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.

Cellular metamaterials arouse broad scientific interests due to the combination of host material and structure together to achieve a wide range of physical properties rarely found in nature. Stochastic foam as one subset has been considered as a competitive candidate for versatile applications including heat exchangers, battery electrodes, automotive, catalyst devices, magnetic shielding, etc. For the engineering of the cellular foam architectures, closed-form models that can be used to predict the mechanical and thermal properties of foams are highly desired especially for the recently developed ultralight weight shellular architectures. Herein, for the first time, a novel packing three-dimensional (3D) hollow pentagonal dodecahedron (HPD) model is proposed to simulate the cellular architecture with hollow struts. An electrochemical deposition process is utilized to manufacture the metallic hollow foam architecture. Mechanical and thermal testing of the as-manufactured foams are carried out to compare with the HPD model. Timoshenko beam theory is utilized to verify and explain the derived power coefficient relation. Our HPD model is proved to accurately capture both the topology and the physical properties of hollow stochastic foam. Understanding how the novel HPD model packing helps break the conventional impression that 3D pentagonal topology cannot fulfill the space as a representative volume element. Moreover, the developed HPD model can predict the mechanical and thermal properties of the manufactured hollow metallic foams and elucidating of how the inevitable manufacturing defects affect the physical properties of the hollow metallic foams. Despite of the macro-scale stochastic foam architecture, nano gradient gyroid lattices are studied using Molecular Dynamics (MD) simulation. The simulation result reveals that, unlike homogeneous architecture, gradient gyroid not only shows novel layer-by-layer deformation behavior, but also processes significantly better energy absorption ability. The deformation behavior and energy absorption are predictable and designable, which demonstrate its highly programmable potential.

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.

Stiffness and flexibility are essential in many fields, including robotics, aerospace, bioengineering, etc. In recent years, origami-based mechanical metamaterials were designed for better mechanical properties including tunable stiffness and tunable collapsibility. However, in existing studies, the tunable stiffness is only with limited range and limited controllability. To overcome these challenges, two objectives were proposed and achieved in this dissertation: first, to design mechanical metamaterials with metamaterials with selective stiffness and collapsibility; second, to design mechanical metamaterials with in-situ tunable stiffness among positive, zero, and negative.In the first part, triangulated cylinder origami was employed to build deployable mechanical metamaterials through folding and unfolding along the crease lines. These deployable structures are flexible in the deploy direction so that it can be easily collapsed along the same way as it was deployed. An origami-inspired mechanical metamaterial was designed for on-demand deployability and selective collapsibility: autonomous deployability from the collapsed state and selective collapsibility along two different paths, with low stiffness for one path and substantially high stiffness for another path. The created mechanical metamaterial yields unprecedented load bearing capability in the deploy direction while possessing great deployability and collapsibility. The principle in this prospectus can be utilized to design and create versatile origami-inspired mechanical metamaterials that can find many applications. In the second part, curved origami patterns were designed to accomplish in situ stiffness manipulation covering positive, zero, and negative stiffness by activating predefined creases on one curved origami pattern. This elegant design enables in situ stiffness switching in lightweight and space-saving applications, as demonstrated through three robotic-related components. Under a uniform load, the curved origami can provide universal gripping, controlled force transmissibility, and multistage stiffness response. This work illustrates an unexplored and unprecedented capability of curved origami, which opens new applications in robotics for this particular family of origami patterns.

Structural/system health monitoring (SHM) and prognostic health management (PHM) are vital techniques to ensure engineering system reliability and safety during the service. As multi-functionality and enhanced performance are in demand, modern engineering systems including aerospace, mechanical, and civil applications have become more complex. The constituent and architectural complexity, and multisource sensing sources in modern engineering systems may limit the monitoring capabilities of conventional approaches and require more advanced SHM/PHM techniques. Therefore, a hybrid methodology that incorporates information fusion, nondestructive evaluation (NDE), machine learning (ML), and statistical analysis is needed for more effective damage diagnosis/prognosis and system safety management.This dissertation presents an automated aviation health management technique to enable proactive safety management for both aircraft and national airspace system (NAS). A real-time, data-driven aircraft safety monitoring technique using ML models and statistical models is developed to enable an early-stage upset detection capability, which can improve pilot’s situational awareness and provide a sufficient safety margin. The detection accuracy and computational efficiency of the developed monitoring techniques is validated using commercial unlabeled flight data recorder (FDR) and reported accident FDR dataset. A stochastic post-upset prediction framework is developed using a high-fidelity flight dynamics model to predict the post-impacts in both aircraft and air traffic system. Stall upset scenarios that are most likely occurred during loss of control in-flight (LOC-I) operation are investigated, and stochastic flight envelopes and risk region are predicted to quantify their severities. In addition, a robust, automatic damage diagnosis technique using ultrasonic Lamb waves and ML models is developed to effectively detect and classify fatigue damage modes in composite structures. The dispersion and propagation characteristics of the Lamb waves in a composite plate are investigated. A deep autoencoder-based diagnosis technique is proposed to detect fatigue damage using anomaly detection approach and automatically extract damage sensitive features from the waves. The patterns in the features are then further analyzed using outlier detection approach to classify the fatigue damage modes. The developed diagnosis technique is validated through an in-situ fatigue tests with periodic active sensing. The developed techniques in this research are expected to be integrated with the existing safety strategies to enhance decision making process for improving engineering system safety without affecting the system’s functions.

Damage and failure of advanced composite materials and structures are often manifestations of nonlinear deformation that involve multiple mechanisms and their interactions at the constituent length scale. The presence and interactions of inelastic microscale constituents strongly influence the macroscopic damage anisotropy and useful residual life. The mechano-chemical interactions between constituents at the atomistic length scale play a more critical role with nanoengineered composites. Therefore, it is desirable to link composite behavior to specific microscopic constituent properties explicitly and lower length scale features using high-fidelity multiscale modeling techniques.In the research presented in this dissertation, an atomistically-informed multiscale modeling framework is developed to investigate damage evolution and failure in composites with radially-grown carbon nanotube (CNT) architecture. A continuum damage mechanics (CDM) model for the radially-grown CNT interphase region is developed with evolution equations derived using atomistic simulations. The developed model is integrated within a high-fidelity generalized method of cells (HFGMC) micromechanics theory and is used to parametrically investigate the influence of various input micro and nanoscale parameters on the mechanical properties, such as elastic stiffness, strength, and toughness. In addition, the inter-fiber stresses and the onset of damage in the presence of the interphase region are investigated to better understand the energy dissipation mechanisms that attribute to the enhancement in the macroscopic out-of-plane strength and toughness. Note that the HFGMC theory relies heavily on the description of microscale features and requires many internal variables, leading to high computational costs. Therefore, a novel reduced-order model (ROM) is also developed to surrogate full-field nonlinear HFGMC simulations and decrease the computational time and memory requirements of concurrent multiscale simulations significantly. The accurate prediction of composite sandwich materials' thermal stability and durability remains a challenge due to the variability of thermal-related material coefficients at different temperatures and the extensive use of bonded fittings. Consequently, the dissertation also investigates the thermomechanical performance of a complex composite sandwich space structure subject to thermal cycling. Computational finite element (FE) simulations are used to investigate the intrinsic failure mechanisms and damage precursors in honeycomb core composite sandwich structures with adhesively bonded fittings.

While understanding of failure mechanisms for polymeric composites have improved vastly over recent decades, the ability to successfully monitor early failure and subsequent prevention has come of much interest in recent years. One such method to detect these failures involves the use of mechanochemistry, a field of chemistry in which chemical reactions are initiated by deforming highly-strained bonds present in certain moieties. Mechanochemistry is utilized in polymeric composites as a means of stress-sensing, utilizing weak and force-responsive chemical bonds to activate signals when embedded in a composite material. These signals can then be detected to determine the amount of stress applied to a composite and subsequent potential damage that has occurred due to the stress. Among mechanophores, the cinnamoyl moiety is capable of stress response through fluorescent signal under mechanical load. The cinnamoyl group is fluorescent in its initial state and capable of undergoing photocycloaddition in the presence of ultraviolet (UV) light, followed by subsequent reversion when under mechanical load. Signal generation before the yield point of the material provides a form of damage precursor detection.This dissertation explores the implementation of mechanophores in novel approaches to overcome some of the many challenges within the mechanochemistry field. First, new methods of mechanophore detection were developed through utilization of Fourier transform infrared (FTIR) spectroscopy signals and in-situ stress sensing. Developing an in-situ testing method provided a two-fold advantage of higher resolution and more time efficiency over current methods involving image analysis with a fluorescent microscope. Second, bonding mechanophores covalently into the backbone of an epoxy matrix mitigated property loss due to mechanophore incorporation. This approach was accomplished through functionalizing either the resin or hardener component of the matrix. Finally, surface functionalization of fibers was performed and allowed for unaltered fabrication procedures of composite layups as well as provided increased adhesion at the fiber-matrix interphase. The developed materials could enable a simple, non-invasive, and non-detrimental structural health monitoring approach.

Collision-free path planning is also a major challenge in managing unmanned aerial vehicles (UAVs) fleets, especially in uncertain environments. The design of UAV routing policies using multi-agent reinforcement learning has been considered, and propose a Multi-resolution, Multi-agent, Mean-field reinforcement learning algorithm, named 3M-RL, for flight planning, where multiple vehicles need to avoid collisions with each other while moving towards their destinations. In this system, each UAV makes decisions based on local observations, and does not communicate with other UAVs. The algorithm trains a routing policy using an Actor-Critic neural network with multi-resolution observations, including detailed local information and aggregated global information based on mean-field. The algorithm tackles the curse-of-dimensionality problem in multi-agent reinforcement learning and provides a scalable solution. The proposed algorithm is tested in different complex scenarios in both 2D and 3D space and the simulation results show that 3M-RL result in good routing policies. Also as a compliment, dynamic data communications between UAVs and a control center has also been studied, where the control center needs to monitor the safety state of each UAV in the system in real time, where the transition of risk level is simply considered as a Markov process. Given limited communication bandwidth, it is impossible for the control center to communicate with all UAVs at the same time. A dynamic learning problem with limited communication bandwidth is also discussed in this paper where the objective is to minimize the total information entropy in real-time risk level tracking. The simulations also demonstrate that the algorithm outperforms policies such as a Round & Robin policy.

Fiber reinforced composites are rapidly replacing conventional metallic or polymeric materials as materials of choice in a myriad of applications across a wide range of industries. The relatively low weight, high strength, high stiffness, and a variety of thermal and mechanical environmental and loading capabilities are in part what make composite materials so appealing to material experts and design engineers. Additionally, fiber reinforced composites are highly tailorable and customized composite materials and structures can be readily designed for specific applications including those requiring particular directional material properties, fatigue resistance, damage tolerance, high temperature capabilities, or resistance to environmental degradation due to humidity and oxidation. The desirable properties of fiber reinforced composites arise from the strategic combination of multiple constituents to form a new composite material. However, the significant material anisotropy that occurs as a result of combining multiple constituents, each with different directional thermal and mechanical properties, complicates material analysis and remains a major impediment to fully understanding composite deformation and damage behavior. As a result, composite materials, especially specialized composites such as ceramic matrix composites and various multifunctional composites, are not utilized to their fullest potential. In the research presented in this dissertation, the deformation and damage behavior of several fiber reinforced composite systems were investigated. The damage accumulation and propagation behavior of carbon fiber reinforced polymer (CFRP) composites under complex in-phase biaxial fatigue loading conditions was investigated and the early stage damage and microscale damage were correlated to the eventual fatigue failure behavior and macroscale damage mechanisms. The temperature-dependent deformation and damage response of woven ceramic matrix composites (CMCs) reinforced with carbon and silicon carbide fibers was also studied. A fracture mechanics-informed continuum damage model was developed to capture the brittle damage behavior of the ceramic matrix. A multiscale thermomechanical simulation framework, consisting of cooldown simulations to capture a realistic material initial state and subsequent mechanical loading simulations to capture the temperature-dependent nonlinear stress-strain behavior, was also developed. The methodologies and results presented in this research represent substantial progress toward increasing understanding of the deformation and damage behavior of some key fiber reinforced composite materials.