Modelling of the geometry of
weft-knitted fabrics
Maarten Moesen, Stepan Lomov, Ignaas Verpoest
Department 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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“WiseTex ” software
family
Predictive
models of
composites
mechanics
Models of textile geometry
and deformability
FE packages
Predictive models of
textile permeability
ANSYS
I-DEAS
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WiseTex textiles
Woven
Braided
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Laminates
Knitted
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Non crimp
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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
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• Knitting type
Purl, rib, interlock
• Stitch type
Plain, float, tuck,
no stitch(empty)
• Knitting scheme
Leicester notation
Front/Back pattern
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Easy to draw!
Loop parameters
• Average yarn
diameter
• Relative to yarn
diameter:
Stitch width A
Stitch height B
Loop width L
Leg opening K
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Algorithm
1. Check correctness of knitting
scheme
2. 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
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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)
rib
plain
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different
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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
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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: Interpenetration 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
calculated parameters
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2003 unit cell
of the
fibres
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Glass/epoxy composite
1
2
θ
7
6
5
4
3
2
1
0
Ex
Ey
0 5.76
4.9
15
5.7 4.95
30 5.54
5.1
45 5.32 5.31
60 5.11 5.53
75 4.96
5.7
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4.9 5.76
Ex
Ey
Gxz
Gxy
0
15
30
GPa
Ez
Gyz
Gxz
Gxy ν yz ν zy
4.77 1.95 2.44 2.12 0.281 0.289
4.77 1.98 2.41 2.12 0.282 0.293
4.77 2.05
2.3 2.11 0.285 0.305
4.77 2.17 2.17
2.1 0.289 0.322
4.77
2.3 2.06 2.11 0.293 0.339
4.77
2.4 1.98 2.11 0.296 0.353
4.77 2.45 1.95 S.V.Lomov
2.12 0.297 0.358
45
ν zx
0.358
0.353
0.34
0.322
0.305
0.293
0.289
Gyz
60
ν xz
0.297
0.295
0.293
0.289
0.285
0.282
0.281
teta, °
75
90
ν xy
0.239
0.24
0.246
0.255
0.266
0.278
0.281
ν yx
0.28
0.277
0.267
0.255
0.246
0.24
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0.239
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
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