Finite Element Detailed Model FINITE ELEMENT MODELING: DETAILED MODEL Our approach to modeling woven fabrics is to model the individual yarns explicitly. This allows us to understand the mechanisms responsible for the high ballistic resistance of polymer fabrics. The finite element model configuration for a woven fabric is shown below. Yarns are modeled individually and combined to form a fabric weave. The shapes and geometry of the yarns were taken from high resolution photographs of the fabrics used in the testing. As seen in the figures, the weave is not symmetric. Typically the warp yarns have more crimp than the fill yarns.
The material model and properties used for the yarns are based on results of yarn tensile tests . We modeled an initially crimped yarn and pulled it to failure at a strain rate of 0.016/s. The measured and simulated stress-strain curves are shown below. The simulation shows very good agreement with the test results.  MEASURED AND CALCULATED YARN RESPONSE We simulated tests with three different boundary conditions as shown in the animations below. In the first case, the fabric patch is firmly gripped on all four edges, in the second case the fabric is gripped firmly along two edges and in the third case no edges are gripped. The steel fragment impacts at a velocity of 120 m/s.
The forces on the fragment applied by the fabric are shown in the figure below. If the fabric is gripped on four edges, the peak force is the greatest, but at 50 microseconds the yarns in both directions break and the fragment penetrates the fabric. If the fabric is gripped on two edges, the initial peak force is less, but as the gripped yarns break, the ungripped yarns transfer the load to adjacent gripped yarns, resulting in a resisting force of a longer duration. For the case with no edges gripped, the fabric still provides a significant amount of resistance due to inertia.
The calculated velocity of the fragment is shown below. For the case with no edges gripped the fragment slows from 120 to about 80 m/s. This result is consistent with conservation of momentum for a simple inelastic collision. For four edges gripped the velocity is reduced from 120 to 38 m/s, and for two edges gripped the velocity of the fragment is reduced to zero. The result of this simulation: that holding on two edges is more effective than holding on four edges agrees with the experimental results . The result for no edges gripped shows that, if the fragment is prevented from cutting through the fabric, significant energy can be absorbed by inertial effects.
The difference in the response mechanism for the different boundary conditions is explainable in terms of load transfer. With four edges gripped, yarns in both directions under the fragment fail locally. However, for two edges gripped, the gripped yarns break locally, but the ungripped yarns do not break and are able to transfer load to adjacent gripped yarns. Effect of Fabric Size
The results of the simulations for the three different sized fabrics are shown in the figure below. We see that the timing of the oscillations for the three cases is quite different: As expected, the larger the fabric, the slower the oscillations.
However, the overall resistance, as shown by the velocity of the fragment, is virtually the same for the three cases, up until the 15-yarn fabric is penetrated.
SUMMARY OF THE DETAILED MODEL
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