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This thesis considers the case of a drone defending a high-value target from a number of inbound attacking drones. The defending drone is equipped with short-range weapons and must destroy each of the attacking drones in the most efficient manner. This problem sits at the intersection of several open problems in applied mathematics, such as optimal motion planning in the presence of attrition, as well as solving a “traveling salesman problem” (TSP) with moving targets. The purpose of our research was to analyze this problem by decomposing it into the component problems and then presenting proof-of-concept solutions of each component. The primary results of this thesis include a modeling framework where optimization can be performed without requiring constraints; comparing the strengths of using different types of cost functions for optimization (e.g., minimizing the chance of high-value unit destruction versus a metric based on the path of the defender relative to attackers); and solving moving-target TSP in certain limits by mapping it onto standard TSP or using machine learning., Cruiser/ONR, Major, United States Marine Corps, Approved for public release. Distribution is unlimited.

This research performs trade-off analysis on attacker-defender swarm engagements to compare the relative efficiency of factors governing swarm behavior, namely targeting algorithms and individual drone parameters. In particular, we examined algorithms developed for the Service Academies Swarm Challenge (SASC), a live-fly drone swarm exercise of swarm-on-swarm engagements. We performed this analysis with dynamic swarm simulations that permitted variations in swarm composition and behavior. This allowed us to confirm the qualitative results of swarm performance from the SASC. In addition, we used scaling analysis methods to perform quantitative trade-off analysis and developed functional forms to assess defender swarm fitness. Our results provide a framework for studying more complex swarm behaviors in follow-on research., Office of Naval Research/CRUSER, Lieutenant, United States Navy, Approved for public release. Distribution is unlimited.

Sound speed dispersion and frequency dependence of attenuation in marine sediments are important for any undersea activities using acoustics, such as remote sensing and target detection. Current established models use grain shearing and fluid viscosity as the source of loss in sediments, both of which may not be significant given the relatively small strains imposed by most acoustics' signals. In this paper, we analyze a source of attenuation due to compressional losses in grains, modeled with a dashpot term. Discrete element modelling (DEM) using Large Scale Atomic Molecular Massively Parallel Simulator (LAMMPS) was used to model motions of distinct particles in the system. A small amplitude pressure wave was introduced into the channel via an oscillating boundary wall and its effect on each discrete particle was measured to obtain the sound speed and attenuation coefficient. The measurements with sets of varying frequencies for system size of up to 50000 particles exhibit similar relationships with experimental data used for comparison in this paper. In particular, we were able to recover the observed frequency dependence of attenuation, following a power law of frequency squared at low frequencies and the square root of frequency at high frequencies for all system sizes used in our analysis. The small number of parameters used in our theory present a much more tractable and parsimonious problem for geo-acoustic inversion than the more complicated established models., Major, Republic of Singapore Navy, Approved for public release. Distribution is unlimited.

Body armor for military applications uses a composite system incorporating a monolithic ceramic front face plate backed by an Ultra High Molecular Weight Polyethylene (UHMWPE) textile system that offers a high mass efficiency. Issues with the current system include mobility, fracture and multi-hit performance degradation. It has been demonstrated that ceramic spheres have a higher mass efficiency as compared to monolithic ceramic tiles when applied against 3/8” chromium steel projectiles and 0.30 caliber M2AP projectiles. Within this study, the penetration resistance performance of two selected projectiles (AK-47 and M80) were studied against multiple front face ceramic armor systems. The back face deflection was measured using high-speed video to determine both in-plane and out-of-plane propagation. This data was correlated with load cell force measurements to provide a means to measure penetration resistance performance through determination of the work performed by the 80-layer UHMWPE backing with the selected front face ceramic systems. This work will enable a higher level of performance fidelity and enable optimized front face ceramic armor systems., Washington, DC, 20301, Lieutenant, United States Navy, Approved for public release. Distribution is unlimited.

Polybenzoxazole fibers (PBO, commercially trademarked as Zylon) were once used as an alternative to ultra-high molecular weight polyethylene (UHMWPE) fibers in body armor systems. PBO fibers exhibit a high Young’s modulus, excellent thermal stability, and tensile strength (nearly twice that of Kevlar), but the physical properties severely degrade when exposed to water. Hydrophobic polymer coatings were applied to PBO fibers and studied for moisture resistance, coating durability, and ballistic performance. Instron tensile testing and a V50 assessment utilizing a light gas gun and 9.525 mm spherical chromium-steel projectiles were conducted on four different textile armor systems, including uncoated PBO weave, uncoated PBO weave exposed to water, polymer-coated PBO weave, and polymer-coated PBO weave exposed to water. Using load cells to measure uni-axial forces, combined with digital image correlation enabling measurement of both in-plane and out-of-plane fiber deflection, stress-strain measurements of the four different textile armor systems were measured and compared. Flex Seal liquid coating proved to be the most effective waterproof coating in terms of consistent hydrophobic performance, flexibility, and ease of application; however, further research is required to refine coating methods as well as collect additional data for the performance of PBO under dynamic loads., http://archive.org/details/effectsofhydroph1094566605, Lieutenant, United States Navy, Approved for public release. distribution is unlimited

Body armor for military applications uses a composite system incorporating a monolithic ceramic front face plate backed by an Ultra High Molecular Weight Polyethylene (UHMWPE) textile system that offers a high mass efficiency. Issues with the current system include mobility, fracture and multi-hit performance degradation. It has been demonstrated that ceramic spheres have a higher mass efficiency as compared to monolithic ceramic tiles when applied against 3/8” chromium steel projectiles and 0.30 caliber M2AP projectiles. Within this study, the penetration resistance performance of two selected projectiles (AK-47 and M80) were studied against multiple front face ceramic armor systems. The back face deflection was measured using high-speed video to determine both in-plane and out-of-plane propagation. This data was correlated with load cell force measurements to provide a means to measure penetration resistance performance through determination of the work performed by the 80-layer UHMWPE backing with the selected front face ceramic systems. This work will enable a higher level of performance fidelity and enable optimized front face ceramic armor systems.

When small, macroscopic, solid particles (like glass beads or grains of starch) are immersed in Newtonian fluids (like water or glycerol), the resulting material demonstrates solidification under sudden driving, like from intrusion of an object above a threshold velocity. The physical means for this effect are not fully understood. One mechanism that has been proposed involves hydrodynamic pressure: the fluid must flow through the pore structure between particles as the material deforms. Consistent with this picture, the viscosity of the fluid has been identified as a contributing factor to this resistance. The ability to control the viscosity in real time would allow for maximum resistive pressure when needed and then for low resistance in between periods of high driving. One possibility for accomplishing this is using ferrofluids. Ferrofluids contain molecules of iron coated in a surfactant and suspended in a solvent. This mixture is capable of changing its viscosity when a magnetic field is present. I will explore the mechanical properties, including the impact resistance, where the simple Newtonian fluid is replaced with a ferrofluid. I compare this with existing data in literature and from previous projects in our group. I find that the experimental results match predicted theory to a point and then data suggests that other forces counteract these predictions. I find that ferrofluids are capable of creating a tunable complex fluid mixture and warrant further research., ONR, Major, United States Army, Approved for public release. distribution is unlimited

Systems of sub-millimeter solid particles immersed in a simple fluid can exhibit a dramatic increase in flow resistance when they are rapidly sheared, often called discontinuous shear thickening (DST). A related process is impact-induced solidification, which occurs when an intruder is driven into a particle-fluid mixture. The resultant hardening is sufficient to dampen the movement of the intruder to essentially stop it in a distance much shorter than it would in other fluids. However, the fundamental physical processes that give rise to these behaviors are not well understood. An improved description would have several military applications, such as under-vehicle armor and pipe jacketing. It also could provide a better understanding of how mines interact with wet soils. This thesis presents a fundamental experimental and theoretical study of low-speed impacts into systems of glass beads of varying sizes mixed with water. Our results show that current models fail to capture many aspects of the behavior (e.g., how the peak stresses during impact depend on the initial impact speed and the particle diameter), suggesting that new theoretical descriptions are needed., Lieutenant, United States Navy, Approved for public release. distribution is unlimited

Polybenzoxazole fibers (PBO, commercially trademarked as Zylon) were once used as an alternative to ultra-high molecular weight polyethylene (UHMWPE) fibers in body armor systems. PBO fibers exhibit a high Young’s modulus, excellent thermal stability, and tensile strength (nearly twice that of Kevlar), but the physical properties severely degrade when exposed to water. Hydrophobic polymer coatings were applied to PBO fibers and studied for moisture resistance, coating durability, and ballistic performance. Instron tensile testing and a V50 assessment utilizing a light gas gun and 9.525 mm spherical chromium-steel projectiles were conducted on four different textile armor systems, including uncoated PBO weave, uncoated PBO weave exposed to water, polymer-coated PBO weave, and polymer-coated PBO weave exposed to water. Using load cells to measure uni-axial forces, combined with digital image correlation enabling measurement of both in-plane and out-of-plane fiber deflection, stress-strain measurements of the four different textile armor systems were measured and compared. Flex Seal liquid coating proved to be the most effective waterproof coating in terms of consistent hydrophobic performance, flexibility, and ease of application; however, further research is required to refine coating methods as well as collect additional data for the performance of PBO under dynamic loads.

Beach breaching is a rapid morphological change to a littoral system where rapid sediment transport creates a new tidal or riverine channel, altering the hydrodynamic response of the region. The dynamics of breaching are difficult to quantify in the field due to uncertainty of environmental forcing parameters. Therefore, this study was done in a controlled laboratory using a small-scale beach model and image processing. The hypothesis tested was that water inflow rates, equivalent to river discharge in the field, control breach behavior. By altering the flow rates during lab simulations, three dynamics of breaching were observed. Fast flow rates led to overtopping. Intermediate flow rates caused slumping within the slope that is followed by overtopping. Last, very slow flow rates produced steady state seepage, and the lab beach did not breach. This research has led to the determination that breaching is not only impacted by just the increase in water on river or ocean side, but that the rate of filling is crucial in determining breaching characteristics.

Understanding how forces propagate through granular media is broadly relevant in acoustic and non-acoustic warfare applications. For example, sediment type can impact acoustic propagation during bottom bounce events that undersea assets use for navigation. There is not yet a complete theory of force propagation in granular media due to several nonlinearities, like friction and Hertzian contact interactions. Of particular interest is the crossover region between linear and nonlinear regimes, where the propagating stresses are comparable to the initial confining stress in the system, as well as the shock regime, where stresses greatly exceed confining prestress. Aiming to develop more complete theories of force propagation in these regimes, we perform experimental impact tests and analyze how forces propagate in two-dimensional, frictional granular media. Assemblies of photo elastic disks are subjected to a vertical confining stress and then impacted from the side by a pendulum. Both the confining stress and the impact speed can be varied, and high-speed video captures the forces propagating through the material. We use image processing to quantify the speed of the moving wave and the force network’s structure. In particular, we focus on the phenomenology of the traveling shock and the stress anisotropy of the force networks, which has never before been experimentally measured., http://archive.org/details/usingimageanalys1094564110, Ensign, United States Navy, Approved for public release; distribution is unlimited.

Dense suspensions, which consist of sub-millimeter particles suspended in a Newtonian fluid, undergo a dramatic solidification when subjected to sudden impact, as first described in M.A. Brassard et al.’s article in the 2020 Bulletin of the American Physical Society. The underlying physical mechanisms for this effect are not known. Recently, a class of added mass models has been proposed to explain this phenomenon. These models give direct predictions on the times and magnitudes associated with the peak stresses during impacts, including how these stresses vary with changes to the intruder mass and size. In this thesis, we performed impact experiments in cornflour and water dense suspensions. We varied the size, speed, mass and shape of the intruder and quantified the forces and times via high-speed imaging and acceleration sensors. We used dimensional and scaling analysis to confirm or disprove added mass models, and the aim is for our results to be used to test current theories and help derive future theories to explain impact-induced solidification in dense suspensions., Outstanding Thesis, Major, Canadian Army, Approved for public release. distribution is unlimited

When small, macroscopic, solid particles (like glass beads or grains of starch) are immersed in Newtonian fluids (like water or glycerol), the resulting material demonstrates solidification under sudden driving, like from intrusion of an object above a threshold velocity. The physical means for this effect are not fully understood. One mechanism that has been proposed involves hydrodynamic pressure: the fluid must flow through the pore structure between particles as the material deforms. Consistent with this picture, the viscosity of the fluid has been identified as a contributing factor to this resistance. The ability to control the viscosity in real time would allow for maximum resistive pressure when needed and then for low resistance in between periods of high driving. One possibility for accomplishing this is using ferrofluids. Ferrofluids contain molecules of iron coated in a surfactant and suspended in a solvent. This mixture is capable of changing its viscosity when a magnetic field is present. I will explore the mechanical properties, including the impact resistance, where the simple Newtonian fluid is replaced with a ferrofluid. I compare this with existing data in literature and from previous projects in our group. I find that the experimental results match predicted theory to a point and then data suggests that other forces counteract these predictions. I find that ferrofluids are capable of creating a tunable complex fluid mixture and warrant further research.

This thesis develops robust tactics for countering multi-domain super swarms. Previous research has provided tools for assessing adversarial swarms’ internal cooperating strategies, quantifying risk based on swarm and weapons models, and generating optimal defender trajectories. In this research, we develop a simulation-based testbed for experimental validation of these strategies and a database of adversarial swarming models against which to test. In this research, the aforementioned simulation-based testbed is examined from the perspective of computational efficiency. A significant computational advantage is obtained by replacing the Runge Kutta with the Verlet integration scheme frequently used in the molecular dynamics community. This almost equally numerically stable framework offers an impressive performance advantage. Additionally, this research seeks to find the ideal balance between the deterministic nature of the dynamics of adversarial swarms and the requirement for a probabilistic approach in order to model the mutual attrition between opposing agents during combat situations. To achieve this end, several models of dynamics and attrition are introduced for optimal motion planning. Their outcomes are compared with a Monte Carlo simulation model, in which survivability is partially influenced by random number generation that aims to simulate the unpredictability exhibited in the real world., Outstanding Thesis, Lieutenant, Hellenic Navy, Approved for public release. distribution is unlimited

Particulate materials (amorphous, athermal substances such as dry grains, foams, emulsions, and colloids) are commonplace in industry and defense, second only to water in their ubiquity. These materials can transition from solid-like to liquid-like in unexpected ways, with failure in one section of a large system rapidly leading to failure across the entire system and giving rise to significant consequences in phenomena as disparate as impact resistance, geological fault interface behavior, soil liquefaction, pharmaceuticals, crater formation, glacier flow, avalanches and landslides. These complex behaviors are the result of simple interaction laws (e.g., Hooke’s law) applied to thousands or more of individual particles. Since no complete theory of flow in these materials exists, accurately predicting or engineering the onset of these transitions can be challenging. Using extensive computer simulations, we show that shear flows occur in particulate materials due to a correlation length (a measure of the distance over which rearrangements propagate) that diverges at the material yield condition. Large ensembles of simulated systems are sheared, and statistics are gathered on the average initial flow distance, slip avalanche distance, and the average internal shear stress at each shear strain step. These properties are found to vary in a manner consistent with a diverging correlation length. My results will be useful in deriving a more complete theory of flow in these material

Ballistic impact into a soil target has broad military relevance. Understanding the forces during impact is crucial to predicting damage and survivability. This process involves several nonlinear physical mechanisms, making it difficult to describe. While some existing models of ballistic impact characterize the average response during penetration well, these models fail during the initial stages of impact when forces are the largest. There currently is no theoretical framework for understanding the forces and dynamics during these crucial early stages. In this thesis, we use numerical simulations of intruders impacting granular media, coupled with existing experimental data, to understand the forces during the initial stages of impact. For slow impacts, forces are independent of speed and set by the weight of the intruder. For fast impacts, the impact forces grow as a non-linear power law in the impact velocity with exponent 4/3. This scaling depends on the size of the intruder and stiffness of the grains, and it is insensitive to gravity, friction, the nonlinear force law between grains, and the density of the intruder. We use dimensional analysis to collapse all data onto a single curve, providing a first step toward a comprehensive theoretical description of this process.

Shock propagation in particulate materials is governed by the nonlinear interactions between particles. Spherical elastic particles have Hertzian contacts, meaning that they effectively interact via nonlinear springs. Hertzian interactions give rise to nonlinear wave behavior, which has been studied extensively for 1D chains of spheres (e.g., Newton’s cradle), where energy is transmitted perfectly from one particle to the next and the internal sound speed of a particle is assumed to be quasi-infinite. In more realistic situations, forces do not propagate along a single network, but along force chains, which are spatially anistotropic structures that transmit stress. Additionally, shocks can propagate at speeds similar to the internal sound speed. Through shock experiments on 2D assemblies of frictional, photoelastic disks, we show three key results: (1) Two distinct wave speeds emerge after impact, one of which represents the primary force propagation wave; (2) this force propagation speed scales (as a power law) with the intruder velocity can indeed approach the characteristic sound speed inside a grain; and (3) in the shock regime, these propagation speeds are independent of confining pressure and fall along a single branch.

Understanding how forces propagate through granular media is broadly relevant in acoustic and non-acoustic warfare applications. For example, sediment type can impact acoustic propagation during bottom bounce events that undersea assets use for navigation. There is not yet a complete theory of force propagation in granular media due to several nonlinearities, like friction and Hertzian contact interactions. Of particular interest is the crossover region between linear and nonlinear regimes, where the propagating stresses are comparable to the initial confining stress in the system, as well as the shock regime, where stresses greatly exceed confining prestress. Aiming to develop more complete theories of force propagation in these regimes, we perform experimental impact tests and analyze how forces propagate in two-dimensional, frictional granular media. Assemblies of photo elastic disks are subjected to a vertical confining stress and then impacted from the side by a pendulum. Both the confining stress and the impact speed can be varied, and high-speed video captures the forces propagating through the material. We use image processing to quantify the speed of the moving wave and the force network’s structure. In particular, we focus on the phenomenology of the traveling shock and the stress anisotropy of the force networks, which has never before been experimentally measured.

Beach breaching is a rapid morphological change to a littoral system where rapid sediment transport creates a new tidal or riverine channel, altering the hydrodynamic response of the region. The dynamics of breaching are difficult to quantify in the field due to uncertainty of environmental forcing parameters. Therefore, this study was done in a controlled laboratory using a small-scale beach model and image processing. The hypothesis tested was that water inflow rates, equivalent to river discharge in the field, control breach behavior. By altering the flow rates during lab simulations, three dynamics of breaching were observed. Fast flow rates led to overtopping. Intermediate flow rates caused slumping within the slope that is followed by overtopping. Last, very slow flow rates produced steady state seepage, and the lab beach did not breach. This research has led to the determination that breaching is not only impacted by just the increase in water on river or ocean side, but that the rate of filling is crucial in determining breaching characteristics., http://archive.org/details/sedimentdynamics1094566067, Lieutenant, United States Navy, Approved for public release. distribution is unlimited