Recent studies of the occurrence of post-flutter limit cycle oscillations (LCO) of the F-16 have provided good support to the long-standing hypothesis that this phenomenon involves a nonlinear structural damping. A potential mechanism for the appearance of nonlinearity in the damping are the nonlinear geometric effects that arise when the deformations become large enough to exceed the linear regime. In this light, the focus of this investigation is first on extending nonlinear reduced order modeling (ROM) methods to include viscoelasticity which is introduced here through a linear Kelvin-Voigt model in the undeformed configuration. Proceeding with a Galerkin approach, the ROM governing equations of motion are obtained and are found to be of a generalized van der Pol-Duffing form with parameters depending on the structure and the chosen basis functions. An identification approach of the nonlinear damping parameters is next proposed which is applicable to structures modeled within commercial finite element software.

The effects of this nonlinear damping mechanism on the post-flutter response is next analyzed on the Goland wing through time-marching of the aeroelastic equations comprising a rational fraction approximation of the linear aerodynamic forces. It is indeed found that the nonlinearity in the damping can stabilize the unstable aerodynamics and lead to finite amplitude limit cycle oscillations even when the stiffness related nonlinear geometric effects are neglected. The incorporation of these latter effects in the model is found to further decrease the amplitude of LCO even though the dominant bending motions do not seem to stiffen as the level of displacements is increased in static analyses.

Structural health management (SHM) is emerging as a vital methodology to help engineers improve the safety and maintainability of critical structures. SHM systems are designed to reliably monitor and test the health and performance of structures in aerospace, civil, and mechanical engineering applications. SHM combines multidisciplinary technologies including sensing, signal processing, pattern recognition, data mining, high fidelity probabilistic progressive damage models, physics based damage models, and regression analysis. Due to the wide application of carbon fiber reinforced composites and their multiscale failure mechanisms, it is necessary to emphasize the research of SHM on composite structures. This research develops a comprehensive framework for the damage detection, localization, quantification, and prediction of the remaining useful life of complex composite structures. To interrogate a composite structure, guided wave propagation is applied to thin structures such as beams and plates. Piezoelectric transducers are selected because of their versatility, which allows them to be used as sensors and actuators. Feature extraction from guided wave signals is critical to demonstrate the presence of damage and estimate the damage locations. Advanced signal processing techniques are employed to extract robust features and information. To provide a better estimate of the damage for accurate life estimation, probabilistic regression analysis is used to obtain a prediction model for the prognosis of complex structures subject to fatigue loading. Special efforts have been applied to the extension of SHM techniques on aerospace and spacecraft structures, such as UAV composite wings and deployable composite boom structures. Necessary modifications of the developed SHM techniques were conducted to meet the unique requirements of the aerospace structures. The developed SHM algorithms are able to accurately detect and quantify impact damages as well as matrix cracking introduced.

Structural integrity is an important characteristic of performance for critical components used in applications such as aeronautics, materials, construction and transportation. When appraising the structural integrity of these components, evaluation methods must be accurate. In addition to possessing capability to perform damage detection, the ability to monitor the level of damage over time can provide extremely useful information in assessing the operational worthiness of a structure and in determining whether the structure should be repaired or removed from service. In this work, a sequential Bayesian approach with active sensing is employed for monitoring crack growth within fatigue-loaded materials. The monitoring approach is based on predicting crack damage state dynamics and modeling crack length observations. Since fatigue loading of a structural component can change while in service, an interacting multiple model technique is employed to estimate probabilities of different loading modes and incorporate this information in the crack length estimation problem. For the observation model, features are obtained from regions of high signal energy in the time-frequency plane and modeled for each crack length damage condition. Although this observation model approach exhibits high classification accuracy, the resolution characteristics can change depending upon the extent of the damage. Therefore, several different transmission waveforms and receiver sensors are considered to create multiple modes for making observations of crack damage. Resolution characteristics of the different observation modes are assessed using a predicted mean squared error criterion and observations are obtained using the predicted, optimal observation modes based on these characteristics. Calculation of the predicted mean square error metric can be computationally intensive, especially if performed in real time, and an approximation method is proposed. With this approach, the real time computational burden is decreased significantly and the number of possible observation modes can be increased. Using sensor measurements from real experiments, the overall sequential Bayesian estimation approach, with the adaptive capability of varying the state dynamics and observation modes, is demonstrated for tracking crack damage.

Composite materials are increasingly being used in aircraft, automobiles, and other applications due to their high strength to weight and stiffness to weight ratios. However, the presence of damage, such as delamination or matrix cracks, can significantly compromise the performance of these materials and result in premature failure. Structural components are often manually inspected to detect the presence of damage. This technique, known as schedule based maintenance, however, is expensive, time-consuming, and often limited to easily accessible structural elements. Therefore, there is an increased demand for robust and efficient Structural Health Monitoring (SHM) techniques that can be used for Condition Based Monitoring, which is the method in which structural components are inspected based upon damage metrics as opposed to flight hours. SHM relies on in situ frameworks for detecting early signs of damage in exposed and unexposed structural elements, offering not only reduced number of schedule based inspections, but also providing better useful life estimates. SHM frameworks require the development of different sensing technologies, algorithms, and procedures to detect, localize, quantify, characterize, as well as assess overall damage in aerospace structures so that strong estimations in the remaining useful life can be determined. The use of piezoelectric transducers along with guided Lamb waves is a method that has received considerable attention due to the weight, cost, and function of the systems based on these elements. The research in this thesis investigates the ability of Lamb waves to detect damage in feature dense anisotropic composite panels. Most current research negates the effects of experimental variability by performing tests on structurally simple isotropic plates that are used as a baseline and damaged specimen. However, in actual applications, variability cannot be negated, and therefore there is a need to research the effects of complex sample geometries, environmental operating conditions, and the effects of variability in material properties. This research is based on experiments conducted on a single blade-stiffened anisotropic composite panel that localizes delamination damage caused by impact. The overall goal was to utilize a correlative approach that used only the damage feature produced by the delamination as the damage index. This approach was adopted because it offered a simplistic way to determine the existence and location of damage without having to conduct a more complex wave propagation analysis or having to take into account the geometric complexities of the test specimen. Results showed that even in a complex structure, if the damage feature can be extracted and measured, then an appropriate damage index can be associated to it and the location of the damage can be inferred using a dense sensor array. The second experiment presented in this research studies the effects of temperature on damage detection when using one test specimen for a benchmark data set and another for damage data collection. This expands the previous experiment into exploring not only the effects of variable temperature, but also the effects of high experimental variability. Results from this work show that the damage feature in the data is not only extractable at higher temperatures, but that the data from one panel at one temperature can be directly compared to another panel at another temperature for baseline comparison due to linearity of the collected data.

Damage detection in heterogeneous material systems is a complex problem and requires an in-depth understanding of the material characteristics and response under varying load and environmental conditions. A significant amount of research has been conducted in this field to enhance the fidelity of damage assessment methodologies, using a wide range of sensors and detection techniques, for both metallic materials and composites. However, detecting damage at the microscale is not possible with commercially available sensors. A probable way to approach this problem is through accurate and efficient multiscale modeling techniques, which are capable of tracking damage initiation at the microscale and propagation across the length scales. The output from these models will provide an improved understanding of damage initiation; the knowledge can be used in conjunction with information from physical sensors to improve the size of detectable damage. In this research, effort has been dedicated to develop multiscale modeling approaches and associated damage criteria for the estimation of damage evolution across the relevant length scales. Important issues such as length and time scales, anisotropy and variability in material properties at the microscale, and response under mechanical and thermal loading are addressed. Two different material systems have been studied: metallic material and a novel stress-sensitive epoxy polymer.

For metallic material (Al 2024-T351), the methodology initiates at the microscale where extensive material characterization is conducted to capture the microstructural variability. A statistical volume element (SVE) model is constructed to represent the material properties. Geometric and crystallographic features including grain orientation, misorientation, size, shape, principal axis direction and aspect ratio are captured. This SVE model provides a computationally efficient alternative to traditional techniques using representative volume element (RVE) models while maintaining statistical accuracy. A physics based multiscale damage criterion is developed to simulate the fatigue crack initiation. The crack growth rate and probable directions are estimated simultaneously.

Mechanically sensitive materials that exhibit specific chemical reactions upon external loading are currently being investigated for self-sensing applications. The "smart" polymer modeled in this research consists of epoxy resin, hardener, and a stress-sensitive material called mechanophore The mechanophore activation is based on covalent bond-breaking induced by external stimuli; this feature can be used for material-level damage detections. In this work Tris-(Cinnamoyl oxymethyl)-Ethane (TCE) is used as the cyclobutane-based mechanophore (stress-sensitive) material in the polymer matrix. The TCE embedded polymers have shown promising results in early damage detection through mechanically induced fluorescence. A spring-bead based network model, which bridges nanoscale information to higher length scales, has been developed to model this material system. The material is partitioned into discrete mass beads which are linked using linear springs at the microscale. A series of MD simulations were performed to define the spring stiffness in the statistical network model. By integrating multiple spring-bead models a network model has been developed to represent the material properties at the mesoscale. The model captures the statistical distribution of crosslinking degree of the polymer to represent the heterogeneous material properties at the microscale. The developed multiscale methodology is computationally efficient and provides a possible means to bridge multiple length scales (from 10 nm in MD simulation to 10 mm in FE model) without significant loss of accuracy. Parametric studies have been conducted to investigate the influence of the crosslinking degree on the material behavior. The developed methodology has been used to evaluate damage evolution in the self-sensing polymer.

A hybrid molecular dynamics (MD) simulation framework is developed to emulate mechanochemical reaction of mechanophores in epoxy-based nanocomposites. Two different force fields, a classical force field and a bond order based force field are hybridized to mimic the experimental processes from specimen preparation to mechanical loading test. Ultra-violet photodimerization for mechanophore synthesis and epoxy curing for thermoset polymer generation are successfully simulated by developing a numerical covalent bond generation method using the classical force field within the framework. Mechanical loading tests to activate mechanophores are also virtually conducted by deforming the volume of a simulation unit cell. The unit cell deformation leads to covalent bond elongation and subsequent bond breakage, which is captured using the bond order based force field. The outcome of the virtual loading test is used for local work analysis, which enables a quantitative study of mechanophore activation. Through the local work analysis, the onset and evolution of mechanophore activation indicating damage initiation and propagation are estimated; ultimately, the mechanophore sensitivity to external stress is evaluated. The virtual loading tests also provide accurate estimations of mechanical properties such as elastic, shear, bulk modulus, yield strain/strength, and Poisson’s ratio of the system. Experimental studies are performed in conjunction with the simulation work to validate the hybrid MD simulation framework. Less than 2% error in estimations of glass transition temperature (Tg) is observed with experimentally measured Tgs by use of differential scanning calorimetry. Virtual loading tests successfully reproduce the stress-strain curve capturing the effect of mechanophore inclusion on mechanical properties of epoxy polymer; comparable changes in Young’s modulus and yield strength are observed in experiments and simulations. Early damage signal detection, which is identified in experiments by observing increased intensity before the yield strain, is captured in simulations by showing that the critical strain representing the onset of the mechanophore activation occurs before the estimated yield strain. It is anticipated that the experimentally validated hybrid MD framework presented in this dissertation will provide a low-cost alternative to additional experiments that are required for optimizing material design parameters to improve damage sensing capability and mechanical properties.

In addition to the study of mechanochemical reaction analysis, an atomistic model of interphase in carbon fiber reinforced composites is developed. Physical entanglement between semi-crystalline carbon fiber surface and polymer matrix is captured by introducing voids in multiple graphene layers, which allow polymer matrix to intertwine with graphene layers. The hybrid MD framework is used with some modifications to estimate interphase properties that include the effect of the physical entanglement. The results are compared with existing carbon fiber surface models that assume that carbon fiber has a crystalline structure and hence are unable to capture the physical entanglement. Results indicate that the current model shows larger stress gradients across the material interphase. These large stress gradients increase the viscoplasticity and damage effects at the interphase. The results are important for improved prediction of the nonlinear response and damage evolution in composite materials.

Damage assessment and residual useful life estimation (RULE) are essential for aerospace, civil and naval structures. Structural Health Monitoring (SHM) attempts to automate the process of damage detection and identification. Multiscale modeling is a key element in SHM. It not only provides important information on the physics of failure, such as damage initiation and growth, the output can be used as "virtual sensing" data for detection and prognosis. The current research is part of an ongoing multidisciplinary effort to develop an integrated SHM framework for metallic aerospace components. In this thesis a multiscale model has been developed by bridging the relevant length scales, micro, meso and macro (or structural scale). Micro structural representations obtained from material characterization studies are used to define the length scales and to capture the size and orientation of the grains at the micro level. Parametric studies are conducted to estimate material parameters used in this constitutive model. Numerical and experimental simulations are performed to investigate the effects of Representative Volume Element (RVE) size, defect area fraction and distribution. A multiscale damage criterion accounting for crystal orientation effect is developed. This criterion is applied for fatigue crack initial stage prediction. A damage evolution rule based on strain energy density is modified to incorporate crystal plasticity at the microscale (local). Optimization approaches are used to calculate global damage index which is used for the RVE failure prediciton. Potential cracking directions are provided from the damage criterion simultaneously. A wave propagation model is incorporated with the damage model to detect changes in sensing signals due to plastic deformation and damage growth.

Although high performance, light-weight composites are increasingly being used in applications ranging from aircraft, rotorcraft, weapon systems and ground vehicles, the assurance of structural reliability remains a critical issue. In composites, damage is absorbed through various fracture processes, including fiber failure, matrix cracking and delamination. An important element in achieving reliable composite systems is a strong capability of assessing and inspecting physical damage of critical structural components. Installation of a robust Structural Health Monitoring (SHM) system would be very valuable in detecting the onset of composite failure. A number of major issues still require serious attention in connection with the research and development aspects of sensor-integrated reliable SHM systems for composite structures. In particular, the sensitivity of currently available sensor systems does not allow detection of micro level damage; this limits the capability of data driven SHM systems. As a fundamental layer in SHM, modeling can provide in-depth information on material and structural behavior for sensing and detection, as well as data for learning algorithms. This dissertation focusses on the development of a multiscale analysis framework, which is used to detect various forms of damage in complex composite structures. A generalized method of cells based micromechanics analysis, as implemented in NASA's MAC/GMC code, is used for the micro-level analysis. First, a baseline study of MAC/GMC is performed to determine the governing failure theories that best capture the damage progression. The deficiencies associated with various layups and loading conditions are addressed. In most micromechanics analysis, a representative unit cell (RUC) with a common fiber packing arrangement is used. The effect of variation in this arrangement within the RUC has been studied and results indicate this variation influences the macro-scale effective material properties and failure stresses. The developed model has been used to simulate impact damage in a composite beam and an airfoil structure. The model data was verified through active interrogation using piezoelectric sensors. The multiscale model was further extended to develop a coupled damage and wave attenuation model, which was used to study different damage states such as fiber-matrix debonding in composite structures with surface bonded piezoelectric sensors.

The focus of this investigation is on the optimum placement of a limited number of dampers, fewer than the number of blades, on a bladed disk to induce the smallest amplitude of blade response. The optimization process considers the presence of random mistuning, i.e. small involuntary variations in blade stiffness properties resulting, say, from manufacturing variability. Designed variations of these properties, known as intentional mistuning, is considered as an option to reduce blade response and the pattern of two blade types (A and B blades) is then part of the optimization in addition to the location of dampers on the disk. First, this study focuses on the formulation and validation of dedicated algorithms for the selection of the damper locations and the intentional mistuning pattern. Failure of one or several of the dampers could lead to a sharp rise in blade response and this issue is addressed by including, in the optimization, the possibility of damper failure to yield a fail-safe solution. The high efficiency and accuracy of the optimization algorithms is assessed in comparison with computationally very demanding exhaustive search results. Second, the developed optimization algorithms are applied to nonlinear dampers (underplatform friction dampers), as well as to blade-blade dampers, both linear and nonlinear. Further, the optimization of blade-only and blade-blade linear dampers is extended to include uncertainty or variability in the damper properties induced by manufacturing or wear. It is found that the optimum achieved without considering such uncertainty is robust with respect to it. Finally, the potential benefits of using two different types of friction dampers differing in their masses (A and B types), on a bladed disk are considered. Both A/B pattern and the damper masses are optimized to obtain the largest benefit compared to using identical dampers of optimized masses on every blade. Four situations are considered: tuned disks, disks with random mistuning of blade stiffness, and, disks with random mistuning of both blade stiffness and damper normal forces with and without damper variability induced by manufacturing and wear. In all cases, the benefit of intentional mistuning of friction dampers is small, of the order of a few percent.

This research examines the current challenges of using Lamb wave interrogation methods to localize fatigue crack damage in a complex metallic structural component subjected to unknown temperatures. The goal of this work is to improve damage localization results for a structural component interrogated at an unknown temperature, by developing a probabilistic and reference-free framework for estimating Lamb wave velocities and the damage location. The methodology for damage localization at unknown temperatures includes the following key elements: i) a model that can describe the change in Lamb wave velocities with temperature; ii) the extension of an advanced time-frequency based signal processing technique for enhanced time-of-flight feature extraction from a dispersive signal; iii) the development of a Bayesian damage localization framework incorporating data association and sensor fusion. The technique requires no additional transducers to be installed on a structure, and allows for the estimation of both the temperature and the wave velocity in the component. Additionally, the framework of the algorithm allows it to function completely in an unsupervised manner by probabilistically accounting for all measurement origin uncertainty. The novel algorithm was experimentally validated using an aluminum lug joint with a growing fatigue crack. The lug joint was interrogated using piezoelectric transducers at multiple fatigue crack lengths, and at temperatures between 20°C and 80°C. The results showed that the algorithm could accurately predict the temperature and wave speed of the lug joint. The localization results for the fatigue damage were found to correlate well with the true locations at long crack lengths, but loss of accuracy was observed in localizing small cracks due to time-of-flight measurement errors. To validate the algorithm across a wider range of temperatures the electromechanically coupled LISA/SIM model was used to simulate the effects of temperatures. The numerical results showed that this approach would be capable of experimentally estimating the temperature and velocity in the lug joint for temperatures from -60°C to 150°C. The velocity estimation algorithm was found to significantly increase the accuracy of localization at temperatures above 120°C when error due to incorrect velocity selection begins to outweigh the error due to time-of-flight measurements.