Approach of the constitutive material behavior of textile composites through simulation

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Laboratoire de Mécanique des Sols Structures et
Matériaux École Centrale Paris / CNRS UMR 8579

• Approach of the constitutive material behavior of
  textile composites through simulation
• Damien Durville

2
Motivations

• Use the finite element method to simulate the
  behavior of actual textile composite samples
• taking into account fibers and interactions
• without having to fit parameters or adjust models

3
Approach

• Unknown
• initial configuration of weaving

• Wanted
• identify behavior, mechanical properties

• Known
• bundle arrangements
• weaving pattern
• elastic properties of fibers

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Analysis of the problem
Textile composite

• woven structure coupled with elastic matrix

beams large transformations contact-friction
coupling elements
3D elements
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How to detect contact ?

• contact anywhere, at any time

• Two issues
• geometrical
• where to search contact ?
• which search direction to use for this ?
• algorithmic
• how to get efficient convergence with a high
  number of contacts (up to 100 000 contacts) ?

-gt intermediate geometry -gt adjustment of
penalty coefficient
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Contact elements

• Contact element two material particles
  predicted to enter into contact
• Non linear kinematical condition

x(x1c,t)
n12
gap (xc) (x(x1c,t) x(x2c,t),n12(xc)) 0
xc
x(x2c,t)
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How to locate contact elements ?

• Question of the contact search direction
• classical approaches use the normal to one
  surface
• but
• problems with high curvatures
• non symmetrical treatment
• need to take into account both geometries
  simultaneously

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Intermediate geometry
proximity zone

• Try to approach, locally, the actual geometry of
  contact
• Determine zones of proximity
• Build intermediate geometries
• support of contact discretization
• provide with contact search directions

intermediate geometry
contact elements
symmetrical contact search direction
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Determination of zones of proximity

• Should be cheap and rapid

nearest points on opposite line
zone of proximity
intermediate geometry
test points for proximity criterion
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Determination of contact elements
plane orthogonal to the intermediate geometry

• Determine couples of cross-sections candidates to
  contact
• Determine positions of contact particles on the
  border of the cross-sections

intermediate geometry
cross-sections candidate to contact
couple of material particles
projection of the direction between centroids
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Iterations on geometrical aspects
gap (xc) (x(x1c,t) x(x2c,t),n12(xc)) 0

• For each loading step, two levels of iterations
• Determination of contact elements (particles)
• Determination of normal direction
• Newton-Raphson algorithm
• update normal directions
• update contact elements

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Visualization of contact elements
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Mechanical model for contact

• Regularized penalty method
• Automatic adaptation of the penalty coefficient
• very different reactions depending on the region
  in the structure
• adapt the penalty coefficient locally
• for each zone of proximity
• control the maximum allowed penetration

k
linear
quadratic
regularization threshold
maximum allowed penetration
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Coupling between fabric and matrix

• Nonconforming meshes for fibers and matrix
• Coarse mesh for the matrix with small overlapping
  between matrix and yarns
• Linking elements for nodes of fibers inside
  matrix elements
• couple two particles
• stiffness matrix modulus

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Applications

• Two types textile samples
• 6x6 yarns made of 36 fibers (3 x 12)
• plain weave and twill
• Simulation of
• initial configuration
• biaxial and shear loadings
• with and without elastic matrix

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Initial data

• Nominal configuration of yarns
• Weaving patterns
• Computation of initial configuration
• impose progressively an order of superposing at
  crossings between yarns, depending on the weaving
  pattern

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Initial configuration making of the fabric

• Initial mesh all yarns in the same plane
• 432 fibers
• 200 000 dofs
• 95 000 contact elements (not all active)
• Conditions between yarns
• make the superposing order at crossings be
  progressively respected

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Initial configuration plain weave
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Initial configuration plain weave
Progressive moving of weft and warp yarns
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Initial configuration twill
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Initial configuration twill
Progressive moving of weft and warp yarns
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Initial configuration twill
Evolution of yarn sections through the fabric
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Application of different loadings
Biaxial traction
Shear loading
with and without matrix
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Comparison of efforts for biaxial loadings
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Shear loading for a plain weave fabric
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Shear loading for a twill fabric
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Comparison of efforts for shear loading
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Conclusions

• A complete approach able to handle complex
  simulations on actual textile composite samples
• contact detection between beams undergoing large
  deformations (intermediate geometry)
• efficient algorithms
• Numerous and rich informations
• detailed geometry of initial and deformed
  configurations
• strains and stresses at meso and macro level
• May be applied to a wide range of structures

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Conclusions

• Useful tool to understand, identify and quantify
• phenomena taking place at the meso scale
• effects of coupling between different directions
• effects of coupling between fabric and matrix
• Optimization of textile structures
• Should be used to elaborate macro models for
  textile structures