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Mechanical metamaterials are becoming an emerging frontier in scientific research and engineering innovation due to its unique properties, arising from innovative geometrical designs rather than constituent materials. Reconfigurable metamaterials can change their shapes and structures dramatically under external forces or environmental stimuli. It offers an enhanced flexibility in performance by coupling dynamically changing structural configuration and tunable properties, which has found broad potential applications in 3D meso-structures assembly and programmable machines. Despite extensive studies on harnessing origami, the ancient paper folding art, for design of mechanical metamaterials, the study on utilizing its close cousin, kirigami (“kiri” means cut), for programmable reconfigurable mechanical metamaterials and machines remains largely unexplored. In this dissertation, I explore harnessing the uniqueness of cuts in kirigami for achieving extraordinary mechanical properties and multifunctionalities in krigami-based metamaterials, as well as its potential applications in programmable machines and soft robotics. I first exploit the design of hierarchical cuts for achieving high strength, high stretchability, and tunable mechanical properties in hierarchical rotation-based kirigami mechanical metamaterials. Hierarchical line cuts are introduced to a thin sheet composed of non-stretchable materials (copy paper), less stretchable materials (acrylics), and highly stretchable materials (silicone rubber, PDMS), to explore the role of constituent material properties. The cut unit in the shape of solid rectangles with the square shape as a special case was demonstrated for achieving the extreme stretchability via rigid rotation of cut units. It shows that a higher hierarchical level contributes to a higher expandability and lower stiffness to constituent material. However, when such kirigami structure is applied onto less-stretchable materials (e.g. acrylics), its stretchability is almost eliminated regardless of the hierarchical level, because severe stress concentration at rotation hinges leads to the structure failure at the very beginning stage of pattern transformation. To address this challenge, I propose a hinge design which can significantly reduce the stress concentration at cut tips and enable high stretchability for rotation-based kirigmai structure, even on acrylic thin sheet. I also study the tunable photonic behavior of proposed hierarchical kirigami metamaterial by simple strain-induced structural reconfiguration. I then explore the programmability of kiri-kirgami structures by introducing notches to the simplest kirigami structure patterned with parallel line cuts for breaking its deformation symmetry. Engraving the flat-cut kirigami structure enables programmable control of its out-of-plane tilting orientation, thus generating a variety of inhomogeneous structural configurations on demand. I find that compared to the its counterpart without engraving notches, the introduced notches have a negligible effect on both the stress-strain curve over the large strain range and the extreme stretchability, however, they reduce the critical buckling force largely. Furthermore, I demonstrate the adaptive kiri-kirigami structure through local actuation with its tilting directions to be programmed and switched in response to the change of environmental temperature. Lastly, I demonstrate the potential promising outcome of kiri-kirigami structures as adaptive building envelope in energy efficient buildings, especially in electric saving for lighting and cooling load saving through numerical simulation. In addition to kirigami based soft metamaterials, I also investigate the utilization of soft materials and soft structures for robotics functions. First, I explore the design of soft doming actuator upon pneumatic actuation and its implications in design of multifunctional soft machines. I propose a novel bilayer actuator, which is composed of patterned embedded pneumatic channel on top for radial expansion and a solid elastomeric layer on bottom for strain-limiting. I show that both the cavity volume and bending angle at the rim of the actuated dome can be controlled by tuning the height gradient of the pneumatic channel along the radial direction. I demonstrate its potential multifunctional applications in swimming, adhesion, and gripping. I further explore harnessing doming-based bilayer doming actuator for developing soft climbing robot. I characterize and optimize the maximum shear adhesion force of the proposed soft adhesion actuator for strong and rapid reversible adhesion on multiple types of smooth and semi-smooth surfaces. Based on the switchable adhesion actuator, I design and fabricate a novel load-carrying amphibious climbing soft robot (ACSR) by combining with a soft bending actuator. I demonstrate that it can operate on a wide range of foreign horizontal and vertical surfaces, including dry, wet, slippery, smooth, and semi-smooth ones on ground, as well as under water with certain load-carrying capability. I show that the vertical climbing speed can reach about 286 mm/min (1.6 body length/min) while carrying over 200g object (over 5 times the weight of ACSR itself) during climbing on ground and under water. / Mechanical Engineering

Yes / This paper presents empirical results of an innovative beam scanning leaky-wave antenna (LWA) which enables scanning over a wide angle from -35o to +34.5o between 57 GHz and 62 GHz, with broadside radiation centered at 60 GHz. The proposed LWA design is based on composite right/left-handed transmission-line (CRLH-TL) concept. The single layer antenna structure includes a matrix of 3×9 square slots that is printed on top of the dielectric substrate; and printed on the bottom ground-plane are Π and Tshaped slots that enhance the impedance bandwidth and radiation properties of the antenna. The proposed antenna structure exhibits metamaterial property. The slot matrix provides beam scanning as a function of frequency. Physical and electrical size of the antenna is 18.7×6×1.6 mm3 and 3.43􀣅􀫙×1.1􀣅􀫙×0.29􀣅􀫙, respectively; where 􀣅􀫙 is free space wavelength at 55 GHz. The antenna has a measured impedance bandwidth of 10 GHz (55 GHz to 65 GHz) or fractional bandwidth of 16.7%. Its optimum gain and efficiency are 7.8 dBi and 84.2% at 62 GHz. / Partially supported by innovation programme under grant agreement H2020-MSCA-ITN-2016 SECRET- 722424 and the financial support from the UK Engineering and Physical Sciences Research Council (EPSRC) under grant EP/E022936/1.

After being theorized by Veselago in 1967, recent developments in metamaterials over the last two decades have allowed scientists and researchers to physically demonstrate that artificial composite media can be engineered to exhibit exotic material properties, such as negative refractive index, by exploiting features in arrays of sub-wavelength unit inclusions. These unconventional electromagnetic properties are realized through the coupling of the microscopic unit inclusions, which govern the macroscopic properties of the structure. After demonstrating that a periodic array of capacitively-loaded loop (CLL) inclusions paired with continuous wire results in negative refraction, this study performs numerical simulations to characterize random metamaterial structures. These structures consist of CLLs that are randomized in both position and orientation. In addition, this thesis introduces an innovative antenna enhancing structure consisting of capacitively-loaded loop (CLL) metamaterial elements loaded radially around a standard dipole antenna at an electrically small distance. As a result of this innovative arrangement, the dipole antenna is easily transformed into a directive mechanically scanned antenna with high realized gain. The desired directivity and gain can be tuned based on the number of radial CLL fins placed around the dipole. Interactions between the antenna and metamaterial elements result in significant enhancement of the maximum radiated field amplitude and front-to-back ratio. This innovative CLL-loaded dipole antenna is compared to the conventional Yagi-Uda antenna. The structures presented in this thesis are modeled using full-wave simulation, and one antenna structure is experimentally verified as a proof-of-concept. / Master of Science

Focused ultrasound (FUS) is an emerging technology, and it plays an essential role in clinical and contactless acoustic energy transfer applications. These applications have critical criteria for the acoustic pressure level, the creation of complex pressure patterns, spatial management of the complicated acoustic field, and the degree of nonlinear waveform distortion at the focal areas, which have not been met to date. This dissertation focuses on introducing experimentally validated novel numerical approaches, optimization algorithms, and experimental techniques to fill existing knowledge gaps and enhance the functionality of holographic acoustic lenses (HALs) with an emphasis on applications related to biomedical-focused ultrasound and ultrasonic energy transfer. This dissertation also aims to investigate the dynamics of nonlinear acoustic beam shaping in engineered HALs. First, We will introduce 3D-printed metallic acoustic holographic mirrors for precise spatial manipulation of reflected ultrasonic waves. Optimization algorithms and experimental validations are presented for applications like contactless acoustic energy transfer. Furthermore, a portion of the present work focuses on designing holographic lenses in strongly heterogeneous media for ultrasound focusing and skull aberration compensation in transcranial-focused ultrasound. To this end, we collaborated with the Biomedical Engineering and Mechanics Department as well as Fralin Biomedical Research Institute to implement acoustic lenses in transcranial neuromodulation, targeting to improve the quality of life for patients with brain disease by minimizing the treatment time and optimizing the ultrasonic energy into the region of interest. We will also delve into the nonlinear regime for High-Intensity Focused Ultrasound (HIFU) applications, this study is structured under three objectives: (1) establishing nonlinear acoustic-elastodynamics models to represent the dynamics of holographic lenses under low- to high-intensity acoustic fields; (2) validating and leveraging the resulting models for high-fidelity lens designs used in generating specified nonlinear ultrasonic fields of complex spatial distribution; (3) exploiting new physical phenomena in acoustic holography. The performed research in this dissertation yields experimentally proven mathematical frameworks for extending the functionality of holographic lenses, especially in transcranial-focused ultrasound and nonlinear wavefront shaping, advancing knowledge in the burgeoning field of the inverse issue of nonlinear acoustics, which has remained underdeveloped for many years. / Doctor of Philosophy / Ultrasonic waves are sound waves that have frequencies higher than the upper audible limit of human hearing. The versatility and non-invasive nature of ultrasonic waves make them a valuable tool in numerous scientific, medical, and industrial applications. In healthcare, ultrasonic waves are employed in diagnostic imaging techniques, such as ultrasound scans, to create images of internal body structures. Ultrasonic waves are also used for non-destructive testing (NDT) of materials, detecting flaws or cracks within structures without causing any damage. Furthermore, this technology finds applications in the field of material science for the manipulation of particles and in biomedical research for drug delivery systems. Focused ultrasound sound is an emerging non-invasive therapeutic modality that uses focused ultrasound waves to target tissue within the body without damaging the surrounding tissue. This technology allows for precise delivery of ultrasound energy to a specific region, where it can induce various desired therapeutic effects depending on the targeting location and parameters. Therapeutic focused ultrasound has the advantage of being non-invasive, reducing the risks and recovery time associated with traditional surgery. It can be precisely controlled and monitored in real-time with imaging techniques such as ultrasound or MRI, ensuring the targeted treatment of pathological tissues while sparing healthy ones. Applications of therapeutic are broad and include tumor ablation, facilitation of drug delivery across the blood-brain barrier, relief of chronic pain, and treatment of essential tremor and other neurological disorders. The domain of therapeutic focused ultrasound is continually advancing, driven by research that seeks to extend its applications. Recent developments in acoustic engineering and 3D printing have led to the creation of acoustic holograms, or holographic acoustic lenses, which allow for more refined control over the spatial structure of the acoustic field. These technological advancements hold the promise of enhancing FUS by improving the accuracy of acoustic field localization and providing a more cost-effective solution compared to conventional systems like phased array transducers. However, the accuracy and applicability of existing models and techniques are constrained by assumptions, including the uniformity of the propagation medium and the linearity of the acoustic field, which limits the functionality and restricts the potential applications of acoustic holograms. In this dissertation, we present novel numerical techniques, algorithms, and proof-of-concept experiments to fill those knowledge gaps and expand the functionality of acoustic holograms in crucial applications.

Mechanical metamaterials are novel materials that display unique properties from their underlying microstructure topology rather than the constituent material they are made from. Their effective properties displayed at macroscale depend on the design of their microstructural topology. In this work, two classes of mechanical metamaterials are studied within the 2D-space. The first class is made of trusses, referred to as truss-based mechanical metamaterials. These materials are studied through their application to a beam component, where finite element analysis is performed to determine how truss-based microstructures affect the displacement behavior of the beam. This analysis is further subsidized with the development of a graphical user interface, where users can design a beam made of truss-based microstructures to see how their design affects the beam's behavior. The second class of mechanical metamaterial investigated is made of self-assembled structures, called spinodoids. Their smooth topology makes them less prone to high stress concentrations present in truss-based mechanical metamaterials. A large database of spinodoids is generated in this study. Through data-driven modeling the geometry of the spinodoids is coupled with their Young's modulus value to approach inverse design under uncertainty. To see mechanical metamaterials applied to industry they need to be better understood and thoroughly characterized. Furthermore, more tools that specifically help push the ease in the design of these metamaterials are needed. This work aims to improve the understanding of mechanical metamaterials and develop efficient computational design strategies catered solely for them. / Master of Science / Mechanical metamaterials are hierarchical materials involving periodically or aperiodically repeating unit cell arrangements in the microscale. The design of the unit cells allows these materials to display unique properties that are not usually found in traditionally manufactured materials. This will enable their use in a multitude of potential engineering applications. The presented study seeks to explore two classes of mechanical metamaterials within the 2D-space, including truss-based architectures and spinodoids. Truss-based mechanical metamaterials are made of trusses arranged in a lattice-like framework, where spinodoids are unit cells that contain smooth structures resulting from mimicking the two phases that coexist in a phase separation process called spinodal decomposition. In this research, computational design strategies are applied to efficiently model and further understand these sub-classes of mechanical metamaterials.

Esta tesis trata sobre el fascinante fenómeno de la transmisión extraordinaria a través de láminas metálicas nonoestructuradas periódicamente con aperturas al corte. Un efecto relacionado con la excitación de un tipo de ondas superficiales como son los plasmones de superficie. Además, en aquellas estructuras formadas por el apilamiento de dos o más láminas metálicas se consiguen nuevas funcionalidades, como magnetismo artificial que da lugar a resonancias magnéticas y por tanto la posibilidad de obtener un índice de refracción negativo.Mediante un estudio teórico y numérico se ha comprobado que este tipo de respuesta magnética efectiva se debe a la excitación de resonancias plasmónicas internas en la estructura. Obteniéndose, bajo incidencia normal, un índice de refracción efectivo negativo en la dirección de propagación en el caso de que dichas resonancias se produzcan en zonas del espectro donde se obtenga la permitividad negativa, conectando el mundo de la plasmónica con el de los metamateriales. Uno de los principales objetivos en el diseño de metamateriales es obtener un índice de refracción negativo en un gran ancho de banda. Sin embargo, este objetivo suele ser complicado de conseguier al basar los diseños en fenómenos resonantes. Es por ello que en esta tesis se ha propuesto un diseño basado en el apilamiento de estructuras fishnet con diferentes grosores de dieléctrico para conseguir aumentar el ancho de banda en el cual se consigue un índice negativo. Básicamente, la obtención de tal efecto se basa en la excitación de resonancias plasmónicas a distintas frecuencias al estar formada la celda unidad por difentes grososres de dieléctrico. La hibridación que se produce entre dichas resonancias permite aumentar el ancho de banda con índice negativo. Aunque la transmisión extraordinaria esta principalmente relacionada con excitación de plasmones de superficie, los resultados mostrados en la tesis demuestran que para el caso de láminas metálicas rodeadas por dieléctricos también se consigue transmisión extraordinaria debido a la adaptación de la luz incidente a los modos soportados por los medios dieléctricos siempre y cuando el metal se encuentre estructurado periódicamente. / Ortuño Molinero, R. (2012). Extraordinary Transmission Filtering Structures based on Plasmonic Metamaterials [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/14639

[EN] Metamaterials are periodic structures whose unit cells are small compared to the wavelength at the operating frequency. Under these conditions, these artificial materials can be considered as homogeneous media whose constitutive parameters depend on the characteristics of the unit cells. The discovery of metamaterials opened a new research field that has produced many works with microwaves, optical waves and acoustic waves. In this context, the main goal of this thesis is the study of new structures based on metamaterials that allow controlling of electromagnetic energy. In particular, new solutions for localization and absorption of electromagnetic waves are proposed. The thesis has been developed in the Wave Phenomena Group of the Polytechnic University of Valencia and in collaboration with the Group of Acoustic and Electromagnetic Metamaterials at the University of Exeter. The problems studied in the first part of this thesis are energy harvesting for subsequent absorption, wireless power transfer and new systems that can be used as position sensors. To solve these problems a new type of cylindrical, multilayer and anisotropic structures known as Radial Photonic Crystals are used. The radial dependence of the constitutive parameters generates, in these structures, a behavior like a one dimensional photonic crystals. Among the results obtained with these structures, it is included the first experimental demonstration of a Radial Photonic Crystals based resonator. Absorption of electromagnetic waves by thin layers of lossy materials is the second topic of this thesis. The main target is the theoretical and experimental study of the absorption enhancement in thin layers by using two-dimensional periodic structures, also called metasurfaces. Specifically, we studied the effects of a square lattice of coaxial cavities covered by a thin layer of lossy material. As a result, an enhancement of the absorption peaks that can produce total absorption is achieved. The semi-analytical study of this structure has allowed obtaining expressions that control the position of the absorption peak and its amplitude; which have helped to develop a design methodology for total absorption systems. / [ES] Los metamateriales son estructuras periódicas cuyas celdas unidad son muy pequeñas en comparación con la longitud de onda a la frecuencia de trabajo. Bajo estas condiciones, estos materiales artificiales pueden considerarse como medios homogéneos cuyos parámetros constitutivos dependen de las características de las celdas unidad que los componen. La aparición de los metamateriales abrió un nuevo campo de investigación que ha generado multitud de trabajos en las líneas de microondas, óptica y acústica. En este contexto, el objetivo principal de esta tesis es el estudio de nuevas estructuras basadas en metamateriales que permitan el control de la energía electromagnética. En particular, plantea nuevas soluciones para problemas de localización y absorción de ondas electromagnéticas. La tesis ha sido desarrollada en el Grupo de Fenómenos Ondulatorios de la Universidad Politécnica de Valencia y en colaboración con el Grupo de Metamateriales Acústicos y Electromagnéticos de la Universidad de Exeter. Los problemas estudiados en la primera parte de esta tesis son la concentración de energía para su posterior absorción, la transferencia inalámbrica de potencia y nuevos sistemas capaces de ser empleados como sensores de posición. Para la solución de estos problemas se emplean un nuevo tipo de estructuras cilíndricas, multicapa y anisótropas conocidas como Cristales Fotónicos Radiales. La dependencia radial de los parámetros constitutivos de los materiales que componen cada una de sus capas genera, en estas estructuras, un comportamiento similar al de los cristales fotónicos unidimensionales. Entre los resultados obtenidos con estas estructuras, cabe destacar la primera demostración experimental de un resonador basado en Cristales Fotónicos Radiales. La absorción de ondas electromagnéticas por capas delgadas de materiales con pérdidas es el segundo tema tratado en esta tesis. El objetivo principal es el estudio teórico y experimental del aumento de la absorción en capas delgadas mediante el uso de estructuras periódicas bidimensionales, también llamadas metasuperficies. En concreto, se han estudiado los efectos de una red cuadrada de cavidades coaxiales sobre la que se coloca una capa delgada de un material con pérdidas. Como resultado, se consigue un aumento de la absorción que permite obtener picos de absorción total. El estudio semianalítico de esta estructura ha permitido obtener expresiones que controlan la posición del pico de absorción y su amplitud; las cuales han permitido desarrollar una metodología de diseño para sistemas de absorción total. / [CA] Els metamateriales són estructures periòdiques en els que les cel·les unitat són molt xicotetes en comparació amb la longitud d'ona a la freqüència de treball. Tenint en consideració aquestes condicions, aquestos materials artificials poden considerar-se com a mitjans homogenis en els que els paràmetres constitutius depenen de les característiques de les cel·les unitat que els componen. A més, l'aparició dels metamateriales va obrir un nou camp d'investigació que ha generat multitud de treballs en les línies de microones, òptica i acústica. En aquest context, l'objectiu principal d'aquesta tesi és l'estudi de noves estructures basades en metamateriales que permeten el control de l'energia electromagnètica. En particular, planteja noves solucions per a problemes de localització i absorció d'ones electromagnètiques. La tesi ha sigut realitzada en el Grup de Fenòmens Ondulatoris de la Universitat Politècnica de València i en col·laboració amb el Grup de Metamateriales Acústics i Electromagnètics de la Universitat d'Exeter. Els problemes analitzats en la primera part de la tesi són la concentració d'energia per a la seua posterior absorció, la transferència inalàmbrica de potència i nous sistemes capaços de ser empleats com a sensors de posició. Per a la solució dels problemas identificats s'utilitza un nou tipus d'estructures cilíndriques, multicapa i anisòtropes conegudes com a Cristalls Fotónics Radials. La dependència radial dels paràmetres constitutius dels materials que componen cadascuna de les seues capes genera, en aquestes estructures, un comportament semblant al dels Cristalls Fotónics Unidimensionals. Entre els resultats obtinguts, cal destacar la primera demostració experimental d'un ressonador basat en Cristalls Fotónics Radials. Pel que respecta a la segon part de la tesi, l'absorció d'ones electromagnètiques per capes primes de materials amb pèrdues és tema tractat. L'objectiu principal és l'estudi teòric i experimental de l'augment de l'absorció en capes primes per mitjà de l'ús d'estructures periòdiques bidimensionals, també denominades metasuperficies. En concret, s'han examinat els efectes d'una xarxa quadrada de cavitats coaxials sobre la qual es col·loca una capa prima d'un material amb pèrdues. Com a resultat, s'aconseguix un augment de l'absorció que permet obtindre pics d'absorció total. Així mateix, l'estudi semi-analític d'aquesta estructura ha permés obtindre expressions que controlen la posició del pic d'absorció i la seua amplitud; les quals han permés desenvolupar una metodologia de disseny per a sistemes d'absorció total. / Díaz Rubio, A. (2015). Control of electromagnetic energy by metamaterials [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/54137

4D printing is a rapidly emerging field in which 3D printed stimuli-responsive materials produce morphing and multifunctional structures, with time being the fourth dimension. This approach enables the 3D printing of pre-programmed responsive sheets, which transition into complex curved shapes upon exposure to external stimuli, resulting in a substantial reduction in material consumption and printing time (70 - 90 %). Commonly used materials for 4D printing are polymer composites, such as hydrogels, polydimethylsiloxane (PDMS), liquid crystal elastomers (LCEs), and shape memory polymers (SMPs). However, the low elastic modulus (E) that these materials exhibit during shape change (E range of 10-4 – 10 MPa) limits their scalability, actuation stress, and load bearing. Moreover, these materials exhibit low ultimate stresses, leading to correspondingly low toughness (K) values in the range of 0.08 to 5 MJ m-3. Consequently, this results in structures with low damage tolerance. Therefore, an existing challenge for the field of 4D printing is to develop materials that can maintain their large and predictable morphing mechanism for complex shape transformation, while improving the E and K for high performance applications. Furthermore, many existing approaches rely on passive structures that necessitate the control of global conditions of the surrounding environment (e.g., hot plates, ovens, external magnets, water baths) to provide the stimulus for actuation. In this work, we tackle these challenges by introducing novel materials, ink formulations, and innovative printing techniques for multi-material Direct Ink Writing (DIW). We aim to create electrically controllable 4D printed structures that exhibit exceptional stiffness and toughness, all while preserving a large and predictable morphing mechanism for intricate shape transformations. First, we introduce multiscale heterogeneous polymer composites as a novel category of stiff, electrically controllable thermally responsive 4D printed materials. These composites consist of an epoxy matrix with an adjustable cross-link density and a plurality of isotropic and anisotropic nanoscale and microscale fillers. Leveraging this platform, we generate a set of 37 inks covering a broad range of negative and positive linear coefficients of thermal expansion. This set of inks exhibits an elastic modulus range that is four orders of magnitude greater than that of existing 4D printed materials and offers tunable electrical conductivities for simultaneous Joule heating actuation and self-sensing capabilities. Utilizing electrically controllable bilayers as building blocks, we design and print a flat geometry that changes shape into a 3D self-standing lifting robot, displaying record actuation stress and specific force when compared to other 3D printed actuators. We integrate this lifting robot with a closed-loop control system, achieving autoregulated actuation exhibiting a 4.8 % overshoot and 0.8 % undershoot, while effectively rejecting disturbances of up to 170 times the robot's weight. Furthermore, we employ our ink palette to create and 3D print planar lattice structures that transform into various self-supporting complex 3D surfaces. Ultimately, we achieve a 4D printed electrically controlled crawling robotic lattice structure, highlighting its capacity to transport loads up to 144 times its own weight. Finally, we introduced a printable PDMS adhesive that serves as synthetic fascia to hold our epoxy-based synthetic muscle together, enhancing the K of our 4D printed structures, all while maintaining high stiffness, large, predictable, and addressable actuation mechanism. Through the integration of these soft adhesive materials with high-stiffness thermally responsive epoxies via DIW, we achieved an improvement of about two orders of magnitude in the K of the resulting synthetic muscle composite, all while maintaining high stiffness and morphing mechanism. Utilizing this fabrication method, we printed an electrically controllable bilayer exhibiting damage detection and tolerance, enduring up to 7 fractures while continuing to function effectively. Furthermore, we integrated the synthetic muscle composite into our lifting robot design, setting yet again new records in specific force and actuation stress when compared to other 3D printed actuators. Notably, even after failure, the actuator maintained its operational integrity and high performance. Ultimately, we present a 4D printed lattice structure featuring the incorporation the synthetic muscle composite, showcasing a sensitive electrically responsive surface with fracture detection capabilities. To emphasize this, we subjected one of these 4D printed lattices to extreme conditions, driving a car over it. Notably, the lattice structure detected fractures and exhibited high resilience, enduring external compressive damage equivalent to 331,060 times its own weight. / 2026-05-23T00:00:00Z

In recent years, the study of metamaterials has been a subject of much interest, with acoustic metamaterials being applied to a wide range of applications. This utility is in part due to the incorporation of various elements in their design. The addition of local resonators provides greater versatility in controlling vibrations. Nonlinear elements introduce features such as discrete breathers and frequency shift. Electromechanical metamaterials have been established to have great potential for use in simultaneous energy harvesting in addition to vibration control. Furthermore, metamaterials with quasiperiodic patterning have been shown to possess useful properties such as edge-localized modes. However, no works investigate the interaction between all these elements, especially in the nonlinear regime. In this work, we investigate a unique metamaterial with local resonators, nonlinearity, electromechanical elements, and quasiperiodicity. The proposed metamaterial is examined using both analytical and numerical techniques in order to firmly establish the effects of each element. First, a nonlinear metamaterial with electromechanical local resonators is studied using the perturbation method of multiple scales, wavepacket excitation and direct integration, and specto-spatial processing techniques. The effect of the electromechanical local resonators is established for both the linear and nonlinear regimes, notably including the addition of new bandgaps and pass bands. The influence of electrical parameters on the system dynamics is explored through parametric analysis, demonstrating their use in tuning the system response. It is also shown that nonlinear phenomena such as localized solitons and frequency shift are present in the voltage response of the electromechanical metamaterial. Next, a nonlinear metamaterial with local resonators and quasiperiodicity is investigated using the method of multiple scales as well as numerical solution of the method of harmonic balance. Topological features stemming from quasiperiodicity are observed in the linear and nonlinear regimes. The presence of local resonators is shown to result in an additional, topologically trivial bandgap. The influence of quasiperiodic parameters and the source of quasiperiodicity on the system's band structure and mode shapes are established in both the linear and nonlinear regimes. Nonlinearity is also shown to affect topological features such as edge modes, resulting in amplitude dependence that can affect the localization of these modes in the nonlinear regime. Finally, a metamaterial with nonlinearity, electromechanical local resonators, and quasiperiodic patterning is modeled and investigated. Multiple configurations are examined, including different shunt circuits coupled to the electromechanical resonators and different sources of quasiperiodic patterning. It is shown that electromechanical local resonators produce two topologically trivial bandgaps, compared to the single trivial bandgap of the purely mechanical resonator. The influence of mechanical, electrical, and quasiperiodic parameters is explored to establish the effects of these parameters on bandgap formation in the linear regime. The behavior of the metamaterial in the nonlinear regime was found to be consistent with a purely mechanical system, with no adverse effects from the presence of electromechanical elements. The impact of nonlinear and quasiperiodic phenomena on energy harvesting is also investigated. Through exploration of this unique metamaterial, it is shown that beneficial features from all elements can be present at once, resulting in a versatile metamaterial with great potential for numerous applications. / Doctor of Philosophy / In recent years, the study of metamaterials has been a subject of much interest. Despite their name, metamaterials are not homogenous materials, but engineered structures designed to possess properties not found in naturally occurring materials. Many elements can be incorporated into metamaterial design, each with its own benefits. These can range from nonlinear springs, which allow the metamaterial to behave differently as its deformation increases, to electromechanical components, which convert the motion of the metamaterial into electrical voltage. While these elements have been examined individually and in certain combinations, no works examine the combination of elements proposed in this dissertation. In this work, we investigate the impact of nonlinearity, electromechanical components, and two other beneficial elements on the system's vibration response. Combinations of these elements are examined using various analysis techniques, which are used to establish the effects of each element individually as well as their interaction when combined. Multiple variations are examined for each element, such as different types of nonlinearity or different circuits attached to the electromechanical elements. This allows us to confirm the presence of valuable features exclusive to the elements incorporated into the metamaterial. Through exploration of multiple combinations of these metamaterial elements, it is shown that beneficial features from all elements can be present at once, resulting in a versatile metamaterial with great potential for numerous applications.