Fabric Drape

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4. Fabric drape

4.1 Deformation modes

The fibre configuration in a textile fabric affects the processing properties porosity andpermeability and also the mechanical properties of the finished composites part. Thus the

characterisation of the distribution of fibre angles, caused by local deformation effects, is an

important task in order to describe the manufacture and the performance of the part. Drape is

the deformation of two-dimensional textiles and fabrics caused by gravity or other external

forces for adaptation of the textiles on doubly-curved surfaces. Body forces such as gravity

act directly on the fibres, while contact forces are transferred by friction. The following

deformation modes can occur for textile materials [1].

In a single fabric layer:

Shearing Straightening Wrinkling Stretching SlippingIn a lay-up of several layers:

Slipping of fibre layers, especially at edges of the surface

Figure 4-1. Illustration of the drape modes fibre shear (a), straightening (b), wrinkling (c), stretching (d), slip (e)

and inter-layer slip (f).

a

b

c

d

e

f


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Fabric shear, as discussed e.g. by Skelton [2,3] and Behre [4], occurs, if the directions of

applied tensile forces do not coincide with the orientations of the fibre tow axes. The fibre tow

orientations change, until the fibre axes coincide with the directions of the applied forces, or

until a fabric specific maximum shear angle (locking angle) is achieved. Actual locking

angles as observed experimentally for various glass fibre woven fabrics are in the rangebetween 15 and 35 (Paper C), depending on the fabric architecture. In case of fibre locking,

the fabric starts to wrinkle due to local shear stresses. Aspects of fibre bending and fabric

wrinkling have been discussed by Grosberg and Swani [5] and Dahlberg [6]. Complex

buckling of fabrics has been described and mechanically analysed by Amirbayat and Hearle

[7]. Fabric shear has been found to be in general the most important fabric deformation effect

[8,9]. Fibre straightening with changes in the curvature of fibres under tensile load in general

is the deformation mode to occur first. This effect is significant for knitted fabrics, while for

most low-crimp textile architectures, the effect is low. Elastic fibre stretching is generally of

minor significance, since the reinforcement textiles are normally processed from fibres withhigh elastic tensile modulus. Slipping of the fibre tows can occur at sharp edges or corners of

the surface and is subject to friction in the crossing points. In addition to the effects mentioned

above, secondary effects such as bending and torsion caused by friction between the fibre

tows and compression caused by forces normal to the axes of the fibre tows can occur on a

microscopic scale in the fibre tows [10].

Parametric studies, carried out by Chen and Govindaraj [11], have shown that the draping

behaviour is mainly determined by

elastic tensile modulus in material principal directions shear modulus material thicknessTensile modulus and shear modulus depend on the type of the fibres and on the fabric

architecture, as has been shown by Long et al. [12] for various non-crimp fabrics. The

Poisson-ratio is of minor importance for the draping behaviour. Collier et al. [13] and Kang

and Yu [14] report experimental determination of the mechanical properties for

characterisation of textiles using the Kawabata evaluation system [15,16]. While Hu andZhang [17] discuss the applicability of the Kawabata system for determination of the fabric

shear modulus, Culpin [18] suggests an alternative approach for quantitative experimental

determination of the shear properties. Hu and Chan [19] investigated the relation between the

fabric drape coefficient, characterising the formability, and the mechanical properties.

Experimental results for the draping behaviour of various commercial fabrics have been

published by Lindberg et al. [20]. Mohammed et al. [21] studied the shear deformation of

woven fabrics of various architectures with respect to mechanical and microstructural aspects.


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4.2 Influence of fabric architecture

Figure 4-2. Qualitative classification of various reinforcement textile architectures with respect to drapability and

shear stiffness [22].

In the diagram shown in Figure 4-2, various reinforcement textiles are classified with respect

to drapability and shear stiffness. For most fabric architectures, there is a relation between

shear stiffness and drapability, i.e. the lower the shear stiffness, the higher the drapability.

Exceptions are UD tapes, which have low shear stiffness and low drapability due to the lack

of fixation of parallel fibres, and random fibre mats, which have high isotropic shear stiffness

due to entanglement of the fibres but due to the lack of internal structure still conform easily

to arbitrary surfaces [23]. In general, the reinforcing effect of the textiles increases from the

upper right corner of the diagram to the lower left corner, although it is hardly possible to

compare all architectures due to the various fields of application (e.g. UD tapes and 3D

woven). Knitted fabrics conform well to arbitrary surfaces, since the mobility of the fibres is

high and there is a significant effect of fibre straightening of the highly curved fibres. The

reinforcing effect in terms of an increase in stiffness of the composite for knitted fabrics is

low. For three-dimensional woven fabrics, on the other hand, the mobility of the fibres is

highly constricted and the reinforcing effect is high. The drapability is low.

4.3 Description of drape

Attempts for description of fabric drape and for numerical drape simulation have not only

been made in the field of composites engineering, aiming at the characterisation of processing

parameters and mechanical properties of the finished parts, but also

in textile industry, for description of the material behaviour regarding visual and sensualimpressions in clothing and fashion [24]

in computer graphics, for realistic representation of textile deformation, e.g. in animatedmovie sequences [25].

shear stiffness

high low

drapability

low

high

3D braided,

wovenUD tape

fibre

mat

2D braided

2D woven

2D knitted


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While in composites engineering a quantitative description of the final state of the draped

textile is relevant, for textile industry ("virtual catwalk") and computer graphics qualitative

real time display of dynamic drape effects is of interest.

The fibre orientations of bi-directional fabrics draped on doubly curved surfaces can be

determined by applying drape simulation techniques. Approaches to describe the draping

behaviour of fabrics have been discussed e.g. by de Jong and Postle [26], van der Ween [27],

Breen et al. [28] and Shanahan et al. [29]. Kinematic models, mapping a geometrical pattern

representing the textile structure on a surface taking into account defined geometrical

constraints [27], and elastic models, describing the fabrics as anisotropic continuous structures

[30], that are discretised to calculate the deformation and determine the fibre orientations

using finite-element-methods (FEM) [13,14], will be discussed in the following sections. In

particle models [28], each point of intersection of fibres is represented by a discrete particle,to which the physical properties of the fabric are attributed. For each particle the energy,

given by interaction with the adjacent particles, is determined. Minimisation of the particle

energy gives the most probable configuration. This approach is similar to the kinematic

model, but does not require a surface for fabric deposition. Since fibre bending is also taken

into consideration, free forming of fabrics under the influence of gravity can be simulated.

Chen et al. [31,32] also suggest application of the finite-volume-method for simulation of

complex deformations of woven fabrics under self-weight or external loads.

4.4 Theory of kinematic / geometrical drape simulation

The fitting of woven fabrics to surfaces has first been discussed by Mack and Taylor [33].

While their method is restricted to fitting of fabrics to analytical surfaces, Heisey and Haller

[34] describe fitting to non-analytical surfaces using numerical analysis techniques. Robertson

et al. determined criteria for fabric wrinkling, applying a kinematic algorithm for calculation

of the fibre arrangement of woven cloth draped on a hemisphere [35] and on a cone [36].

Examples for kinematic simulation of fabric drape and its applications have been presentede.g. by van West et al. [37], Bergsma [38] (for fibre reinforced thermoplastics), Long and

Rudd [39], Trochu et al. [40] and Wang et al. [41]. Potluri et al. [42] extended the capabilities

of kinematic drape algorithms to draping of closed preforms. The basics of kinematic drape

simulation are discussed by van der Ween [27] and Tucker [43]. Each point x on a doubly

curved surface can be described parametrically in surface co-ordinates ui:

),( 21 uuxx= .

The elementary length ds of a surface segment between two points is given by the firstfundamental form of the surface


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jiji ududGsd =2 (4-1)

with the coefficients

ji

jiuu

G

=

xx. (4-2)

The textile is described by co-ordinates vi oriented along the fibre directions. The elementary

length ds of a section of the deformed textile is given by

jijiji vdvdEsd )2(2

+= d . (4-3)

Eij is the Green-Lagrange-tensor with

011 =E , 022 =E (4-4)

(inextensible fibres) and

acos2 21 =E , (4-5)

i.e. the textile deformation is assumed to be given by pure shear with a fibre angle a.

For deposition of the textile on the surface the elementary length of a surface segment and a

textile section are equal

jijijijiji vdvdEududG )2( += d . (4-6)

With the Einstein convention and substitution of Equations (4-4) and (4-5), Equation (4-6)

gives

2

221

2

1

2

2222121

2

111 cos22 vdvdvdvdudGududGudG ++=++ a . (4-7)

Drape of the fabric on the surface is described by mapping

),( 21 vvuu ii = ,

for which various approaches can be chosen [27]. Inserting of

2

2

11

1

11 vd

v

uvd

v

uud

+

= and 2

2

21

1

22 vd

v

uvd

v

uud

+

= (4-8)


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in Equation (4-7) gives

2

221

2

1

21

2

2

1

222

1

2

2

1

2

2

1

121

2

1

1

111

2

2

2

2

222

2

2

2

121

2

2

111

2

1

2

1

2

221

2

1

1

21

2

1

1

11

cos2

2

2

2

vdvdvdvd

vdvdv

u

v

uG

v

u

v

u

v

u

v

uG

v

u

v

uG

vdv

uG

v

u

v

uG

v

uG

vdv

uG

v

u

v

uG

v

uG

++=

+

+

+

+

+

+

+

+

+

a

(4-9)

Comparison of the left hand side and right hand side of Equation (4-9) gives the set ofequations

12

2

1

222

1

2

1

121

2

1

111 =

+

+

v

uG

v

u

v

uG

v

uG , (4-10)

12

2

2

222

2

2

2

121

2

2

111 =

+

+

v

uG

v

u

v

uG

v

uG , (4-11)

acos2

2

1

222

1

2

2

1

2

2

1

121

2

1

1

111 =

+

+

+

v

u

v

uG

v

u

v

u

v

u

v

uG

v

u

v

uG . (4-12)

Boundary conditions are defined e.g. by the requirement that for

01 =v and 02 =v (4-13)

the fibres are put on the surface along geodesic lines.

For numerical solution of the non-linear set of Equations (4-10) to (4-12), the fabric is

discretised in a grid with edge length d, such that the grid point (i,j) is characterised by the

fibre co-ordinates

div =1 and djv =2 (4-14)

as illustrated in Figure 4-3. Transformation of the position of each grid point to surface co-

ordinates or spatial co-ordinates allows to determine the angle a between the fibre

orientations.


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(0,0)v1v2

(i,j)

(i - 1,j - 1)

d

a

d

Figure 4-3. Kinematic simulation of drape on a spherical surface; illustration of discretised fabric.

The drape simulation is based on an algorithm with the following steps:

1. choose starting point for deposition of the fabric on the surface2. define initial orientation for fibres with v2 = 03. put fibre with v2 = 0 along geodesic line on surface4. repeat steps 2 and 3 for fibres with v1 = 05. loop overi andj and determine the positions of the grid point (i,j), such that for each cell

with grid points (i,j) and (i-1, j-1) as diagonally opposite corners the conditions imposed

by Equations (4-10) to (4-12) are satisfied

Inversion of the mapping

),( 21 uuvv ii =

gives the set of equations

11

2

1

2

1

2

1

1

2

1

1 cos2 Gu

v

u

v

u

v

u

v=

+

+

a (4-15)

22

2

2

2

2

2

2

1

2

2

1 cos2 Gu

v

u

v

u

v

u

v=

+

+

a (4-16)

21

2

2

1

2

1

2

2

1

2

2

1

1

2

1

1

1 cos G

u

v

u

v

u

v

u

v

u

v

u

v

u

v

u

v=

+

+

+

a (4-17)


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The results of the drape simulation, depending on the starting point for draping of the textile

and on the initial orientation of the fibres [41], are angles for the two directions of fibre

orientation with respect to the local co-ordinate axes of the corresponding finite element and

the thickness of the draped material for each element. For laminates with different propertiesof the layers, fabric drape is simulated for each single layer. The results are saved in text

format in a data file and can be read for manipulation. Since the drape simulation is performed

on a mesh representing the final geometry of the composite part, the mesh can be simulated

such that it can be used for the finite element injection simulation.

4.6 Theory of finite element drape simulation

In finite element drape simulation, textiles are treated as continuous structures, discretised for

numerical analysis. For modelling of the material in finite element analysis two approaches

exist. One approach considers the microscopic structure of the material with micromechanical

interactions between the fibres. The continuous fibres are discretised in beam elements,

representing segments of the fibres between two intersection points [6]. Mass and elastic

modulus of the fibres are attributed to the beams. If, in addition to fibre shear, also the effect

of fibre slip is considered, contacts are simulated in the nodes of the beam elements. In a

macroscopic approach, textiles are treated as two-dimensional orthotropic continuous

structures [45,46]. Averaged homogeneous properties are attributed to each finite element.Micromechanical effects are implicitly taken into consideration by specification of effective

values for elastic tensile modulus, shear modulus and Poisson-number of the textiles. This

statistical treatment is justified, if the elements include a minimum number of textile unit

cells. In two dimensions, fabrics are mostly modelled as shells [14,47,48], while there are also

approaches to simulate sheet forming processes implementing membrane [49] or plate [13]

elements. Due to the large deformations occurring in fabric drape, the forming behaviour of

textiles is to be considered geometrically non-linear [29,50,51]. Similar considerations are

applied for forming processes of fabrics pre-impregnated with thermoset or thermoplastic

matrix material [52,53].

The description of forming processes is based on continuum mechanics. The momentum of a

continuous system with density distribution r, velocity distribution v and volume Vis

=V

dVvP r . (4-18)

The system is subject to body forces

=V

V VdaF r (4-19)


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with acceleration a. Contact forces

=A

C dAnF (4-20)

with the stress tensors and the normal vectorn of dA are exerted on the surface A of thesystem. With Gau's theorem this formulation can be replaced by

=V

C VdF . (4-21)

In each inertial system the balance of momentum equation, stating that the change of

momentum corresponds to the sum of body and contact forces

CVtd

dFF

P+= , (4-22)

must be satisfied. The change of momentum is in Lagrange formulation expressed as

Vdtd

d

td

d

V

vPr= . (4-23)

Substitution of body and contact forces:

+=VVV

VdVdVdtd

da

vrr . (4-24)

The weak formulation of Equation (4-24) is

+=

VVVVduVduVdu

ax rr&&

(4-25)

with the weight function u. With Green's theorem

+-=V AV

AduVduVdu n (4-26)

Equation (4-25) gives

+-=V AVV

AduVduVduVdu nax rr && . (4-27)


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Equation (4-27) is discretised in finite elements, on which the acceleration is described by

jjW Xx&&&& = (4-28)

with the vectors of nodal accelerations jX&& and the shape functions Wj. Choice of the weight

functions according to Galerkin

iWu = (4-29)

gives

+-= V Aii

V

ij

V

ji AdWVdWVdWVdWW naX rr&&

. (4-30)

Equation (4-30) corresponds to a set of equations

uKFuM +=&& (4-31)

with mass matrix

VdWW jV

i r=M (4-32)

and acceleration vector

jXu&&&& = . (4-33)

The term

AdWVdWA

i

V

i naF += r (4-34)

corresponds to external forces Fext, the term

VdWV

i uK -= (4-35)

is identified with internal forces Fint. Transformation of Equation (4-31) gives a system of

equations for the vector of nodal acceleration


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)(1 intext FFMu -=-

&& (4-36)

with given right hand side. If the mass of the system is "lumped" in the nodes, i.e. the

continuous mass distribution is approximated by discrete masses located in the nodes, the

inversion of the resulting diagonal matrix is trivial and Equation (4-36) gives a system ofdecoupled equations that can be solved for the nodal accelerations.

Equation (4-36) is discretised in time such that

)(1 nintnextn FFMu -=-

&& (4-37)

with the notation

)( nn tuu &&&& = .

The nodal velocities and displacements are calculated from the nodal accelerations according

to the explicit central differences scheme

nnnn tD+= -+ uuu &&&& 2/12/1 , 2/12/1 -+ -=D nnn ttt (4-38)

and

2/12/11 +++ D+= nnnn tuuu & , nnn ttt -=D ++ 12/1 (4-39)

with the initial conditions

0)0( uu && = and 0)0( uu = .

The values with index n+1/2 are interpolated in the middle of the interval from tn to tn+1.

Forming of thin sheets is simulated using shell elements with 6 degrees of freedom per node,

i.e. 3 degrees of freedom for translation and 3 for rotation. Equation (4-37) then corresponds

to a set of 6Nequations forNnodes. In practice, four-noded quadrilateral elements with bi-

linear shape functions are often used. Procedures like this [48] are extensively discussed in the

standard literature, e.g. by Zienkiewicz and Taylor [54] and Bathe [55].


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4.7 Drape simulation with PAM-FORM

The commercial software code PAM-FORM for forming simulation of metallic or non-

metallic sheet materials [53] has originally been developed for the simulation of structural

responses to transient dynamic loading, especially in crash situations. The Lagrangian non-linear dynamic numerical analysis is based on an explicit finite element method with central

differences time integration scheme as discussed above [56]. Forming by contact forces is

simulated, taking into consideration the material properties of the sheet materials.

The sheet material is described as an orthotropic continuum without modelling of the

individual fibres and their interactions. Forming of thin sheets is simulated using shell

elements. For the shell elements macroscopic material models

)(=

are implemented. The composite material is treated as a three-phase material [56]:

The first phase represents a uni-directional or bi-directional fibre material with linear-elastic properties. Two initial fibre orientations can be defined by vectors. The fibres do

not only contribute to membrane stresses, but also to bending moments calculated by

classical beam theory.

The second phase represents the effect of the textile architecture on the material propertiesdue to interaction of the fibre tows. This isotropic linear-elastic phase has no real

equivalent. It is characterised by a shear modulus G and a Poisson-numbern. The various

drape effects that can occur are expressed in the effective shear stiffness and are not

formulated separately. The shear modulus changes for a given value of the fibre angle

(locking angle alock). For values of the fibre angle smaller than the locking angle, the shear

stiffness changes abruptly and the fabric starts to buckle or to wrinkle (Figure 4-5).

1GG = , lockaa

2GG= , lockaa (4-40)


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Figure 4-5. Shear modulus as function of fibre angle a for a fabric with an initial fibre angle of 90.

A third optional phase represents a thermo-visco-elastic matrix, characterised by aMaxwell model with a spring and a dashpot in series. Introduction of this phase is useful

for description of the forming behaviour of fibre reinforced thermoplastic materials.

The mechanical behaviour of the fabric is given by superposition of the three phases in

parallel. When all phases are in parallel, the strains are identical

tmf == , (4-41)

while the stresses in the three phases sum up as

tmf ++= . (4-42)

The fibre orientations in the fabric are calculated from the shear strains of the deformed shell

elements. Forming of multi-layer structures such as preforms for laminates is simulated by

layering of shell elements, each layer representing one material ply.

Figure 4-6. Example for finite element drape simulation: Forming of a hemisphere. Surfaces of punch, die,

blankholder and fabric sheet are modelled.

a

G

alock

G1

G2

90

punch

die

blankholder

fabric sheet


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In forming processes, forces are transferred from the tools to the fabric by contacts. For the

simulation the surfaces of the sheet, the tools (punch and die) and blankholders are modelled

(Figure 4-6). The surfaces of the tools and blankholders are modelled using "null"-elements

with no calculation of nodal displacements, that are used for contact definition only. Since no

deformations are supposed to occur in the tools, they are modelled as rigid bodies, i.e.translational and rotational degrees of freedom are fixed relative to the centre of mass. A

contact between two objects is detected, if the distance between the surfaces of the objects

vanishes locally. Contacts are characterised by restrictions on the relative movement of the

objects normal to the contact interface. The relative movement of the objects tangential to the

contact interface is subject to frictional forces. For simulation of contacts an asymmetric

formulation is applied [56]. The surfaces of the tools are defined as "Master", the surface of

the sheet as "Slave". In given time intervals the distance between master-surface and slave-

nodes is controlled. If the distance between any segment of the master-surface and any slave-

node is smaller than the contact thickness, penetration is detected. The contact thickness isgiven by the thickness of the sheet, represented by the thickness of the shell elements. In case

of penetration, restoring forces in form of step functions are activated, avoiding further

penetration of the surfaces. The restoring forces are proportional to the depth of penetration

and the contact stiffness (penalty contact). The contact stiffness is again dependent on the

stiffness and density values of the objects being in contact with each other.

4.8 Comparison of kinematic and finite element drape simulation

Figure 4-7 shows the results of the kinematic drape simulation for fabric drape on a

hemisphere. The simulation gives the pattern of the fibres placed on the surface of the final

geometry. The results of the FE simulation for draping of the same fabric on the same surface

geometry are illustrated in Figure 4-8, showing the vectors for the fibre axes on the deformed

sheet. Comparison of Figures 4-7 and 4-8 shows qualitative correspondence of the fibre

orientation patterns achieved by both simulation methods. Quantitative differences can be

observed, since Figure 4-8 does not show the final state of the simulation. In the finite

element simulation, local deviations of the vectors from the general fibre orientations arecaused by numerical effects such as hourglassing of the shell elements. This effect can occur

for shell elements with reduced numerical integration schemes. Discussion of the theory of

shell elements is beyond the scope of this work and can be found e.g. in the work published

by Belytschko et al. [57,58].


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Figure 4-7. Drape of a 0/90 fabric on a hemisphere; kinematic simulation using PATRAN Laminate Modeler.

Figure 4-8. Drape of a 0/90 fabric on a hemisphere; Lagrangian non-linear dynamic finite element simulation

using PAM-FORM.


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Figure 4-9. Drape of a 0/90 twill weave 2x2 glass fibre fabric on a hemisphere.

Figure 4-10. Drape of a 0/90 twill weave 2x2 carbon/aramid hybrid fabric on a hemisphere.


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Figures 4-9 and 4-10 show typical results of drape experiments of 0/90 fabrics on a

hemisphere. Especially from Figure 4-9 it can be seen, that under experimental conditions, it

is difficult to achieve a perfectly symmetrical fibre pattern. Nonetheless, both experimental

pictures show the same characteristics: Under 0 and 90, there is no change in fibre angle

and no fabric extension. Under 45, the fibre angle is reduced and the fabric is extended dueto fibre shear. These observations are in agreement with the quantitative results of draping

experiments of various fabrics on a hemisphere, presented by Mohammed et al. [59].

Comparison of the simulated and experimentally determined fibre patterns shows qualitative

correspondence of the results. Quantitative correspondence depends on correct information on

the locking angle (for the kinematic simulation) and of the effective stiffness values of the

shell elements (for the finite element simulation).

Draping experiments on a hemisphere for validation of results for both kinematic and finiteelement drape simulation have frequently been documented in the literature. In general, good

agreement between experiment and simulation has been found: Van West et al. [37] and Long

et al. [12], for example, report good agreement between predicted and measured fibre patterns

for kinematic drape simulation methods. For unbalanced fabrics, however, Long et al. [10]

found the results of standard kinematic drape simulation less satisfactory and developed a

strain energy based iterative mapping scheme. For finite element methods, Dong et al. [48]

studied the influence of numerical parameters on the simulation results for explicit dynamic

analysis implementing shell elements, applying the ABAQUS commercial code. The

presented results are similar to the results shown in Figure 4-8. Simon et al. [52] simulated thehot drape forming of carbon fibre/epoxy prepregs using PAM-STAMP and found good

coincidence with experiments. For a finite element method implementing membrane

elements, Boisse et al. [49] report good agreement with drape experiments.

The kinematic simulation does not consider the actual material behaviour and the mechanics

of the draping process and is based on geometrical information only. Main problems of the

FEM approach, on the other hand, are related to the experimental determination of the

effective material stiffness [45] and to the numerical solution of the complex mathematical

problem (non-linear effects in material behaviour, large deformations, contacts, friction). Forthe example shown in Figures 4-7 and 4-8, the CPU time for kinematic drape simulation is in

the order of magnitude of 1 s on a PC (Pentium II, 400 MHz), for finite element drape

simulation it is in the order of magnitude of 20 h on a workstation (SUN Blade 1000). Finite

element modelling is complex since a high number of null elements is required to mesh the

spherical surfaces of the tools with reasonable accuracy.

The mesh for kinematic drape simulation can be generated with respect to the needs of the

LCM resin flow simulation formulated in Euler co-ordinates. In case of FE drape simulation

formulated in Lagrange co-ordinates, the information on fibre orientations needs to bemapped from the deformed mesh representing the draped fabric onto a second mesh, meeting


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the requirements of the flow simulation. Kinematic drape simulation is thus to be preferred to

finite element drape simulation for combination with LCM-simulation.

References

[1] Long, A.C., Rudd, C.D., Blagdon, M., Kendall, K.N., Demeri, M.Y.: "Simulation andMeasurement of Reinforcement Deformation During Preform Manufacture", Polymers

& Polymer Composites 4(5), 1996

[2] Skelton, J.: "Fundamentals of Fabric Shear", Textile Research Journal46(1), 1976

[3]

Skelton, J.: "Shear of Woven Fabrics"in "Mechanics of Flexible Fibre Assemblies", Sijthoff & Noordhoff, Alphen, 1980

[4] Behre, B.: "Mechanical Properties of Textile Fabrics. Part I: Shearing", TextileResearch Journal31(2), 1961

[5] Grosberg, P., Swani, N.M.: "The Mechanical Properties of Woven Fabrics. Part III: TheBuckling of Woven Fabrics", Textile Research Journal36(4), 1966

[6] Dahlberg, B.: "Mechanical Properties of Textile Fabrics. Part II: Buckling", TextileResearch Journal31(2), 1961[7] Amirbayat, J., Hearle, J.W.S.: "The Anatomy of Buckling of Textile Fabrics: Drape and

Conformability",Journal of the Textile Institute 80(1), 1989

[8] Potter, K.D.: "The influence of accurate stretch data for reinforcements on theproduction of complex structural mouldings. Part 1: deformation of aligned sheets and

fabrics", Composites 10(3), 1979

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