BUCKLING OF WOVEN FABRICS

Crushed Or Bent Under A Weight Or Force

BUCKLING……… In engineering science, buckling is a failure

mode characterized by high compressive stress at the point of failure when it is more than the ultimate compressive stresses the material is capable of withstand

The mode of failure is also called ’Elastic inability’

It is very common phenomena when we are using the fabric as a garment

FABRIC BUCKLING....

The simplest form of fabric buckling is known as

PLATE BUCKLING

Woven fabrics and buckling

We will try to find out……

Simple model of woven fabric bucklingPossibilities of modification of simple modelGlimpse of 3d-fabric modeling using buckling model

EARLIER WORKs....Dahlberg, B., Mechanical Properties of

Textile Fabrics, Part II: Buckling,Textile Research Journal 1961 31: 94

Lindberg, J., Behre, B. and Dahlberg, B., Shearing and Buckling of Various Commercial Fabrics, Textile Research Journal 1961 31: 99

Lindberg, J., Dimensional Changes in Multi Component Systems of Fabrics: A Theoretical Study , Textile Research Journal 1961 31: 664

SIMPLE MODEL OF WOVEN FABRIC AND BUCKLING....Woven fabric consist of two regions..

We have to overcome the Frictional Couple ( ) to bend the fabric

1. Intersection region where yarns are in

tension

2. Region between two intersection where fibers of yarn are in tension

Grosberg, P., The Mechanical Properties of Woven Fabrics : Part II: The Bending of Woven Fabrics; Textile Res. J~36(3) (1966)

ELASTIC BUCKLINGEuler’s equation of critical load when both ends

are clamped

For this simply supported beamBending moment at A=Curvature at A =So…

Integrating this we get....

Behera,B. K., Hari, P. K., Woven Textile Structure: Theory and application; W. P. L., 2010

y

α x

P

P

A

B

O

s

φ

Now let..

Contd.…

So , at point O

And at point B

And

Substituting these values we get

y

α x

P

P

A

B

O

s

φ

Behera,B. K., Hari, P. K., Woven Textile Structure: Theory and application; W. P. L., 2010

At B, s=l/2, θ=0 ; l =Total length of beam

Contd.…

Now if α→0, k=0, F=π/2;

This gives the minimum critical load ( )

Now for compression

y

α x

P

P

A

B

O

s

φ

We KnowSo,

As, at B , ф=0, x=x/2)

Behera,B. K., Hari, P. K., Woven Textile Structure: Theory and application; W. P. L., 2010

So the fractional compression is:Contd.…

Load

P

l^2/B

Compression 1-x/l

10

9

Behera,B. K., Hari, P. K., Woven Textile Structure: Theory and application; W. P. L., 2010

IDEAL FABRIC BUCKLINGP

P

A

A’

αK →

M ↑

M0

The length will follow the elastic buckling

Grosberg, P., Swani, N.M., The Mechanical Properties of Woven Fabrics : Part III: The Buckling of Woven Fabrics; Textile Res. J~36 (1966)

IDEAL FABRIC BUCKLINGFor elastic buckling

So, P

P

A

A’

α

Now, total length of fabric is

This equation is a quadratic equation of can be solved for

different values of αIf

Grosberg, P., Swani, N.M., The Mechanical Properties of Woven Fabrics : Part III: The Buckling of Woven Fabrics; Textile Res. J~36 (1966)

P

P

A

A’

α

IDEAL FABRIC BUCKLING Compressed height of this fabric model…

will follow the elastic body equation

Total compressed height

Fractional compression ( )

Grosberg, P., Swani, N.M., The Mechanical Properties of Woven Fabrics : Part III: The Buckling of Woven Fabrics; Textile Res. J~36 (1966)

CLAMPED FABRIC BUCKLINGBuckling equations..

=

As we are considering the fabric ends are clamped during buckling, simple modification of these equations is

needed For clamped beam orSo, and

Grosberg, P., Swani, N.M., The Mechanical Properties of Woven Fabrics : Part III: The Buckling of Woven Fabrics; Textile Res. J~36 (1966)

RECOVERY FROM BUCKLING

Fabric starts recovering when bending moment reduced by

Grosberg, P., Swani, N.M., The Mechanical Properties of Woven Fabrics : Part III: The Buckling of Woven Fabrics; Textile Res. J~36 (1966)

BUCKLING CURVE….

Theoretical vs. Experimental Buckling curve

Theoretical Buckling Curve

Grosberg, P., Swani, N.M., The Mechanical Properties of Woven Fabrics : Part III: The Buckling of Woven Fabrics; Textile Res. J~36 (1966)

EFFECT OF VARIOUS PARAMETERS

Variation of Buckling load with gauge length

Grosberg, P., Swani, N.M., The Mechanical Properties of Woven Fabrics : Part III: The Buckling of Woven Fabrics; Textile Res. J~36 (1966)

Experimental and theoretical variation of hysteresis in

buckling

CottonWorstedWool/TeryleneWool/Acrylan

Experimental and Theoretical variation of % compression

remaining with M0

CottonWorsted

CROSS CHECKING OF MODEL….

Variation of Frictional resistance

between two methods

Variation of Bending rigidity

between two methodsGrosberg, P., Swani, N.M., The Mechanical Properties of Woven Fabrics : Part III: The

Buckling of Woven Fabrics; Textile Res. J~36 (1966)

SCOPE OF MODIFICATION….

Fabric initial curvature is zero…

P

P

A

A’

α

Effect of fabric weight…

NormallyThe effect of fabric

weight is neglected

because the ratio of weight to

bending rigidity is negligible

Direction of applied force…

Yarn and fiber properties…Modeling taking

various practical aspects…

NONLINER BUCKLING….Infinitely large initial bending rigidity of the fabric is removed by Huang’s bilinear bending rule.

If B*=0, then it follows the Grosberg, P., Swani N. M. Model

Anandjiwala , R. D. & Gonsalves, J. W., Nonlinear Buckling of Woven Fabrics Part I: Elastic and Nonelastic Casess; Textile Res. J~76:160 (2006)

NONLINER BUCKLING….

Anandjiwala , R. D. & Gonsalves, J. W., Nonlinear Buckling of Woven Fabrics Part I: Elastic and Nonelastic Casess; Textile Res. J~76:160 (2006)

Anandjiwala , R. D. & Gonsalves, J. W., Nonlinear Buckling of Woven Fabrics Part II: Recovery from Buckling and Experimental Verification; Textile Res. J~76:160 (2006)

Other Works on BUCKLING….Buckling of Woven Fabrics : Part I: Effect of Fabric WeightT. G. Clapp and H. Peng, Textile Research Journal, 1990:60:228

Buckling of Woven Fabrics : Part II: Effect of Weight and Frictional CoupleT. G. Clapp and H. Peng, Textile Research Journal, 1990:60:285

Buckling of Woven Fabrics : Part III: Experimental Validation of Theoretical ModelT. G. Clapp and H. Peng, Textile Research Journal, 1990:60:641

Buckling Analysis of woven Fabric Under Simple Shear along Arbitrary DirectionsY. T. Zhang and J. F. Xu, Textile Research Journal, 2002:72:147

BUCKLING & FABRIC…. Modeling and animating the

garments worn by virtual characters

DIAMOND BUCKLING TWIST BUCKLING

Decaudin, P., Thomaszewski, B., Cani ,M. P., Virtual Garments Based on Geometric Features of Fabric Buckling ; INRIA , April (2005)

Real fabric show that whatever the fabric thickness and the cylinder’s radius, the number of diamond patterns that appear around a cross-section of the cylinder is always an integer say n.

In their experiments with real fabric, n varies from 2 to 8 with a cylinder of a few centimeters of radius and different thickness of cloth

the height b of the diamond patterns is also related to the radius R and to the physical properties of the fabric λ

Cylindrical fabric of known radius R0 around a slightly smaller rigid cylinder and observe Diamond buckling and get the associated value n0 get λ

PARAMETERS…

Decaudin, P., Thomaszewski, B., Cani ,M. P., Virtual Garments Based on Geometric Features of Fabric Buckling ; INRIA , April (2005)

FABRIC MODLLING….

Decaudin, P., Thomaszewski, B., Cani ,M. P., Virtual Garments Based on Geometric Features of Fabric Buckling ; INRIA , April (2005)

Grosberg, P., Swani, N.M., The Mechanical Properties of Woven Fabrics : Part III: The Buckling of Woven Fabrics; Textile Res. J~36 (1966)

Decaudin, P., Thomaszewski, B., Cani ,M. P., Virtual Garments Based on Geometric Features of Fabric Buckling ; INRIA , April (2005)

Behera,B. K., Hari, p. K., Woven Textile Structure: Theory and application; W. P. L., 2010

Anandjiwala , R. D., Gonsalves, J. W., Nonlinear Buckling of Woven Fabrics Part I: Elastic and Nonelastic Cases ; Textile Res. J~76(2) (2006)

REFERENCES….

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