TechTextil 2003 S.V.Lomov 1

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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WiseTex textiles

Woven

Braided Non crimp

Laminates

Knitted

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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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Hexagonal grid (2)

plain

rib

different stitches

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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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Variability of structures

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Variability of loop parameters

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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

2

0

1

2

3

4

5

6

7

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

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WeftKnit demo

http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm