformability
Predictive models of textile permeability
FE packages
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Content
• WiseTex textile modelling
• Model of the weft-knit geometry• Examples and discussion• Applications to micro-mechanical modelling of
composites• Conclusions
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WeftKnit
Features
• Relaxed state of weft-knit fabric
• Approximate geometrical model
• Plain, rib, interlock, purl patterns
• Maximum pattern size 25x25
• 3D imaging
• Definition of yarn properties
• Export as WiseTex family compatible file (*.fab)
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Coding of the pattern
• Knitting typePurl, rib, interlock
• Stitch typePlain, float, tuck, no stitch(empty)
• Knitting schemeLeicester notationFront/Back patternEasy to draw!
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Loop parameters
• Average yarn diameter
• Relative to yarn diameter:
Stitch width AStitch height BLoop width LLeg opening K
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Algorithm
1. Check correctness of knitting scheme2. Calculate in-plane components of anchor points(Topology coding with hexagonal grid)3. Calculate out-of-plane component of anchor points(Energy minimisation with constraints)4. Create yarns by connecting anchor points (B-spline interpolation)
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Hexagonal grid (1)
• Grid consisting of adjacent hexagons, suited for approximating the shape of most kinds of yarn loops (plain loops, floats, tucks).• Grid dimensions are determined by the geometric parameters. • Suited for plain/purl as well as for rib.• Only grid points are candidates for anchor points (Points at which interlacing yarns cross)
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Out-of-plane geometry• ‘Energy’-minimisation with constraints
– Target-function = a quadratic function measuring the curvature in the yarns between the anchor points.
– Constraints = equations defining the out-of-plane structure of the weft knitted fabric.
• E.g. Yarn A is right above yarn B in one anchor point, B is right above A in the next anchor point.
z-coordinates of anchor points along the yarn
distance between centerlines at yarn
crossing
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Content
• WiseTex textile modelling• Model of the weft-knit geometry
• Examples and discussion• Applications to micro-mechanical modelling of
composites• Conclusions
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Limitations: Uncompressible yarns
• Yarns are assumed uncompressible: Calculated knits are more loose than knits with compressible yarns.
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Limitations: Simplified energy function
• Energy function is simplified: height differences are only qualitative. (Here: too large)
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Limitations: Loop shape
• Continuous yarn shape is formed by interpolation between anchor points: loop parts may be more sharp or flat
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Limitations: Inter-penetration of the yarns
• Simplified model: yarns may cut each other:– interlacing zones– interlock fabric
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Content
• WiseTex textile modelling• Model of the weft-knit geometry• Examples and discussion
• Applications to micro-mechanical modelling of composites
• Conclusions
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Glass plain knitted fabric
pattern fibres
calculated parameters of the unit cell
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Glass/epoxy composite
θ1
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0 15 30 45 60 75 90teta, °
Ex Ey GyzGxz Gxy
Ex Ey Ez Gyz Gxz Gxy ν yz ν zy ν zx ν xz ν xy ν yx0 5.76 4.9 4.77 1.95 2.44 2.12 0.281 0.289 0.358 0.297 0.239 0.28
15 5.7 4.95 4.77 1.98 2.41 2.12 0.282 0.293 0.353 0.295 0.24 0.27730 5.54 5.1 4.77 2.05 2.3 2.11 0.285 0.305 0.34 0.293 0.246 0.26745 5.32 5.31 4.77 2.17 2.17 2.1 0.289 0.322 0.322 0.289 0.255 0.25560 5.11 5.53 4.77 2.3 2.06 2.11 0.293 0.339 0.305 0.285 0.266 0.24675 4.96 5.7 4.77 2.4 1.98 2.11 0.296 0.353 0.293 0.282 0.278 0.2490 4.9 5.76 4.77 2.45 1.95 2.12 0.297 0.358 0.289 0.281 0.281 0.239
GPa
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Content
• WiseTex textile modelling• Model of the weft-knit geometry• Examples and discussion• Applications to micro-mechanical modelling of
composites
• Conclusions
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Benefits
• Diversity: – structures: purl, rib, interlock– stitches: plain, float, tuck, empty
• Fast and memory-efficient• Robust• Easy to use• Integrated with WiseTex
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Limitations
• The algorithm is designed to be fast and diverse vis-a-vis knit pattern, while delivering qualitatevly good results.
• … due to simplicity of the model:– No yarn compression.– Max 8 anchor points per loop.– Simplified energy function