A finite element model that replicates the experimental procedure to test and certify soft body armor has been developed. The model consists of four components: bullet, clay, straps, and shoot pack with different material models that closely capture the behavior of each component when subjected to ballistic impact loading. To test the fidelity of the model, three metrics are used - back face signature (BFS), the number of penetrated shoot pack layers, and the number of damaged shoot pack layers on the clay side of the shoot pack assembly. In addition, the shape and size of the bullet, and the shape and size of the hole in the shoot pack are also considered as qualitative measures to assess the developed model. The focus of this research work is to improve the shoot pack material model, while the constitutive model for the components is taken from earlier work done at ASU. Results show considerable improvement in the model in terms of capturing the number of penetrated layers, the size and shape of the holes in the shoot pack layer, and the predicted BFS. The developed finite element models can be used to predict the behavior of soft body armor for different initial conditions, shoot pack materials, and arrangement of the layers.

It is well–established that physical phenomena occurring at the macroscale are the result of underlying molecular mechanisms that occur at the nanoscale. Understanding these mechanisms at the molecular level allows the development of semicrystalline polymers with tailored properties for different applications. Molecular Dynamics (MD) simulations offer significant insight into these mechanisms and their impact on various physical and mechanical properties. However, the temporostpatial limitations of all–atomistic (AA) MD simulations impede the investigation of phenomena with higher time– and length–scale. Coarse–grained (CG) MD simulations address the shortcomings of AAMD simulations by grouping atoms based on their chemical, structural, etc., aspects into larger particles, beads, and reducing the degrees offreedom of the atomistic system, allowing achievement of higher time– and length–scales. Among the approaches for generating CG models, the hybrid approach is capable of capturing the underlying mechanisms at the molecular level while replicating phenomena at temporospatial scales attainable by the CG model. In this dissertation, a novel hybrid method is developed for the systematic coarse–graining of semicrystalline polymers that uniquely blends the potential functions of both phases. The obtained blended potential not only faithfully reproduces the structural distributions of multiple phases simultaneously but also allows control over the dynamics of the obtained CG models employing a tunable parameter. Given that accelerated dynamics of the CG models hinder the investigation of phenomena in the crystal phase, such as α–α-relaxation, by utilizing the developed method, this phenomenon was successfully modeled for a semicrystalline polyethylene (PE) system with obtained values for the diffusion constant at room temperature and the activation energy in close agreement with experimental results. In a subsequent study, a family of potentials was developed for a sample semicrystalline polyethylene (PE) to investigate the impact of different potential functions on some physical properties, such as crystal diffusion and glass transition temperature, and their correlation with some mechanical properties obtained from uniaxial deformation.

Aromatic polymers, with benzene-like rings in their main chains, include materials such as polyurea, an amorphous elastomer capable of dissipating large amounts of energy under dynamic loading, which makes it a promising coating for defensive systems. Although computational research exists that investigates the atomic-level response of polyurea and other amorphous aromatic polymers to extreme conditions, there is little experimental work to validate these models 1) at the atomic-scale and 2) under high pressures characteristic of extreme dynamic loading. Understanding structure-property relationships at the atomic-level is important for polymers, considering many of them undergo pressure and temperature-induced structural transformations, which must be understood to formulate accurate predictive models. This work aims to gain a deeper understanding of the high-pressure structural response of aromatic polymers at the atomic-level, with emphasis into the mechanisms associated with high-pressure transformations. Hence, atomic-level structural data at high pressures was obtained in situ via multiangle energy dispersive X-ray diffraction (EDXD) experiments at the Advanced Photon Source (APS) for polyurea and another amorphous aromatic polymer, polysulfone, chosen as a reference due to its relatively simple structure. Pressures up to 6 GPa were applied using a Paris Edinburgh (PE) hydraulic press at room temperature. Select polyurea samples were also heated to 277 °C at 6 GPa. The resulting structure factors and pair distribution functions, along with molecular dynamics simulations of polyurea provided by collaborators, suggest that the structures of both polymers are stable up to 6 GPa, aside from reductions in free-volume between polymer backbones. As higher pressures (≲ 32 GPa) were applied using diamond anvils in combination with the PE press, indications of structural transformations were observed in both polymers that appear similar in nature to the sp2-sp3 hybridization in compressed carbon. The transformation occurs gradually up to at least ~ 26 GPa in PSF, while it does not progress past ~ 15 GPa in polyurea. The changes are largely reversible, especially in polysulfone, consistent with pressure-driven, reversible graphite-diamond transformations in the absence of applied temperature. These results constitute some of the first in situ observations of the mechanisms that drive pressure-induced structural transformations in aromatic polymers.

The technology and science capabilities of SmallSats continue to grow with the increase of capabilities in commercial off the shelf components. However, the maturation of SmallSat hardware has also led to an increase in component power consumption, this poses an issue with using traditional passive thermal management systems (radiators, thermal straps, etc.) to regulate high-power components. High power output becomes limited in order to maintain components within their allowable temperature ranges. The aim of this study is to explore new methods of using additive manufacturing to enable the usage of heat pipe structures on SmallSat platforms up to 3U’s in size. This analysis shows that these novel structures can increase the capabilities of SmallSat platforms by allowing for larger in-use heat loads from a nominal power density of 4.7 x 10^3 W/m3 to a higher 1.0 x 10^4 W/m3 , an order of magnitude increase. In addition, the mechanical properties of the SmallSat structure are also explored to characterize effects to the mechanical integrity of the spacecraft. The results show that the advent of heat pipe integration to the structures of SmallSats will lead to an increase in thermal management capabilities compared to the current state-of-the-art systems, while not reducing the structural integrity of the spacecraft. In turn, this will lead to larger science and technology capabilities for a field that is growing in both the education and private sectors.

Uncertainty quantification is critical for engineering design and analysis. Determining appropriate ways of dealing with uncertainties has been a constant challenge in engineering. Statistical methods provide a powerful aid to describe and understand uncertainties. This work focuses on applying Bayesian methods and machine learning in uncertainty quantification and prognostics among all the statistical methods. This study focuses on the mechanical properties of materials, both static and fatigue, the main engineering field on which this study focuses. This work can be summarized in the following items: First, maintaining the safety of vintage pipelines requires accurately estimating the strength. The objective is to predict the reliability-based strength using nondestructive multimodality surface information. Bayesian model averaging (BMA) is implemented for fusing multimodality non-destructive testing results for gas pipeline strength estimation. Several incremental improvements are proposed in the algorithm implementation. Second, the objective is to develop a statistical uncertainty quantification method for fatigue stress-life (S-N) curves with sparse data.Hierarchical Bayesian data augmentation (HBDA) is proposed to integrate hierarchical Bayesian modeling (HBM) and Bayesian data augmentation (BDA) to deal with sparse data problems for fatigue S-N curves. The third objective is to develop a physics-guided machine learning model to overcome limitations in parametric regression models and classical machine learning models for fatigue data analysis. A Probabilistic Physics-guided Neural Network (PPgNN) is proposed for probabilistic fatigue S-N curve estimation. This model is further developed for missing data and arbitrary output distribution problems. Fourth, multi-fidelity modeling combines the advantages of low- and high-fidelity models to achieve a required accuracy at a reasonable computation cost. The fourth objective is to develop a neural network approach for multi-fidelity modeling by learning the correlation between low- and high-fidelity models. Finally, conclusions are drawn, and future work is outlined based on the current study.

Advanced Polymer and Ceramic Matrix Composites (PMCs and CMCs) are currently employed in a variety of airframe and engine applications. This includes PMC jet engine fan cases and CMC hot gas path turbine components. In an impact event, such as a jet engine fan blade-out, PMCs exhibit significant deformation-induced temperature rises in addition to strain rate, temperature, and pressure dependence. CMC turbine components experience elevated temperatures, large thermal gradients, and sustained loading for long time periods in service, where creep is a major issue. However, the complex nature of woven and braided composites presents significant challenges for deformation, progressive damage, and failure prediction, particularly under extreme service conditions where global response is heavily driven by competing time and temperature dependent phenomena at the constituent level. In service, the constituents in these advanced composites experience history-dependent inelastic deformation, progressive damage, and failure, which drive global nonlinear constitutive behavior. In the case of PMCs, deformation-induced heating under impact conditions is heavily influenced by the matrix. The creep behavior of CMCs is a complex manifestation of time-dependent load transfer due to the differing creep rates of the constituents; simultaneous creep and relaxation at the constituent level govern macroscopic CMC creep. The disparity in length scales associated with the constituent materials, woven and braided tow architectures, and composite structural components therefore necessitates the development of robust multiscale computational tools. In this work, multiscale computational tools are developed to gain insight into the deformation, progressive damage, and failure of advanced PMCs and CMCs. This includes multiscale modeling of the impact response of PMCs, including adiabatic heating due to the conversion of plastic work to heat at the constituent level, as well as elevated temperature creep in CMCs as a result of time-dependent constituent load transfer. It is expected that the developed models and methods will provide valuable insight into the challenges associated with the design and certification of these advanced material systems.

Modern life is full of challenging optimization problems that we unknowingly attempt to solve. For instance, a common dilemma often encountered is the decision of picking a parking spot while trying to minimize both the distance to the goal destination and time spent searching for parking; one strategy is to drive as close as possible to the goal destination but risk a penalty cost if no parking spaces can be found. Optimization problems of this class all have underlying time-varying processes that can be altered by a decision/input to minimize some cost. Such optimization problems are commonly solved by a class of methods called Dynamic Programming (DP) that breaks down a complex optimization problem into a simpler family of sub-problems. In the 1950s Richard Bellman introduced a class of DP methods that broke down Multi-Stage Optimization Problems (MSOP) into a nested sequence of ``tail problems”. Bellman showed that for any MSOP with a cost function that satisfies a condition called additive separability, the solution to the tail problem of the MSOP initialized at time-stage k>0 can be used to solve the tail problem initialized at time-stage k-1. Therefore, by recursively solving each tail problem of the MSOP, a solution to the original MSOP can be found. This dissertation extends Bellman`s theory to a broader class of MSOPs involving non-additively separable costs by introducing a new state augmentation solution method and generalizing the Bellman Equation. This dissertation also considers the analogous continuous-time counterpart to discrete-time MSOPs, called Optimal Control Problems (OCPs). OCPs can be solved by solving a nonlinear Partial Differential Equation (PDE) called the Hamilton-Jacobi-Bellman (HJB) PDE. Unfortunately, it is rarely possible to obtain an analytical solution to the HJB PDE. This dissertation proposes a method for approximately solving the HJB PDE based on Sum-Of-Squares (SOS) programming. This SOS algorithm can be used to synthesize controllers, hence solving the OCP, and also compute outer bounds of reachable sets of dynamical systems. This methodology is then extended to infinite time horizons, by proposing SOS algorithms that yield Lyapunov functions that can approximate regions of attraction and attractor sets of nonlinear dynamical systems arbitrarily well.

Ultra-fast 2D/3D material microstructure reconstruction and quantitative structure-property mapping are crucial components of integrated computational material engineering (ICME). It is particularly challenging for modeling random heterogeneous materials such as alloys, composites, polymers, porous media, and granular matters, which exhibit strong randomness and variations of their material properties due to the hierarchical uncertainties associated with their complex microstructure at different length scales. Such uncertainties also exist in disordered hyperuniform systems that are statistically isotropic and possess no Bragg peaks like liquids and glasses, yet they suppress large-scale density fluctuations in a similar manner as in perfect crystals. The unique hyperuniform long-range order in these systems endow them with nearly optimal transport, electronic and mechanical properties. The concept of hyperuniformity was originally introduced for many-particle systems and has subsequently been generalized to heterogeneous materials such as porous media, composites, polymers, and biological tissues for unconventional property discovery. An explicit mixture random field (MRF) model is proposed to characterize and reconstruct multi-phase stochastic material property and microstructure simultaneously, where no additional tuning step nor iteration is needed compared with other stochastic optimization approaches such as the simulated annealing. The proposed method is shown to have ultra-high computational efficiency and only requires minimal imaging and property input data. Considering microscale uncertainties, the material reliability will face the challenge of high dimensionality. To deal with the so-called “curse of dimensionality”, efficient material reliability analysis methods are developed. Then, the explicit hierarchical uncertainty quantification model and efficient material reliability solvers are applied to reliability-based topology optimization to pursue the lightweight under reliability constraint defined based on structural mechanical responses. Efficient and accurate methods for high-resolution microstructure and hyperuniform microstructure reconstruction, high-dimensional material reliability analysis, and reliability-based topology optimization are developed. The proposed framework can be readily incorporated into ICME for probabilistic analysis, discovery of novel disordered hyperuniform materials, material design and optimization.

Two of the most fundamental barriers to the exploration of the solar system are the cost of transporting material to space and the time it takes to get to destinations beyond Earth’s sphere of influence. Space elevators can solve this problem by enabling extremely fast and propellant free transit to nearly any destination in the solar system. A space elevator is a structure that consists of an anchor on the Earth’s surface, a tether connected from the surface to a point well above geostationary orbit, and an apex counterweight anchor. Since the entire structure rotates at the same rate as the Earth regardless of altitude, gravity is the dominant force on structures below GEO while centripetal force is dominant above, allowing climber vehicles to accelerate from GEO along the tether and launch off from the apex with large velocities. The outcome of this project is the development of a MATLAB script that can design and analyze a space elevator tether and climber vehicle. The elevator itself is designed to require the minimum amount of material necessary to support a given climber mass based on provided material properties, while the climber is simulated separately. The climber and tether models are then combined to determine how the force applied by the climber vehicle changes the stress distribution inside the tether.

One potential application of multi-robot systems is collective transport, a task in which multiple mobile robots collaboratively transport a payload that is too large or heavy to be carried by a single robot. Numerous control schemes have been proposed for collective transport in environments where robots can localize themselves (e.g., using GPS) and communicate with one another, have information about the payload's geometric and dynamical properties, and follow predefined robot and/or payload trajectories. However, these approaches cannot be applied in uncertain environments where robots do not have reliable communication and GPS and lack information about the payload. These conditions characterize a variety of applications, including construction, mining, assembly in space and underwater, search-and-rescue, and disaster response.
Toward this end, this thesis presents decentralized control strategies for collective transport by robots that regulate their actions using only their local sensor measurements and minimal prior information. These strategies can be implemented on robots that have limited or absent localization capabilities, do not explicitly exchange information, and are not assigned predefined trajectories. The controllers are developed for collective transport over planar surfaces, but can be extended to three-dimensional environments.

This thesis addresses the above problem for two control objectives. First, decentralized controllers are proposed for velocity control of collective transport, in which the robots must transport a payload at a constant velocity through an unbounded domain that may contain strictly convex obstacles. The robots are provided only with the target transport velocity, and they do not have global localization or prior information about any obstacles in the environment. Second, decentralized controllers are proposed for position control of collective transport, in which the robots must transport a payload to a target position through a bounded or unbounded domain that may contain convex obstacles. The robots are subject to the same constraints as in the velocity control scenario, except that they are assumed to have global localization. Theoretical guarantees for successful execution of the task are derived using techniques from nonlinear control theory, and it is shown through simulations and physical robot experiments that the transport objectives are achieved with the proposed controllers.