This dissertation includes the study of effective medium theories (EMTs) and their applications in describing wave propagation in anisotropic metamaterials, which can guide the design of metamaterials. An EMT based on field averaging is proposed to describe a peculiar anisotropic dispersion relation that is linear along the symmetry line but quadratic in the perpendicular direction. This dispersion relation is associated with the topological transition of the iso-frequency contours (IFCs), suggesting interesting wave propagation behaviors from beam shaping to beam splitting. In the framework of coherent potential approximation, an analytical EMT is further developed, with the ability to build a direct connection between the microscopic structure and the macroscopic material properties, which overcomes the requirement of prior knowledge of the field distributions. The derived EMT is valid beyond the long-wavelength limit. Using the EMT, an anisotropic zero-index metamaterial is designed. Moreover, the derived EMT imposes a condition that no scattered wave is generated in the ambient medium, which suggests the input signal cannot detect any object that might exist, making it invisible. Such correspondence between the EMT and the invisibilityinspires us to explore the wave cloaking in the same framework of coherent potential approximation. To further broaden the application realm of EMT, an EMT using the parameter retrieval method is studied in the regimes where the previously-developed EMTs are no longer accurate. Based on this study, in conjunction with the EMT mentioned above, a general scheme to realize coherent perfect absorption (CPA) in anisotropic metamaterials is proposed. As an exciting area in metamaterials, the field of metasurfaces has drawn great attention recently. As an easily attainable device, a grating may be the simplest version of metasurfaces. Here, an analytical EMT for gratings made of cylinders is developed by using the multiple scattering theory (MST) method and the lattice sum. Validation of the theory is verified by the agreement between the EMT predictions and the numerical calculations. It is found the EMT is capable of accurately predicting the wave transport behaviors, even for frequencies where the Mie resonances happen.

L'allègement des structures est un enjeu économique important dans les domaines d'activités industrielles telles que l'automobile, l'aéronautique ou le naval, qui intègrent peu à peu les matériaux composites dans la fabrication des structures. Cet allègement s'accompagne d'un raidissement de la matière qui implique des problèmes de vibrations et d'isolation acoustique. Plusieurs méthodes de traitement existent pour diminuer les vibrations ou le bruit rayonné d'une paroi, mais ces méthodes ont l'inconvénient d'augmenter significativement la masse de la paroi. Afin de répondre à cette problématique, il est proposé dans cette thèse de modifier le comportement dynamique des structures à partir d'un réseau périodique de patchs piézoélectriques shuntés avec un circuit électrique dont il est possible de modifier l'impédance. En contrôlant ainsi le comportement dynamique des patchs piézoélectriques, il est possible de contrôler le comportement vibratoire de la structure et donc de traiter les problèmes de transmissions solidiennes ou de transmissions aériennes.La méthode de shunt choisie est la méthode dite de shunt à capacité négative qui permet de modifier la rigidité d'une structure. Cette méthode dite semi-passive présente plusieurs avantages : la mise en œuvre est simple, il est possible d'intégrer les patchs directement à l'intérieur de la paroi, elle consomme une faible quantité d'énergie électrique et sa mise en application est peu onéreuse. / Making the structure lighter is an important economic stake in the field of industrial activities such as automotive, aeronautic or naval, which gradually integrate composite materials in the manufacturing of structures. This reduction of the mass goes along with a stiffening of the matter implying acoustics and vibrations issues. Several methods exist to reduce vibrations or acoustic radiations of structures, but these methods increase the mass. In order to answer the problematic, we propose to change the dynamic behavior of structures with a periodic lattice of piezoelectric patches shunted with an electrical circuit whose the impedance can be controlled. Therefore, the control of the coupled behavior of the piezoelectric patches allows the control of vibrational wave's diffusion inside the structure and so to treat the structure-borne vibrations and airborne acoustics emission. The shunt method chosen is negative capacitance shunt which allows to modify the rigidity of a structure. This semi-passive method has several advantages: the implementation is simple, it is possible to integrate the patches directly inside the wall, it consumes a low amonte of electrical energy and its implementation is inexpensive.

This document presents the modelling and characterization of novel photonic devices based on periodic arrays of multiwalled carbon nanotubes. Multiwalled carbon nanotubes are mostly metallic in nature and interesting plasmonic effects are observed when nanotubes are grown close together, with spacing of about 400 nm. The effective electronic mass on the nanotubes changes, due to mutual coupling between them and they start displaying dielectric properties which are inherently different from the their own, forming metamaterials. We present a plasmonic high pass filtering application of carbon nanotube based metamaterials. Some promising modelling and experimental results are demonstrated showing a strong cut-off filtering effect at the plasma frequency displayed by the periodic arrays of multiwalled carbon nanotubes. The artificial negative dielectric constant displayed by the nanotube arrays was also successfully utilised for producing micron-scaled applications like optical waveguides and negative lenses for overcoming the diffraction limit. The fabrication of these optical devices using the arrays of silicon nanopillars was also considered. These arrays when fabricated at nano-scaled dimensions (of about 400 nm) present a greater degree of periodicity and require a simpler fabrication process compared to carbon nanotubes. We report the detailed computational analysis on silicon nanopillars based photonic crystals, waveguides and metamaterials which operate well within in the optical regime. However, due to the fabrication limitations, the fabricated Si nanopillars presented an inverted cone shape profile along their lengths. These inverted nanocone structures were successfully utilised for enhancing reflection from Si surfaces for applications in photovoltaic devices. Lastly we present a novel application of carbon nanotube arrays for producing micron-scale Fresnel lens arrays. Forests of carbon nanotubes were utilised as absorbing media on top of a bare silicon substrate. Optical diffraction of light across the nanotube forests produced strong focusing of light, at focal lengths of order 125 microns. Numerical simulations were in excellent agreement with the measured results.

Ce travail de thèse est composé de deux partie distinctes. La première partie est consacrée à l'étude et la modélisation des métamatériaux et tout particulièrement à leur caractérisation. Il s'agit donc de proposer des paramètres constitutifs équivalents (permittivité, perméabilité et couplage magnéto-électrique) qui permettent de remplacer les métamatériaux, composés à l'origine de réseaux périodiques de cellules discrètes, par des milieux homogènes et continus. Deux régimes sont considérés : sub-longueur d'onde et longueur d'onde. Dans le premier régime, les dimensions de la cellule de base, en particulier la période du réseau, sont très faibles devant la longueur d'onde. Le métamatériau est alors modélisé par un milieu bi-anisotrope continu. Pour le deuxième régime, les dimensions et la période sont comparables à la longueur d'onde. Les paramètres constitutifs sont alors définis au sens "local" qui prend en compte le caractère discret et périodique de la structure. Enfin, la caractérisation consiste à extraire les paramètres constitutifs à partir des coefficients de réflexion et de transmission d'une lame de métamatériau. Pour cela, nous appliquons la méthode d'inversion sous sa forme classique pour le régime "sub-longueur d'onde" et son extension aux structures périodiques pour le régime "longueur d'onde". L'une des contributions majeure de ce travail est l'application des incidences obliques (à l'interface air-métamatériau) pour extraire les paramètres constitutifs longitudinaux. La seconde partie de ce travail de thèse concerne le développement d'antennes directives à partir de sources rayonnantes à modes orthogonaux. Il est bien connu que la directivité est directement limitée par les dimensions de l'antenne ou par le nombre de sources dans un réseau. L'objectif est de mettre en œuvre une méthode alternative qui, tout au moins sur le plan conceptuel et théorique, ne relie pas la directivité à la taille de l'antenne. Nous utilisons donc la combinaison de modes rayonnants orthogonaux pour maximiser la directivité d'antennes tout en minimisant les dimensions du réseau et en limitant le couplage. Chaque source du réseau se doit rayonner un mode propre et unique qui, combiné avec une autre source, permet d'augmenter la directivité. Pour cette étude, le développement théorique des modes sphériques puis cylindriques est tout d'abord présenté afin de mettre en évidence le lien entre la directivité et les modes. En pratique, la mise en œuvre de modes sphériques a révélé des difficultés de conception, si bien que des solutions d'antennes basées sur l'anneau rayonnant sont proposées pour réaliser des sources à modes orthogonaux "cylindriques". Les topologies de structures rayonnantes directives proposées associant des antennes anneaux sont validées en simulation et par la conception puis la mesure de prototypes. / The work presented in this thesis concerns two parts: characterisation methods for metamaterials and directive antennas using space eigen-modes. The first one describes the homogenisation methods of metamaterials to retrieve the constitutive parameters from scattering parameters of the metamaterial's slab. We investigated the metamaterials which present the most common properties of media: bi-isotropic metamaterials (chiral), anisotropic metamaterials (BC-SRR), uni-axial bi-anisotropic metamaterials (double omega medium) and bi-axial bi-anisotropic metamaterials (EC-SRR). The transverse and longitudinal constitutive parameters characterising the anisotropic and bi-anisotropic require to examine the media at normal and oblique incidences. In the analysis we considered to distinguish continuous media restricted to long wave limit and resonating particles lattice which are out of long wave limit. The application of continuous media approach to the resonating particle lattice with size not satisfying the long wave limit can leads to violation of causality and passivity laws. The main different between proposed two approaches is interpretation of boundary conditions (Maxwellian/non-Maxwellian) for the metamaterial slab. The inclusions of lattice we ascribe as electric and magnetic dipole moments to develop an homogeneous resonating particles lattice and to retrieve the constitutive parameters. We validated the proposed approaches and compared the retrieved constitutive parameters according to physical laws. We found that the application of Bloch admittance and equivalence to electric and magnetic dipole moments provides the physical constitutive parameters. The second part of the thesis refers to directive antenna using space eigen-modes. The directivity of the antennas is limited to the size of the antenna or number of elements in an array. In common with keeping small sizes of the array the space between radiation elements has to be minimised. The proposed directive antenna considers the radiation elements determine by the orthogonal modes, i.e. each radiator of the array corresponds to unique space eigen-mode. This allows to ensure small distance between the array elements without introduction of high mutual coupling between them. The original approach refers to superposition of spherical modes however it is not practical. Instead of spherical modes we propose superposition of cylindrical modes which are easy to be realised. For the constructive summation of cylindrical modes and maximisation of directivity in end-fire plane we determine amplitudes of the cylindrical modes excited by electric and/or magnetic vector potentials. The cylindrical modes we obtain by the annular ring antennas and miniaturised annular rings. The superposition of cylindrical modes is achieved with a stacked antenna of annular rings and a coplanar cylindrical annular rings antenna. The both antennas we realised and measured.

En accord avec l'équation de propagation des ondes élastiques dans la matière, l'expression de la vitesse du son n'interdit pas à la masse volumique et à la compressibilité effectives du milieu d'être toutes deux négatives. Comment concevoir alors un tel matériau qualifié de métamatériau acoustique ? Qu'elles sont ses principales propriétés ? Cette thèse expérimentale a pour objectif la conception et la caractérisation d'un métamatériau pour les ondes de Lamb (ondes de plaque) de fréquences comprises entre 1MHz et 10MHz.L'approche mise en place repose sur le théorème d'Helmholtz qui permet de voir la propagation d'une onde élastique d'énergie finie comme le résultat d'un processus de couplage entre deux états de vibration de la matière, l'un de cisaillement sans changement de volume (vibration de symétrie dipolaire), l'autre se faisant avec changement de volume sans cisaillement (vibration monopolaire). Ainsi, la modification des paramètres effectifs décrivant la propagation pourrait passer par un contrôle local de ces deux états élémentaires de vibration, au moyen par exemple de résonateurs locaux homogénéisables.Le modèle de matériau choisi dans le cadre de cette thèse est une hétérostructure formée par un wafer de silicium sur lequel sont gravés, en tant que cellules mécaniques élémentaires, des paire de trous et des piliers isolés de silicium. La démarche expérimentale a consisté à étudier la diffusion élastique des ondes de Lamb sur ces deux types de cellules élémentaires à l'aide d'un montage tout optique. La génération des ondes fut assurée par la focalisation le long d'une ligne d'un faisceau laser Nd:YAG picoseconde permettant d'obtenir une source blanche acoustique. La détection fut réalisée à l'aide d'un interféromètre de Michelson doté d'un bras opto-mécanique permettant une cartographie point par point du champ de déformation de l'onde avec une sensibilité d'environ 1pm (pour une largeur de bande de 1MHz) sur une surface de 25x25mm2 avec une résolution spatiale et temporelle d'environ 1microns et 0.2nanosecondes.Cette étude aura permis de mettre en évidence la présence d'une ondelette réémise par la paire de trous ou le pilier autour de leurs fréquences de résonance et de décrire la diffusion cohérente résonante comme le résultat de l'interférence entre l'onde incidente et l'ondelette réémise. Dans le cas de la paire de trous, ces résultats ont permis d'interpréter et de comprendre le domaine de fréquences interdites d'un cristal phononique, ainsi que de décrire la dynamique de formation des modes d'une cavité phononique planaire. Dans le cas du pilier, il fut possible d'envisager la fabrication d'un système possédant les propriétés attendues pour un métamatériau acoustique.Cette thèse s'inscrit dans le projet de recherche de l'équipe Acoustique pour les Nanosciences de l'Institut des Nanosciences de Paris consacré à la structuration artificielle de la matière aux échelles micro et nanométriques pour le contrôle de la propagation des ondes élastiques. Les applications potentielles couvrent des domaines allant de la santé (imagerie haute résolution) à la défense (cape d'invisibilité) en passant par les télécommunications ou encore le bâtiment (isolation phonique).De par son caractère stratégique pour la Défense, ce travail a bénéficié du soutien de la DGA et de l'ANR sous la forme du projet ANR-ASTRID "METACTIF". Il a été effectué en collaboration avec une équipe de l'Université Lille 1, spécialisée dans la simulation numérique. Les échantillons ont été fabriqués dans le cadre d'une collaboration avec la salle blanche MIMENTO de l'Institut Femto-St de Besançon. / According with the elastic wave equation, the expression of the speed allows the motion of waves with an effective density and an effective compressibility both negative. How can we imagine and create a material of this kind, called metamaterial? What would be its properties?This experimental thesis involved to produce and to characterize a metamaterial for elastic Lamb waves (sismic waves) in the frequency range [1MHz-10MHz].On the basis of the Helmholtz theorem, the wave motion of Lamb waves is due to a coupling process between two vibrations states of the matter; one dipolar vibration (pure bending mode) coupling with one monopolar vibration (pure compressional mode). As a result, the modification of the macroscopic parameters governing the wave motion could be realised by the control of these only two vibrations states, thanks to homogeneous local resonators.Isolated silicon pillars and pairs of holes in silicon plate as potentially "good" candidate to fulfill this requirement. Structures were elaborated with deep reactive-ion etching technique (DRIE) using Bosch process in a silicon wafer.We had an experimental approach consisting in measuring the eigenfrequencies of the structures to select the one which allows fulfilling the homogenization criteria at the best and then mapping the scattered field associated to a Lamb wave interacting with the structures while vibrating onto the preselected eigenmode.To conduct this study, we used an all-optical experimental device. Generation of Lamb waves were managed to use an Nd:YAG laser focused along a line on the surface to get a white elastic source. The detection was realized with a power-operated Michelson interferometer, allowing to measure the displacement field with a resolution of around 1pm (on frequencies range of 1MHz).This study had allowed to evidence a scattering process described by the interference between the incident field and a reemitted wave emitted by the resonator. For the pairs of hole structures, these results enabled to understand the description of the bandgap of a phononic crystal in terms of bragg reflexion and to describe the dynamic of formation of phononic cavity modes. Concerning the pillars, these results enabled to make a device, using the Huygens-Fresnel principal, with the properties of a metamaterial.This PhD work follows on from the research projet of the team Acoustique pour les Nanoscience of the Nanosciences Institut of Paris (INSP).This work is jointly supported by the Agence Nationale de la Recherche and Direction Générale de l’Armement under grant ANR METACTIF. The simulations were realised in collaboration with a team at the Université Lille 1. The samples have been elaborated in MIMENTO facilities at Femto-ST institute in Besançon.

abstract: Within the past two decades, metasurfaces, with their unique ability to tailor the wavefront, have attracted scientific attention. Along with many other research areas, RADAR cross-section (RCS)-reduction techniques have also benefited from metasurface technology. In this dissertation, a novel technique to synthesize the RCS-reduction metasurfaces is presented. This technique unifies the two most widely studied and two well-established modern RCS-reduction methods: checkerboard RCS-reduction andgradient-index RCS-reduction. It also overcomes the limitations associated with these RCS-reduction methods. It synthesizes the RCS-reduction metasurfaces, which can be juxtaposed with almost any existing metasurface, to reduce its RCS. The proposed technique is fundamentally based on scattering cancellation. Finally, an example of the RCS-reduction metasurface has been synthesized and introduced to reduce the RCS of an existing high-gain metasurface ground plane. After that, various ways of obtaining ultrabroadband RCS-reduction using the same technique are proposed, which overcome the fundamental limitation of the conventional checkerboard metasurfaces, where the reflection phase difference of (180+-37) degrees is required to achieve 10-dB RCS reduction. First, the guideline on how to select Artificial Magnetic Conductors (AMCs) is explained with an example of a blended checkerboard architecture where a 10-dB RCS reduction is observed over 83% of the bandwidth. Further, by modifying the architecture of the blended checkerboard metasurface, the 10-dB RCS reduction bandwidth increased to 91% fractional bandwidth. All the proposed architectures are validated using measured data for fabricated prototypes. Critical steps for designing the ultrabroadband RCS reduction checkerboard surface are summarized. Finally, a broadband technique to reduce the RCS of complex targets is presented. By using the proposed technique, the problem of reducing the RCS contribution from such multiple-bounces simplifies to identifying and implementing a set of orthogonal functions. Robust guidelines for avoiding grating lobes are provided using array theory. The 90 degree dihedral corner is used to verify the proposed technique. Measurements are reported for a fabricated prototype, where a 70% RCS-reduction bandwidth is observed. To generalize the method, a 45 degree dihedral corner, with a quadruple-bounce mechanism, is considered. Generalized guidelines are summarized and applied to reduce the RCS of complex targets using the proposed method. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2020

Work is focused on both theoretical knowledge of the electromagnetic field and the specific properties of metamaterials measured. First, be informed about the fundamentals of electromagnetic fields, the issue of periodic structures to the properties required metastructures. Further experimental work is designed to measure the properties of metamaterials. The measurements will be used as harmonic signals and broadband signals in the frequency range 100MHz to 10GHz. In the last part of the proposed work is carried out experimental work and are evaluated some characteristics of the antennas and measurement of the selected sample.

Le concept de l'optique de transformation qui permet de contrôler le trajet des ondes électromagnétiques à volonté en appliquant une variation spatiale judicieusement définie dans les paramètres constitutifs, est exploré pour concevoir des nouveaux types d'antennes et de dispositifs micro-ondes. Dans une première partie, basée sur la transformation de coordonnées, un dispositif d'illusion capable de modifier l'apparence d'une émission électromagnétique et de la délocaliser, est validé par le biais de simulations numériques. Un dispositif de transition de guide d'ondes, permettant d'assurer une transmission quasi totale entre deux guides d'ondes de sections transversales différentes est également conçu et validé expérimentalement par l'utilisation des résonateurs à métamatériaux. Dans une seconde partie, la transformation de l'espace basée sur l'équation de Laplace est étudiée pour concevoir des lentilles pour les applications antennaires. Une lentille de focalisation capable de restaurer les émissions en phase d'un réseau conforme d'éléments rayonnants et une lentille à dépointage qui permet de dévier la direction du faisceau rayonné d'une antenne sont conçues. Des prototypes fabriqués à partir d'un matériau isotrope tout-diélectrique grâce à la technologie d'impression en trois dimensions (3D) permettent de valider expérimentalement la fonctionnalité des lentilles sur une large bande de fréquence. / The concept of transformation optics which can control electromagnetic waves at will by applying a judiciously defined spatial variation in the constitutive parameters is explored to design novel type antennas and microwave devices. In a first part, based on coordinate transformation, an illusion device able to modify the appearance of an electromagnetic emission and then delocalize it is validated through numerical simulations. A waveguide tapering device allowing to assure quasi-total transmission between two waveguides of different cross-sections is also designed and validated experimentally through the use of metamaterial resonators. In a second part, space transformation based on Laplace's equation is studied to design lenses for antenna applications. A beam focusing lens able to restore in-phase emissions from a conformal array of radiators and a beam steering lens that allows deflecting the radiated bema of an antenna are designed. Prototypes fabricated by an all-dielectric isotropic material through three-dimensional (3D) polyjet printing technology allow to experimentally validate the functionality of the lenses on a wide frequency range.

<div>Lattices composed of bistable elements are of great significance across various fields of science and engineering due to their ability to support a class of solitary waves, called transition waves. Common with all solitary waves, transition waves carry highly concentrated energy with minimal degradation and thus have many useful engineering applications, such as extreme waveguides, bandgap transmission, vibration absorption, and energy harvesting. The rich dynamics arising from the strong nonlinearities of the constitutive bistable microstructures still have much to be unveiled for the practical implementation of the transition waves in real-world engineering structures. Especially, the quasi-particle characteristics of the transition waves can potentially address the performance limits posed by the unit cell size in linear metamaterials.</div><div><br></div><div>In this thesis, we first present an input-independent generation of transition waves in the lattices of asymmetric bistable unit cells when snap-through transitions occur at any site within the lattice. The resulting responses are invariant across the lattice except near the boundaries. These characteristics imply useful applications in broadband energy harvesting, exploiting the highly concentrated energy of the transition waves. We further observe that the inherent lattice discreteness induces dominantly monochromatic oscillatory tail following the main transition wave. This radiated energy of the tail can always be efficiently harvested through resonant transduction regardless of the input excitations. This type of bistable lattice transforms any input disturbance into an output form that can be conveniently transduced; thus, energy harvesting becomes an inherent metamaterial property of the bistable lattice.</div><div><br></div><div>To enhance the responses further for improved energy harvesting capability, we introduce engineered defects in the form of a mass impurity, inhomogeneous inter-site stiffness, and their combinations, achieving localization of energy at desired sites. Remarkably, we also observe a long-lived breather-like mode for the first time in this type of lattice. To enhance the tail motions globally across the lattice, we investigate the responses in a set of bistable lattices with the same mass and elastic densities but with different lattice spacing distances (or lattice discreteness). From the available tail energy, we observe a significant increase in the harvesting capability with the increased lattice discreteness.</div><div><br></div><div>Next, the effect of functional grading on the onsite and inter-site stiffnesses are investigated to augment the control of the transition waves in the bistable lattices. The unidirectionality still remains in the direction of decreasing stiffness, while a boomerang-like wave reversal occurs in the direction of increasing stiffness. Both the compression and rarefaction transition waves are allowed to propagate, enabling continuous transmission of the transition waves without complex resetting mechanisms, thus expanding the bistable lattices' functionality for practical applications.</div><div><br></div><div>The observed input-independent dynamics of the one-dimensional bistable lattices can be extended to higher-dimensional metastructures by allowing macrostructural flexibility. Metabeams composed of spring-joined bistable elements are subjected to in-plane sinusoidal input at the microstructural level, and the out-of-plane responses at the macrosctructural level are measured. As long as transition waves are triggered within the metabeam, the most dominant output frequency occurs near the natural frequency of the macroscopic structure regardless of the input excitations initiating the transition waves, yielding energy transfer between uncorrelated frequencies.</div><div><br></div><div>Finally, high-fidelity in-house numerical solvers are developed for the massively parallelized computation of the problems involving generic bistable architectures, addressing the problem size limit. The improved numerical solution accuracy and computational performance, compared to those of commercial solvers, provide great potential to discover new dynamics by drastically expanding the accessible analysis regimes.</div><div><br></div><div>The experiments, simulations, and theoretical contributions in this thesis illustrate the possibilities afforded by strongly nonlinear phenomena to tailor the dynamics of materials systems. Importantly, the presented results show mechanisms to affect global dynamic properties unconstrained by the unit cell size, thereby offering new routes to extreme dynamics beyond current metamaterial architectures.</div>

Lightweight mechanical metamaterials with exception specific stiffness and strength are useful in many applications, such as transportation, aerospace, architectures and etc. These materials show great potential in mechanical tasks where weight of the material is restrained due to economy or energy reasons. To achieve both the lightweight and the high specific mechanical properties, the metamaterials are often in form of periodic cellular structures with well-designed unit cells. The strategies in designing and improving such cellular structures become the key in the studies of such mechanical metamaterials. In this work, we use both experimental and numerical approaches while probing three types of mechanical metamaterials: i) composite bending dominated hollow lattices (HLs); ii) triply periodic minimal surfaces (TPMSs) and extended TPMSs (eTPMSs); iii) corrugated TPMSs. We have demonstrated a few strategies in designing and improving the specific stiffness or strength via these examples of mechanical metamaterials. Using carbon/ceramic composite in the bending dominated HLs, we prove that using the composite layered material against the single layer ceramic is effective in improving the specific mechanical performances of the mechanical metamaterials. Next, while studying the nature of TPMS, we discover that under isotropic deformation TPMSs are stretch dominated with no stress concentrations within the shell structure. They also have an optimal specific bulk modulus approaching the H-S upper bound. Furthermore, we establish a strategy to smoothly connect the zero-mean-curvature surfaces in TPMSs with the extension of zero-Gaussion-curvature surfaces, forming new ‘eTPMSs”. These new shellular structures trade off its isotropy and have improved specific Young’s modulus along their stiffest orientation compared to their TPMS base structures. Lastly, we introduce corrugated sub-structures to existing TPMSs to improve their mechanical properties, such as Young’s modulus, yield strength and failure strength in compression. It is found that the corrugated sub-structure can effectively suppress the local bending behavior and redirect crack propagation while such structures were under uniaxial compression.