Project 1-1: Ballistic Impact and Optimization of Composite Shields
Principal Investigators: Charbel Farhat (Stanford), Tarek Zohdi (UC Berkeley)

Body armor ranks with water, ammunition, and weapons as one of the heaviest items worn or carried by troops, according to engineers on the Ballistics Technology Team at the U.S. Army Soldier Systems Center (Natick, MA). Protecting soldiers and their vehicles and equipment from flying projectiles requires shielding that resists penetration and that is lightweight enough to not interfere with normal activities and operations. In addition, shielding material must retain its effectiveness even after long periods in storage and exposure to light, heat, and humidity.

High performance computing simulations allow researchers to develop better ballistic shielding materials by examining the effects of ballistic impact frame-by-frame. Researchers can use simulations to test various armor components singly or in groups. Simulations may suggest effective material configurations that are not intuitively obvious from experimental data alone. After simulations narrow the field to the most promising armor configurations, they can be fabricated and tested under real-life conditions.

AHPCRC primary investigators Tarek Zohdi (associate professor, mechanical engineering, University of California, Berkeley), Charbel Farhat (professor, aeronautics, astronautics, and mechanical engineering, Stanford University), and Stanford research associate Philip Avery and postdoc David Powell are bringing ballistic fabric modeling into the high performance computing arena by adapting existing codes for simulation and finite element analysis to run in parallel processing environments.

Because there has not been an abundance of new materials to test, recent efforts have focused on optimizing the performance of existing materials. Fiber strength is important, but fabric geometry also matters, because projectiles can penetrate by pushing fibers aside, even if the fibers remain unbroken. Factors that affect performance of ballistic fabrics include the thickness and strength of the fibers, weaving patterns, and the method of attaching the fabrics to their substrates (pinned at the corners vs. fastened along the sides, for example). Customarily, the Army has evaluated ballistic fabrics by making and testing physical prototypes. Testing every combination of characteristics to find optimal combinations is time-consuming and expensive, however.

Ballistic impact produces multiple physical effects at high speeds—understanding these effects will assist in designing protective fabrics that can withstand impact by various types of projectiles. Using computer simulations to model the behavior of a fabric under impact from a high-speed bullet or shrapnel fragment requires the capability to model the nonlinear solid dynamics typical of materials undergoing rapid deformation caused by localized impact.

In addition to adapting existing software codes, Zohdi, Farhat, Avery, and Powell are building new capabilities into their modeling and simulation software to account for such rapid deformation effects. They are adding simulations for various projectile shapes, accounting for imperfections incorporated during the weaving of protective fabrics, examining the way the protective fabric is attached to the underlying structure, and simulating the propagation and growth of flaws in fabrics. They have begun preliminary work on modeling fiber-based composite materials in order to explore the properties of these complex systems.

Putting the Model to the Test
The simulation method developed for this project represents ballistic fabrics from the fibril level up, so that the same method can be applied to many different materials, weaving types, and modes of attachment to a substrate. For both the simulation and the real-world fabrics, thin filaments called fibrils are twisted together into strands of yarn, which are then woven into fabric sheets. Fibril properties are relatively simple to model, they can be obtained readily from the manufacturer, and they are simple to test and verify.

The model addresses tensile strains only, as tension (rather than compression) is most important when assessing rupture properties due to ballistic impact. Because a fibril is very thin relative to its length, tensile deformation can be described as a one-dimensional response to an applied uniaxial stress. Axial strain for the fabric is assumed to lie in the region between 2% and 10% prior to rupturing. Zylon fabric, which was used in the experiments with which the simulations were compared, ruptures at 3% strain. Zylon yarn has 350 fibrils per strand, and the simulated yarn response is obtained by summing the responses for all the fibrils.

Misalignment, in which the directions of the fibril axes exhibit a statistical distribution, occurs during manufacturing (indeed, it is almost impossible to avoid). This misalignment is a beneficial property of the yarn. Individual fibrils fail at different times in response to stress, because of the variation in their orientation with respect to that stress. This causes a given yarn strand to fail gradually rather than catastrophically. Differences in yarn strands tend to be small, because the large number of fibrils in each strand average out statistically, but the misalignment effect is a necessary component of a good macroscale model.

The AHPCRC model treats a woven fabric as a network of nonlinear trusses (yarn) pinned together at nodes where two trusses meet. (“Nonlinear” refers to materials that do not experience strain in proportion to the amount of stress applied.) This model was constructed using FEM, a finite element modeling program used at Stanford. Sandia Laboratories’ ACME contact library was added to FEM to supply appropriate algorithms to search for contact entities and to enforce contact constraints.

When simulations deal with parts of various bodies (e.g., a projectile or a sheet of fabric) that are in physical contact, such as during an impact event, significant amounts of information are passed back and forth between computer processors, which increases the time needed to complete the calculations. Optimizing the performance of the contact search proved to be dependent on the choice of subdomains, because separate processors perform calculations for each subdomain. Typically, subdomains group together elements that are in the same body. A more efficient method defines subdomains as those regions which are in close spatial proximity to each other, regardless of which body they are in.

The problem of a small projectile striking a single fabric sheet presents an area of contact that involves only a few elements. This makes it difficult to divide the workload over more than about 10 processors. At the other extreme, when two sheets come together and the contact is distributed evenly across the entire problem (approximately one million degrees of freedom), the algorithm scales well up to about 200 processors. Optimum scalability requires at least 50,000 degrees of freedom per processor. The majority of problems expected to be of interest to producers and users of ballistic fabrics will involve a combination of localized and distributed contacts, so the scalability of the algorithm should fall somewhere between these two extremes.

Ballistic impact has been simulated for a 50-caliber (0.5-inch) cylindrical projectile and a Zylon square 10 inches on a side, fastened at the corners to a substrate, for comparison with experimental studies done at Berkeley. In both the experiments and the simulation, fabric failure occurred at the corners as a result of impact.

In the region of the ballistic limit (the impact velocity below which penetration does not occur), the simulation agreed closely with the experimental results. The simulation predicted a ballistic limit of 39.6 m/sec, which compares well with the experimentally observed ballistic limit of 39.3 m/sec.

Sources:

AHPCRC Bulletin, Vol. 1, Issue 3 (2009)

Multi-scale Modeling and Large-scale Transient Simulation of Ballistic Fabric. D. Powell, C. Farhat, , T. I. Zohdi. Oral presentation CO-03, Proceedings of the 26th Army Science Conference, Orlando, FL, December 2008. http://www.asc2008.com/sessions/sessionc.htm