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.

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.

Extensive efforts have been devoted to understanding material failure in the last several decades. A suitable numerical method and specific failure criteria are required for failure simulation. The finite element method (FEM) is the most widely used approach for material mechanical modelling. Since FEM is based on partial differential equations, it is hard to solve problems involving spatial discontinuities, such as fracture and material interface. Due to their intrinsic characteristics of integro-differential governing equations, discontinuous approaches are more suitable for problems involving spatial discontinuities, such as lattice spring method, discrete element method, and peridynamics. A recently proposed lattice particle method is shown to have no restriction of Poisson’s ratio, which is very common in discontinuous methods. In this study, the lattice particle method is adopted to study failure problems. In addition of numerical method, failure criterion is essential for failure simulations. In this study, multiaxial fatigue failure is investigated and then applied to the adopted method. Another critical issue of failure simulation is that the simulation process is time-consuming. To reduce computational cost, the lattice particle method can be partly replaced by neural network model.First, the development of a nonlocal maximum distortion energy criterion in the framework of a Lattice Particle Model (LPM) is presented for modeling of elastoplastic materials. The basic idea is to decompose the energy of a discrete material point into dilatational and distortional components, and plastic yielding of bonds associated with this material point is assumed to occur only when the distortional component reaches a critical value. Then, two multiaxial fatigue models are proposed for random loading and biaxial tension-tension loading, respectively. Following this, fatigue cracking in homogeneous and composite materials is studied using the lattice particle method and the proposed multiaxial fatigue model. Bi-phase material fatigue crack simulation is performed. Next, an integration of an efficient deep learning model and the lattice particle method is presented to predict fracture pattern for arbitrary microstructure and loading conditions. With this integration, computational accuracy and efficiency are both considered. Finally, some conclusion and discussion based on this study are drawn.

Engineering materials and structures undergo a wide variety of multiaxial fatigue loading conditions during their service life. Some of the most complex multiaxial loading scenarios include proportional/non-proportional loading, mix-mode loading, overload/underload, etc. Such loadings are often experienced in many critical applications including aircraft, rotorcraft, and wind turbines. Any accidental failure of these structures during their service life can lead to catastrophic damage to life, property, and environment. All fatigue failure begins with the nucleation of a small crack, followed by crack growth, and ultimately the occurrence of final failure; however, the mechanisms governing the crack nucleation and the crack propagation behavior depend on the nature of fatigue loading and microstructure of the material. In general, ductile materials witness multiple nucleation sites leading to its failure; however, high strength material fails from the nucleation of a single dominant crack. Crack propagation, on the other hand, is governed by various competing mechanisms, which can act either ahead of the crack tip or in the wake region of the crack. Depending upon the magnitude of load, overload/underload, mode-mixity, and microstructure, dominant governing mechanisms may include: crack tip blunting; crack deflection, branching and secondary cracking; strain hardening; residual compressive stresses; plasticity-induced closure, etc. Therefore, it is essential to investigate the mechanisms governing fatigue failure of structural components under such complex multiaxial loading conditions in order to provide a reliable estimation of useful life. The research presented in this dissertation provides the foundation for a comprehensive understanding of fatigue damage in AA 7075 subjected to a range of loading conditions. A series of fatigue tests were conducted on specially designed specimens under different forms of multiaxial loading, which was followed by fracture-surface analysis in order to identify the governing micromechanisms and correlate them with macroscopic fatigue damage behavior. An empirical model was also developed to predict the crack growth rate trend under mode II overloads in an otherwise constant amplitude biaxial loading. The model parameters were calculated using the shape and the size of the plastic zone ahead of the crack tip, and the degree of material hardening within the overload plastic zone. The data obtained from the model showed a good correlation with the experimental values for crack growth rate in the transient region.

Information exists in various forms and a better utilization of the available information can benefit the system awareness and response predictions. The focus of this dissertation is on the fusion of different types of information using Bayesian-Entropy method. The Maximum Entropy method in information theory introduces a unique way of handling information in the form of constraints. The Bayesian-Entropy (BE) principle is proposed to integrate the Bayes’ theorem and Maximum Entropy method to encode extra information. The posterior distribution in Bayesian-Entropy method has a Bayesian part to handle point observation data, and an Entropy part that encodes constraints, such as statistical moment information, range information and general function between variables. The proposed method is then extended to its network format as Bayesian Entropy Network (BEN), which serves as a generalized information fusion tool for diagnostics, prognostics, and surrogate modeling.

The proposed BEN is demonstrated and validated with extensive engineering applications. The BEN method is first demonstrated for diagnostics of gas pipelines and metal/composite plates for damage diagnostics. Both empirical knowledge and physics model are integrated with direct observations to improve the accuracy for diagnostics and to reduce the training samples. Next, the BEN is demonstrated in prognostics and safety assessment in air traffic management system. Various information types, such as human concepts, variable correlation functions, physical constraints, and tendency data, are fused in BEN to enhance the safety assessment and risk prediction in the National Airspace System (NAS). Following this, the BE principle is applied in surrogate modeling. Multiple algorithms are proposed based on different type of information encoding, such as Bayesian-Entropy Linear Regression (BELR), Bayesian-Entropy Semiparametric Gaussian Process (BESGP), and Bayesian-Entropy Gaussian Process (BEGP) are demonstrated with numerical toy problems and practical engineering analysis. The results show that the major benefits are the superior prediction/extrapolation performance and significant reduction of training samples by using additional physics/knowledge as constraints. The proposed BEN offers a systematic and rigorous way to incorporate various information sources. Several major conclusions are drawn based on the proposed study.

This investigation focuses on the development of uncertainty modeling methods applicable to both the structural and thermal models of heated structures as part of an effort to enable the design under uncertainty of hypersonic vehicles. The maximum entropy-based nonparametric stochastic modeling approach is used within the context of coupled structural-thermal Reduced Order Models (ROMs). Not only does this strategy allow for a computationally efficient generation of samples of the structural and thermal responses but the maximum entropy approach allows to introduce both aleatoric and some epistemic uncertainty into the system.

While the nonparametric approach has a long history of applications to structural models, the present investigation was the first one to consider it for the heat conduction problem. In this process, it was recognized that the nonparametric approach had to be modified to maintain the localization of the temperature near the heat source, which was successfully achieved.

The introduction of uncertainty in coupled structural-thermal ROMs of heated structures was addressed next. It was first recognized that the structural stiffness coefficients (linear, quadratic, and cubic) and the parameters quantifying the effects of the temperature distribution on the structural response can be regrouped into a matrix that is symmetric and positive definite. The nonparametric approach was then applied to this matrix allowing the assessment of the effects of uncertainty on the resulting temperature distributions and structural response.

The third part of this document focuses on introducing uncertainty using the Maximum Entropy Method at the level of finite element by randomizing elemental matrices, for instance, elemental stiffness, mass and conductance matrices. This approach brings some epistemic uncertainty not present in the parametric approach (e.g., by randomizing the elasticity tensor) while retaining more local character than the operation in ROM level.

The last part of this document focuses on the development of “reduced ROMs” (RROMs) which are reduced order models with small bases constructed in a data-driven process from a “full” ROM with a much larger basis. The development of the RROM methodology is motivated by the desire to optimally reduce the computational cost especially in multi-physics situations where a lack of prior understanding/knowledge of the solution typically leads to the selection of ROM bases that are excessively broad to ensure the necessary accuracy in representing the response. It is additionally emphasized that the ROM reduction process can be carried out adaptively, i.e., differently over different ranges of loading conditions.

This dissertation presents the development of structural health monitoring and prognostic health management methodologies for complex structures and systems in the field of mechanical engineering. To overcome various challenges historically associated with complex structures and systems such as complicated sensing mechanisms, noisy information, and large-size datasets, a hybrid monitoring framework comprising of solid mechanics concepts and data mining technologies is developed. In such a framework, the solid mechanics simulations provide additional intuitions to data mining techniques reducing the dependence of accuracy on the training set, while the data mining approaches fuse and interpret information from the targeted system enabling the capability for real-time monitoring with efficient computation.

In the case of structural health monitoring, ultrasonic guided waves are utilized for damage identification and localization in complex composite structures. Signal processing and data mining techniques are integrated into the damage localization framework, and the converted wave modes, which are induced by the thickness variation due to the presence of delamination, are used as damage indicators. This framework has been validated through experiments and has shown sufficient accuracy in locating delamination in X-COR sandwich composites without the need of baseline information. Besides the localization of internal damage, the Gaussian process machine learning technique is integrated with finite element method as an online-offline prediction model to predict crack propagation with overloads under biaxial loading conditions; such a probabilistic prognosis model, with limited number of training examples, has shown increased accuracy over state-of-the-art techniques in predicting crack retardation behaviors induced by overloads. In the case of system level management, a monitoring framework built using a multivariate Gaussian model as basis is developed to evaluate the anomalous condition of commercial aircrafts. This method has been validated using commercial airline data and has shown high sensitivity to variations in aircraft dynamics and pilot operations. Moreover, this framework was also tested on simulated aircraft faults and its feasibility for real-time monitoring was demonstrated with sufficient computation efficiency.

This research is expected to serve as a practical addition to the existing literature while possessing the potential to be adopted in realistic engineering applications.

Aging-related damage and failure in structures, such as fatigue cracking, corrosion, and delamination, are critical for structural integrity. Most engineering structures have embedded defects such as voids, cracks, inclusions from manufacturing. The properties and locations of embedded defects are generally unknown and hard to detect in complex engineering structures. Therefore, early detection of damage is beneficial for prognosis and risk management of aging infrastructure system.

Non-destructive testing (NDT) and structural health monitoring (SHM) are widely used for this purpose. Different types of NDT techniques have been proposed for the damage detection, such as optical image, ultrasound wave, thermography, eddy current, and microwave. The focus in this study is on the wave-based detection method, which is grouped into two major categories: feature-based damage detection and model-assisted damage detection. Both damage detection approaches have their own pros and cons. Feature-based damage detection is usually very fast and doesn’t involve in the solution of the physical model. The key idea is the dimension reduction of signals to achieve efficient damage detection. The disadvantage is that the loss of information due to the feature extraction can induce significant uncertainties and reduces the resolution. The resolution of the feature-based approach highly depends on the sensing path density. Model-assisted damage detection is on the opposite side. Model-assisted damage detection has the ability for high resolution imaging with limited number of sensing paths since the entire signal histories are used for damage identification. Model-based methods are time-consuming due to the requirement for the inverse wave propagation solution, which is especially true for the large 3D structures.

The motivation of the proposed method is to develop efficient and accurate model-based damage imaging technique with limited data. The special focus is on the efficiency of the damage imaging algorithm as it is the major bottleneck of the model-assisted approach. The computational efficiency is achieved by two complimentary components. First, a fast forward wave propagation solver is developed, which is verified with the classical Finite Element(FEM) solution and the speed is 10-20 times faster. Next, efficient inverse wave propagation algorithms is proposed. Classical gradient-based optimization algorithms usually require finite difference method for gradient calculation, which is prohibitively expensive for large degree of freedoms. An adjoint method-based optimization algorithms is proposed, which avoids the repetitive finite difference calculations for every imaging variables. Thus, superior computational efficiency can be achieved by combining these two methods together for the damage imaging. A coupled Piezoelectric (PZT) damage imaging model is proposed to include the interaction between PZT and host structure. Following the formulation of the framework, experimental validation is performed on isotropic and anisotropic material with defects such as cracks, delamination, and voids. The results show that the proposed method can detect and reconstruct multiple damage simultaneously and efficiently, which is promising to be applied to complex large-scale engineering structures.

Non-Destructive Testing (NDT) is integral to preserving the structural health of materials. Techniques that fall under the NDT category are able to evaluate integrity and condition of a material without permanently altering any property of the material. Additionally, they can typically be used while the material is in active use instead of needing downtime for inspection.
The two general categories of structural health monitoring (SHM) systems include passive and active monitoring. Active SHM systems utilize an input of energy to monitor the health of a structure (such as sound waves in ultrasonics), while passive systems do not. As such, passive SHM tends to be more desirable. A system could be permanently fixed to a critical location, passively accepting signals until it records a damage event, then localize and characterize the damage. This is the goal of acoustic emissions testing.
When certain types of damage occur, such as matrix cracking or delamination in composites, the corresponding release of energy creates sound waves, or acoustic emissions, that propagate through the material. Audio sensors fixed to the surface can pick up data from both the time and frequency domains of the wave. With proper data analysis, a time of arrival (TOA) can be calculated for each sensor allowing for localization of the damage event. The frequency data can be used to characterize the damage.
In traditional acoustic emissions testing, the TOA combined with wave velocity and information about signal attenuation in the material is used to localize events. However, in instances of complex geometries or anisotropic materials (such as carbon fibre composites), velocity and attenuation can vary wildly based on the direction of interest. In these cases, localization can be based off of the time of arrival distances for each sensor pair. This technique is called Delta T mapping, and is the main focus of this study.