# Theoretical modeling of the behavior of woven fabrics subjected to stabbing

Nathan Iderne, Pauline Texier, Cuong Ha-Minh

► To cite this version:

Nathan Iderne, Pauline Texier, Cuong Ha-Minh. Theoretical modeling of the behavior of woven fabrics subjected to stabbing. AuxDefense 2024 – 4th World Conference on Advanced Materials for Defense – Beyond Boundaries, Jun 2024, Braga, Portugal. hal-05030075

HAL Id: hal-05030075

https://hal.science/hal-05030075v1

Submitted on 11 Apr 2025

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# THEORETICAL MODELING OF THE BEHAVIOR OF WOVEN FABRICS SUBJECTED TO STABBING

Nathan Iderne, Pauline Texier, Cuong Ha-Minh

LMPS, ENS Paris Saclay

## Analytical macroscale model of the fabric with Matlab

MatLab is used to compute the equations to obtain various results for the behavior of the fiber.

### Data needed to compute

**Material data:**

* *E*: Yarn Young's modulus

* *ρ*: Yarn mass density

* *ε*<sub>f</sub>: Yarn failure deformation

* *d*: Yarn diameter

* *d*<sub>y*: Yarns' density in the plan of fabric

* *n*: Layer number

* *l*: Size of the fabric

* *m*<sub>s*: Surface mass of a layer

### Energy repartition on the macroscopic model

<figure><img src="image_3.png" /></figure>

### Macroscopic model: dissipation

<figure><img src="image_4.png" /></figure>

## Macroscale fabric modeling on LS Dyna, with finite element method

<figure><img src="image_5.png" /></figure>

* 10-layers model to compare with experimental data

* FSP projectile (2,82g – diameter 7,62mm)

<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /></figure>

Experimental picture [1] compared with numerical simulation

<figure><img src="image_8.png" /></figure>

*only the last layer is displayed

## Analytical and simulation results comparison (W and H)

<figure><img src="image_9.png" /></figure>

## Comparison of the analytical friction model and simulated one (initial velocity = 0.3m/s)

<figure><img src="image_10.png" /><figcaption>Cumulative friction energy during perforation function of the time</figcaption></figure>

$$ \Delta E_{fri} = 2\pi erV_i dt(-s \sin(90 - \alpha)m_p a) $$

<figure><img src="image_11.png" /><figcaption>Friction energy</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Angle (θ) of the incidence cone</figcaption></figure>

From now on, the projectile has the shape of a cone to represent the contact with the fabric and the friction energy related.

<figure><img src="image_13.png" /></figure>

Fabric (1 layer)

<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /></figure>