<p>In this work we propose and validate a computational method for reconstructing constitutive relations (material properties) in complex multiphysics phenomena based on incomplete and noisy measurements which is applicable to different problems arising in nonequilibrium thermodynamics and continuum mechanics. The parameter estimation problem is solved as PDE–constrained optimization using a gradient–based technique in the optimize–then–discretize framework. The reconstructed material properties taken as an example here are the transport coefficients characterizing diffusion processes such as the viscosity and the thermal conductivity, and we focus on problems in which these coefficients depend on the state variables in the system. The proposed method allows one to reconstruct a smooth constitutive relation defined over a broad range of the dependent variable. This research is motivated by questions arising in the computational analysis and optimization of advanced welding processes which involves modelling complex alloys in the liquid phase at high temperatures.</p> / Doctor of Philosophy (PhD)

Ultrasound acoustic energy transfer (UAET) is an emerging contactless technology that offers the capability to safely and efficiently power sensors and devices while eliminating the need to replace batteries, which is of interest in many applications. It has been proposed to recharge and communicate with implanted medical devices, thereby eliminating the need for invasive and expensive surgery and also to charge sensors inside enclosed metal containers typically found in automobiles, nuclear power plants, space stations, and aircraft engines. In UAET, energy is transferred through the reception of acoustic waves by a piezoelectric receiver that converts the energy of acoustic waves to electrical voltage. It has been shown that UAET outperforms the conventional CET technologies that use electromagnetic waves to transfer energy, including inductive coupling and capacitative coupling. To date, the majority of research on UAET systems has been limited to modeling and proof-of-concept experiments, mostly in the linear regime, i.e., under small levels of acoustic pressure that result in small amplitude longitudinal vibrations and linearized piezoelectricity. Moreover, existing models are based on the "piston-like" deformation assumption of the transmitter and receiver, which is only accurate for thin disks and does not accurately account for radiation effects. The linear models neglect nonlinear effects associated with the nonlinear acoustic wave propagation as well as the receiver's electroelastic nonlinearities on the energy transfer characteristics, which become significant at high source strengths. In this dissertation, we present experimentally-validated analytical and numerical multiphysics modeling approaches aimed at filling a knowledge gap in terms of considering resonant acoustic-piezoelectric structure interactions and nonlinear effects associated with high excitation levels in UAET systems. In particular, we develop a reduced-order model that can accurately account for the radiation effects and validate it by performing experiments on four piezoelectric disks with different aspect ratios. Next, we study the role of individual sources of nonlinearity on the output power characteristics. First, we consider the effects of electroelastic nonlinearities. We show that these nonlinearities can shift the optimum load resistance when the acoustic medium is fluid. Next, we consider the nonlinear wave propagation and note that the shock formation is associated with the dissipation of energy, and as such, shock formation distance is an essential design parameter for high-intensity UAET systems. We then present an analytical approach capable of predicting the shock formation distance and validate it by comparing its prediction with finite element simulations and experimental results published in the literature. Finally, we experimentally investigate the effects of both the nonlinearity sources on the output power characteristics of the UAET system by considering a high intensity focused ultrasound source and a piezoelectric disk receiver. We determine that the system's efficiency decreases, and the maximum voltage output position drifts towards the source as the source strength is increased. / Doctor of Philosophy / Advancements in electronics that underpinned the development of low power sensors and devices have transformed many fields. For instance, it has led to the innovation of implanted medical devices (IMDs) such as pacemakers and neurostimulators that perform life-saving functions. They also find applications in condition monitoring and wireless sensing in nuclear power plants, space stations, automobiles and aircraft engines, where the sensors are enclosed within sealed metal containers, vacuum/pressure vessels or located in a position isolated from the operator by metal walls. In all these applications, it is desired to communicate with and recharge the sensors wirelessly. Such a mechanism can eliminate the need for invasive and expensive surgeries to replace batteries of IMDs and preserve the structural integrity of metal containers by eliminating the need for feed through wires. It has been shown that ultrasound acoustic energy transfer (UAET) outperforms conventional wireless power transfer techniques. However, existing models are based on several assumptions that limit their potential and do not account for effects that become dominant when a higher output power is desired. In this dissertation, we present experimentally validated numerical and theoretical investigations to fill those knowledge gaps. We also provide crucial design recommendations based on our findings for the efficient implementation of UAET technology.

<p>Предмет истраживања су фракциона и тополошка уопштења једначине<br />телеграфичара као модела електричног вода. Фракционо уопштење се<br />огледа у томе што су класичне конститутивне релације електричних<br />елемената замењене фракционим. Модификација конститутивних<br />релација омогућује да се узму у обзир коначно време релаксације и<br />поларизације диелектрика, као и формирања магнетског поља, односно<br />историја процеса поларизације и магнетизације. Тополошко уопштење<br />огледа се у томе што елементарно коло вода, поред стандардних<br />елемената, има кондензатор и у редној грани којим се моделира ефекат<br />нагомилавања наелектрисања дуж елекричног вода, односно коначно<br />време релаксације.</p> / <p>Predmet istraživanja su frakciona i topološka uopštenja jednačine<br />telegrafičara kao modela električnog voda. Frakciono uopštenje se<br />ogleda u tome što su klasične konstitutivne relacije električnih<br />elemenata zamenjene frakcionim. Modifikacija konstitutivnih<br />relacija omogućuje da se uzmu u obzir konačno vreme relaksacije i<br />polarizacije dielektrika, kao i formiranja magnetskog polja, odnosno<br />istorija procesa polarizacije i magnetizacije. Topološko uopštenje<br />ogleda se u tome što elementarno kolo voda, pored standardnih<br />elemenata, ima kondenzator i u rednoj grani kojim se modelira efekat<br />nagomilavanja naelektrisanja duž elekričnog voda, odnosno konačno<br />vreme relaksacije.</p> / <p>The subject of research is the fractional and topological generalization of the<br />telegraphers&rsquo;s equation in transmission line modeling. The fractional<br />generalization is reflected in the fact that the classical constitutive relations of<br />electrical elements are replaced by the fractional ones. The modification of<br />constitutive relations allows for taking into account the finite relaxation and<br />polarization time of dielectric material, as well as the creation of the magnetic<br />field, it also allows for taking into account the history of polarization and<br />magnetization processes. The topological generalization of the elementary<br />circuit of transmission line, in addition to the standard elements, introduces a<br />capacitor in the series branch, which models the effect of charge<br />accumulation along the transmission line, i.e., the finite relaxation time.</p>

A comprehensive background is herein presented for lumbar skin strain and its effect on skin adhered wearable (SAW) products. A background of the development of computational models of the interaction of skin and novel SAWs being researched is also presented. These include products involving the use of high deflection strain gauges to measure skin strain during functional movements (FMs) as a method to address the complicated phenotyping of the etiological causes of low back pain (LBP). The background concludes with the mathematical calculation of the principal skin strain magnitudes and orientations using retroreflective marker coordinate data in a motion capture lab setting and the potential role of principal skin strain on the post-operative management of wounds to accelerate healing and minimize infection and scarring. The mechanics response of lumbar skin among 30 participants was measured during various FMs, for which high strain movements (Flexion, Flexion right/left, Sit To Stand) exhibited principal strain magnitudes repeatedly above 50% while others (Rotation right/left, Lateral Bending right/left, Extension, and Extension right/left) exhibited magnitudes repeatedly below 50%. Principal strain orientation was presented in easily visualizable mappings that demonstrated minimal variability both within and between participants for a given FM. Principal strain rates were measured, ranging between 25% and 151% per second among movements. The mechanics response of lumbar skin was again measured for a single participant, albeit this time between bare skin and skin with a SAW; which in this example was kinesiology tape with a high deflection nanocomposite strain gauge. Results indicated very significant skin restriction during Flexion, for which a macroscopic skin strain of 65% was reduced to 22% because of the KT tape and additionally down to 13% because of the addition of the sensor (on top of the KT tape). A FEM was created based off this scenario, for which it was shown that the mechanical properties of skin in vitro are insufficient in representing the mechanical response of skin due to its stiffness. This was hypothesized to be due to the increased hydration (lower stiffness) of in vivo skin, for which high deformation stiffness in the literature is not available. The thesis is concluded with future research directions that would benefit the design of SAWs where high deformation is considered. Future research directions are also discussed regarding post-operative wound healing and the potential role of repeated skin strains, such as concerning scarring and infection.