Elastography has emerged as a groundbreaking technique in recent decades, playing a pivotal role in enhancing medical imaging, especially in the realms of ultrasound diagnostics and magnetic resonance imaging. This research study delved deeply into these applications, distilling core procedures, effective methodologies, and universal computational strategies. It represents a pivotal advancement in proposing CT-based Dynamic Elastography (CTDE), establishing the theoretical and practical framework for its study and application.Venturing further, this research conducted meticulous virtual experiments to validate hypotheses and methodologies in CT-based elastography. This study utilized the finite element method to conduct simulations, which can obtain the same results as real-world dynamic vibration and CT-based imaging. Through analyzing CT data, the infinitesimal displacement generated as mechanical waves propagate through various tissues and materials can be measured, thereby determining the elasticity map. The two-dimensional simulations yielded a clear modulus map, not only affirming the proposed CTDE method but also laying a solid foundation for three-dimensional exploration. In the realm of three-dimensional experiments, we utilized CT imaging data, from which both displacement and modulus maps were generated upon processing. Our analysis revealed that this elastography technique refines the contours within CT images, supplementing them with comprehensive modulus data, and thus equips physicians with an advanced diagnostic tool for the precise identification of potential tissue anomalies. Looking forward, the prospects of CT elastography hold significant promise, indicative of a forthcoming era in advanced medical imaging that could revolutionize both research and clinical practice.

Magnetorheological elastomer (MRE) is a rubbery composite material filled with micron-sized ferromagnetic particles whose mechanical properties can be tailored by the application of external magnetic fields. Due to its magnetic and mechanical coupling effect, MRE is increasingly used in the field of engineering. Capturing the responses of MRE is essential for materials modeling and can be reached either by the physics-based finite element modeling or data-based artificial intelligence modeling. In this thesis, machine learning-based data-driven models are built to discover the structure-property linkages of MRE. The proposed method employs a pre-trained Convolutional Neural Network (CNN) and also an artificial neural network (ANN) to evaluate the critical features of the material microstructures that lead to precise predictions for the critical mechanical properties of MRE. It has been proven that these approaches can make compelling predictions while dramatically reduce the time needed for the calculation process. With low computation cost, the machine learning models also exhibit great potential in microstructure optimization.

Elastography is of great interest in the fields of solid mechanics and biomechanics due to its nondestructive capability of mapping elasticity of materials and tissues. The elastography framework relies on external excitations which stimulate deformation inside an object. The internal response is then acquired and analyzed to map the distribution of elastic moduli. The first method developed in this dissertation is that, with no need of measuring any internal responses, an elastography method integrated with tomography is proposed, only requiring the transmitted responses of applied sound waves. During the process, the tomography image (e.g., CT or MRI) and the applied waves are integrated into a computational model. Following the principle of factorial design, elastic distribution of all phases in the object is reconstructed when the computational transmission of waves matches with the measured transmission. As an improved algorithm to the integration method, in the dissertation, deep convolutional neural networks (CNNs) are studied for mapping elastography with much less computation time. A CNNs architecture is developed, considering the contribution of raw features.

In the dissertation, another elastography method is developed by untangling the complex wave-induced strain field into the one due to pure compressional or shear disturbance. The proposed untangling method is realized according to the fact that the volumetric strain is caused by compressional waves. By transforming both the volumetric strain tensor and the general tangled strain tensor to the shear wave direction, the transient vibration velocity and strain generated by compression wave can be separated from their initial coupled fields and used to reconstruct elastography.

Nondestructive ultrasound-based methods have been applied to evaluate the elastic properties of composite materials. While the wave modulus of elasticity is frequently reported higher than the static counterpart, the microstructural and physical mechanisms are not well understood. In the dissertation, a computational micromechanics is conducted to investigate the effects of inclusions on both the effective wave modulus of elasticity and static modulus of elasticity. Taking concrete as an example, based on concrete microstructures resolved with X-ray micro-tomography. It is demonstrated that the existence of void defects plays a significant role on the elastic properties of concrete when compared with the particles that are also called aggregate. It is shown that the higher wave modulus of elasticity of concrete than the static one is caused by the existence of crack-like voids with small aspect ratios.

Electromechanical devices like Dielectric Elastomers (DEs) have been recently developed with spectacular features. They have been widely used in biomedical devices such as artificial muscles and sensors. Other use of this material is for robotics, loud speakers, and dampers in bridges.

Although there are several advantages regarding the use of Dielectric Elastomers (DEs), there is still challenge on reducing the amount of voltage that it needs in order to get high strain.

This challenge is solved by adding Multi-Walled Nano-Tube inside the material which will increase the dielectric constant or relative permittivity. By increasing the relative permittivity, the strain that is got from the material will also be increased.

In 2015, Yu Wang started to do the experiments for DEs with MWNT inside to see how much higher strain we can get by adding those particles. In this report, those experimental data are validated by doing numerical simulation and also understanding of how other factors can be effective on increasing that strain ratio.

The objective of the research in this dissertation is to use novel adaptive materials called magnetorheological nanocomposites (MRNs) to build semi-active structures, and further apply such smart structures into the vehicle-bridge coupling system of high-speed rail so that the dynamic responses of the bridge can be controlled and suppressed significantly.

First, the dynamic behavior of a simplified double-beam system interconnected by an elastic layer is investigated. A semi-analytical method is developed to analyze the natural frequencies and corresponding mode shapes. The dynamic responses of forced system vibration are determined by the modal-expansion method using the natural frequencies and mode shapes obtained from the free vibration analysis.

Second, considering the damping effect of the viscoelastic layer, a double-beam system with a viscoelastic layer between two beams is observed. An iteration algorithm with modal-expansion method is used to analyze the dynamic responses of forced system vibration.

Third, an active control structure, a semi-active control structure and corresponding control algorithms are developed to suppress the vibration of the double-beam system with elastic layer or viscoelastic layer. In the active control structure, the independent modal space control and linear quadratic regulator are adopted to determine the active control force. With the mode shape filter and dynamic mechanical model, the determinations of stiffness increase and damping increase are obtained.

Fourth, a co-simulation method is proposed to complete the dynamic simulation of vehicle-bridge coupling system. The Matlab/Simulink is used to build a platform to ensure MSC/NASTRAN for bridge model and MSC/ADAMS for vehicle model working together. The vehicle-bridge coupling relationships are coded as a program block and inputted into that platform.

Finally, the semi-active control structure based on MRNs is inputted into the vehicle-bridge coupling system of high-speed railway to control and suppress the vibration of the bridge. MRNs are applied as the viscoelastic layer between floating slab track and bridge main beam to build the semi-active control structure for bridges. The semi-active control algorithm for MRNs is developed and inputted into that co-simulation platform. Numerical experiments have been made to illustrate and verify the efficiency of the proposed semi-active control structure in the end.

After the 1994 Northridge earthquake, to prevent the existing buildings from brittle damage and failure at the beam-column connections, a variety of energy dissipation devices have been developed. The magnetorheological (MR) fluid dampers stand out for their endurance, instant response, and adjustable damping force, etc. This study evaluates the seismic performances of the MR dampers applied with the Bouc-Wen model (MR-BW) and BWBN model (MR-BWBN), respectively, via comparing with a conventional viscoelastic damper model (VE) under the ground motions with three different peak ground acceleration (PGA) levels. The damper systems along with a moment-resisting frame (MF) simplified as SDOF system were modeled, and modal, pushover, harmonic, and transient analyses were performed using the finite element method. The results show that the natural frequency of an MF will be increased with the application of damper systems. Under the same transverse loading, the MR-BWBN may reduce more plastic deformation than the MR-BW and VE. Additionally, the maximum drift ratios of MR-BWBN were lower than the others subjected to PGA = 0.4 g and PGA = 0.588 g earthquakes, respectively. The cumulative energy dissipated by MR-BWBN is less than MR-BW subjected to the PGA = 0.2 g earthquake, but more under the PGA = 0.4 g and PGA = 0.588 g earthquakes.

Magneto-Rheological Elastomers (MREs) are smart materials whose mechanical properties can be altered by external magnetic fields rapidly and reversibly. In this thesis, the large-strain behavior of MREs was studied by nonlinear finite element simulations under uniaxial tension and pure shear deformation. A modeling approach has been employed to investigate the mechanical behavior of silicone-rubber based MREs. Mooney-Rivlin model was used to simulate the mechanical response of matrix. Cohesive-zone model depending on the assumption of rubber-iron adhesion energy was used to define interface properties between particles and matrix. All types of models showed strongly non-linear stress-strain behavior. The simulation results agreed well with the experiments carried out by other researchers. Parametric studies were created to analyze the impacts of particle fraction, interface adhesion and microstructures in composite on the mechanical response of MREs models. Simulations outlined the influence of interface adhesion

on the mechanical properties of MREs, which was more obvious in the case of higher particle volume fraction. Anisotropic Representative Volume Element (RVE) models revealed that the increase stiffness response due to the enhancement of chain-like particle alignment structures.

During the Northridge earthquake of 1994, many steel structures collapsed as a result of the connection failures in the structure. After investigation, it was concluded that the connections in the steel structure, including the column base connection, have to be made stronger and to be able to dissipate energy during seismic motion. To facilitate that, a new kind of damper system having Magnetorheological Elastomers (MRE) as the damping material is proposed here. MRE was taken because of its ability to dissipate energy and provide extra stiffness when needed. The damper system along with the column base connection was then modelled, and modal, harmonic and transient analyses were performed on the model using Finite Element Analysis in ANSYS. The results showed that MRE successfully decreased the moment reaction at the connection, making it more reliable during strong earthquakes. The analyses were performed with prescribed loading by SAC, and El Centro ground motion, and in both the cases the designed damper system showed its capability of dissipating energy. It was also seen that with MRE as damper, the natural frequency of the connection can also be controlled, which can prove useful in certain cases. A parametric study was then conducted to see how the effect varies with different material and physical parameters of MRE.

Stress analysis of Solid Rocket Motors (SRMs) using the finite element method provides insightful data that can be used to develop a structural diagnosis methodology. Finite element models with and without flaws were designed and subjected to thermal loads to simulate post-production storage cooling of SRMs. The models are designed with dimensions and material properties provided by researchers from the Air Force Research Laboratory (AFRL) at Edwards Air Force Base, CA. It was concluded that during the simulated cooling process, flaws create unique stress signatures dependent on flaw type, size, and location. These trends were then validated and contextualized using fracture and damage mechanic concepts. Existing methodologies for health diagnosis of SRMs are discussed and their limitations addressed. Specifically, limitations of a two-dimensional sensor-based methodology developed by AFRL and UC Irvine collaborators are critiqued for improvement. It is then proposed that a three-dimensional finite element analysis of SRMs with flaws produces more viable data for an improved health diagnosis method. In the future, results from the three-dimensional finite element analysis will serve as the basis for a new methodology supported by multi-sensor arrays and machine learning algorithms for a holistic health prognosis and diagnosis of SRMs.

Magnetorheological elastomers (MREs), as one of smart composites, exhibit characteristics of both particle reinforced composites and magnetorheological materials. Their mechanical properties (e.g., stiffness and damping) can be tailored rapidly, continuously and reversibly with applied magnetic field.

In this research MREs specimens have been fabricated, with their micro-structures and dynamic properties subsequently characterized via scanning electron microscope (SEM) and dynamic mechanical analysis (DMA). The magneto-viscoelastic behaviors have been systematically studied under different external magnetic fields, excitation frequencies and strain amplitudes.

A new linear GMM (Generalized Maxwell model)-based magneto-viscoelastic model of MREs is proposed and investigated under small strain. Further, a nonlinear magneto-viscoelastic constitutive model of MREs is developed under large strain. The model predicts the frequency-, amplitude-, and magneto-dependent behaviors of MREs. The internal damping mechanisms are considered by multiplicative decomposition of the deformation gradient and magnetic induction into elastic and inelastic parts. The energy dissipation is assumed to occur due to the frequency- and amplitude-dependent mechanical viscoelasticity as well as the frequency-, amplitude-, and magneto-dependent magnetic-viscoelasticity. Constitutive laws for material behaviors and evolution equations are derived that agree with the laws of thermodynamics. Both mechanical force-induced Payne effect and magneto-induced Payne effect are considered for the amplitude-induced nonlinearities by the introduction of internal state variables integrated in the model, which are interpreted as phenomenological measures for the current state of the filler network. The parameters of the proposed constitutive model are identified by experimental data. Then the shear storage and loss moduli are analyzed and compared with the experimental results to validate the model’s effectiveness.

Instantaneous-minimum-input-energy-based semi-active control algorithm (IMIEKC) for the base isolation system with both stiffness and damping varying simultaneously has been proposed and applied to MREs-based smart isolation system. The algorithm has been demonstrated by numerical simulations and compared with other methods to indicate it as an efficient semi-active control method. The passive controls and IMIEKC-based semi-active controls of a 5-story building with both linear and nonlinear magneto-viscoelastic models-based isolation systems have been demonstrated and analyzed to evaluated the corresponding control performance.