This thesis focuses on the continued extension, validation, and application of combined thermal-structural reduced order models for nonlinear geometric problems. The first part of the thesis focuses on the determination of the temperature distribution and structural response induced by an oscillating flux on the top surface of a flat panel. This flux is introduced here as a simplified representation of the thermal effects of an oscillating shock on a panel of a supersonic/hypersonic vehicle. Accordingly, a random acoustic excitation is also considered to act on the panel and the level of the thermo-acoustic excitation is assumed to be large enough to induce a nonlinear geometric response of the panel. Both temperature distribution and structural response are determined using recently proposed reduced order models and a complete one way, thermal-structural, coupling is enforced. A steady-state analysis of the thermal problem is first carried out that is then utilized in the structural reduced order model governing equations with and without the acoustic excitation. A detailed validation of the reduced order models is carried out by comparison with a few full finite element (Nastran) computations. The computational expedience of the reduced order models allows a detailed parametric study of the response as a function of the frequency of the oscillating flux. The nature of the corresponding structural ROM equations is seen to be of a Mathieu-type with Duffing nonlinearity (originating from the nonlinear geometric effects) with external harmonic excitation (associated with the thermal moments terms on the panel). A dominant resonance is observed and explained. The second part of the thesis is focused on extending the formulation of the combined thermal-structural reduced order modeling method to include temperature dependent structural properties, more specifically of the elasticity tensor and the coefficient of thermal expansion. These properties were assumed to vary linearly with local temperature and it was found that the linear stiffness coefficients and the "thermal moment" terms then are cubic functions of the temperature generalized coordinates while the quadratic and cubic stiffness coefficients were only linear functions of these coordinates. A first validation of this reduced order modeling strategy was successfully carried out.

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.

The mechanical behavior of Pb-free solder alloys is important, since they must maintain mechanical integrity under thermomechanical fatigue, creep, and mechanical shock conditions. Mechanical shock, in particular, has become an increasing concern in the electronics industry, since electronic packages can be subjected to mechanical shock by mishandling during manufacture or by accidental dropping. In this study, the mechanical shock behavior of Sn and Sn-Ag-Cu alloys was systematically analyzed over the strain rate range 10-3 - 30 s-1 in bulk samples, and over 10-3 - 12 s-1 on the single solder joint level. More importantly, the influences of solder microstructure and intermetallic compounds (IMC) on mechanical shock resistance were quantified. A thorough microstructural characterization of Sn-rich alloys was conducted using synchrotron x-ray computed tomography. The three-dimensional morphology and distribution of contiguous phases and precipitates was analyzed. A multiscale approach was utilized to characterize Sn-rich phases on the microscale with x-ray tomography and focused ion beam tomography to characterize nanoscale precipitates. A high strain rate servohydraulic test system was developed in conjunction with a modified tensile specimen geometry and a high speed camera for quantifying deformation. The effect of microstructure and applied strain rate on the local strain and strain rate distributions were quantified using digital image correlation. Necking behavior was analyzed using a novel mirror fixture, and the triaxial stresses associated with necking were corrected using a self-consistent method to obtain the true stress-true strain constitutive behavior. Fracture mechanisms were quantified as a function of strain rate. Finally, the relationship between solder microstructure and intermetallic compound layer thickness with the mechanical shock resistance of Sn-3.8Ag-0.7Cu solder joints was characterized. It was found that at low strain rates the dynamic solder joint strength was controlled by the solder microstructure, while at high strain rates it was controlled by the IMC layer. The influences of solder microstructure and IMC layer thickness were then isolated using extended reflow or isothermal aging treatments. It was found that at large IMC layer thicknesses the trend described above does not hold true. The fracture mechanisms associated with the dynamic solder joint strength regimes were analyzed.

With the increasing focus on developing environmentally benign electronic packages, lead-free solder alloys have received a great deal of attention. Mishandling of packages, during manufacture, assembly, or by the user may cause failure of solder joint. A fundamental understanding of the behavior of lead-free solders under mechanical shock conditions is lacking. Reliable experimental and numerical analysis of lead-free solder joints in the intermediate strain rate regime need to be investigated. This dissertation mainly focuses on exploring the mechanical shock behavior of lead-free tin-rich solder alloys via multiscale modeling and numerical simulations. First, the macroscopic stress/strain behaviors of three bulk lead-free tin-rich solders were tested over a range of strain rates from 0.001/s to 30/s. Finite element analysis was conducted to determine appropriate specimen geometry that could reach a homogeneous stress/strain field and a relatively high strain rate. A novel self-consistent true stress correction method is developed to compensate the inaccuracy caused by the triaxial stress state at the post-necking stage. Then the material property of micron-scale intermetallic was examined by micro-compression test. The accuracy of this measure is systematically validated by finite element analysis, and empirical adjustments are provided. Moreover, the interfacial property of the solder/intermetallic interface is investigated, and a continuum traction-separation law of this interface is developed from an atomistic-based cohesive element method. The macroscopic stress/strain relation and microstructural properties are combined together to form a multiscale material behavior via a stochastic approach for both solder and intermetallic. As a result, solder is modeled by porous plasticity with random voids, and intermetallic is characterized as brittle material with random vulnerable region. Thereafter, the porous plasticity fracture of the solders and the brittle fracture of the intermetallics are coupled together in one finite element model. Finally, this study yields a multiscale model to understand and predict the mechanical shock behavior of lead-free tin-rich solder joints. Different fracture patterns are observed for various strain rates and/or intermetallic thicknesses. The predictions have a good agreement with the theory and experiments.

Concrete columns constitute the fundamental supports of buildings, bridges, and various other infrastructures, and their failure could lead to the collapse of the entire structure. As such, great effort goes into improving the fire resistance of such columns. In a time sensitive fire situation, a delay in the failure of critical load bearing structures can lead to an increase in time allowed for the evacuation of occupants, recovery of property, and access to the fire. Much work has been done in improving the structural performance of concrete including reducing column sizes and providing a safer structure. As a result, high-strength (HS) concrete has been developed to fulfill the needs of such improvements. HS concrete varies from normal-strength (NS) concrete in that it has a higher stiffness, lower permeability and larger durability. This, unfortunately, has resulted in poor performance under fire. The lower permeability allows for water vapor to build up causing HS concrete to suffer from explosive spalling under rapid heating. In addition, the coefficient of thermal expansion (CTE) of HS concrete is lower than that of NS concrete. In this study, the effects of introducing a region of crumb rubber concrete into a steel-reinforced concrete column were analyzed. The inclusion of crumb rubber concrete into a column will greatly increase the thermal resistivity of the overall column, leading to a reduction in core temperature as well as the rate at which the column is heated. Different cases were analyzed while varying the positioning of the crumb-rubber region to characterize the effect of position on the improvement of fire resistance. Computer simulated finite element analysis was used to calculate the temperature and strain distribution with time across the column's cross-sectional area with specific interest in the steel - concrete region. Of the several cases which were investigated, it was found that the improvement of time before failure ranged between 32 to 45 minutes.

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.

Gels are three-dimensional polymer networks with entrapped solvent (water etc.). They bear amazing features such as stimuli-responsive (temperature, PH, electric field etc.), high water content and biocompatibility and thus find a lot of applications. To understand the complex physics behind gel's swelling phenomenon, it is important to build up fundamental mechanical model and extend to complicated cases. In this dissertation, a coupled large deformation and diffusion model regarding gel's swelling behavior is presented. In this model, free-energy of the total gel is constituted by polymer stretching energy and polymer-solvent mixing energy. In-house nonlinear finite element code is implemented with fast computational capability. Complex phenomenon such as buckling and healing of cracked gel by swelling are studied. Due to the wide coverage of polymeric materials and solvents, solvent diffusion in gels not only follows Fickian diffusion law where concentration map is continuous but also follows non-Fickian diffusion law where concentration map shows high gradient. Phenomenological model with viscoelastic polymer constitutive and concentration dependent diffusivity is created. The model well captures this special diffusion phenomenon such as sharp diffusion front and distinctive swollen and unswollen region.

Skin electronics is one of the most promising applications of stretchable electronics. The versatility of skin electronics can only be guaranteed when it has conformal contact with human skin. While both analytical and numerical solutions for contact between serpentine interconnects and soft substrate remain unreported, the motivation of this thesis is to render a novel method to numerically study the conformability of the serpentine interconnects. This thesis explained thoroughly how to conduct finite element analysis for the conformability of skin electronics, including modeling, meshing method and step setup etc.. User-defined elements were implemented to the finite element commercial package ABAQUS for the analysis of conformability. With thorough investigation into the conformability of Fermat’s spiral, it has been found that the kirigami based pattern exhibits high conformability. Since thickness is a key factor to design skin electronics, the thesis also talked about how the change of thickness of the skin electronics impacts on the conformability.

This research focuses on the benefits of using nanocomposites in aerospace structural components to prevent or delay the onset of unique composite failure modes, such as delamination. Analytical, numerical, and experimental analyses were conducted to provide a comprehensive understanding of how carbon nanotubes (CNTs) can provide additional structural integrity when they are used in specific hot spots within a structure. A multiscale approach was implemented to determine the mechanical and thermal properties of the nanocomposites, which were used in detailed finite element models (FEMs) to analyze interlaminar failures in T and Hat section stringers. The delamination that first occurs between the tow filler and the bondline between the stringer and skin was of particular interest. Both locations are considered to be hot spots in such structural components, and failures tend to initiate from these areas. In this research, nanocomposite use was investigated as an alternative to traditional methods of suppressing delamination. The stringer was analyzed under different loading conditions and assuming different structural defects. Initial damage, defined as the first drop in the load displacement curve was considered to be a useful variable to compare the different behaviors in this study and was detected via the virtual crack closure technique (VCCT) implemented in the FE analysis.

Experiments were conducted to test T section skin/stringer specimens under pull-off loading, replicating those used in composite panels as stiffeners. Two types of designs were considered: one using pure epoxy to fill the tow region and another that used nanocomposite with 5 wt. % CNTs. The response variable in the tests was the initial damage. Detailed analyses were conducted using FEMs to correlate with the experimental data. The correlation between both the experiment and model was satisfactory. Finally, the effects of thermal cure and temperature variation on nanocomposite structure behavior were studied, and both variables were determined to influence the nanocomposite structure performance.

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.