![(a) Auxiliary space filled with an isotropic, homogeneous medium, wherein heat-flux and electrical current-density follow parallel straight paths. Two coordinate transformations are applied which induce different behaviors in the thermal (e.g., concentrator) and electrical (e.g., cloak) domains. (b) Equivalent interpretation, in a flat-metric space filled with a transformation medium [cf. Eqs. (4)]. The heat-flux and current-density paths are distorted in different fashions. (c) Metamaterial-based approximate implementation of the required nominal constitutive parameters via a mixture of inclusions of different shapes and materials (as qualitatively depicted in the magnified details) embedded in a host medium.](https://www.researchgate.net/profile/Salvatore-Savo/publication/258849369/figure/fig1/AS:297103562690561@1447846417288/a-Auxiliary-space-filled-with-an-isotropic-homogeneous-medium-wherein-heat-flux-and_Q320.jpg)
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Transformation Multiphysics
Abstract and Figures
Spatial tailoring of the material constitutive properties is a well-known
strategy to mold the local flow of given observables in different physical
domains. Coordinate-transformation-based methods (e.g., transformation optics)
offer a powerful and systematic approach to design anisotropic,
spatially-inhomogeneous artificial materials ("metamaterials") capable of
precisely manipulating wave-based (electromagnetic, acoustic, elastic) as well
as diffusion-based (heat) phenomena in a desired fashion. Most studies
available in the literature deal with the design of a single specific
functionality in a given physical domain. We address here the simultaneous
manipulation of multiple physical phenomena in independent fashions. As a proof
of principle of this "transformation multiphysics" framework, we design and
synthesize (in terms of realistic material constituents) a metamaterial shell
that simultaneously behaves as a thermal concentrator and an electrical
"invisibility cloak". Our numerical results open up intriguing possibilities in
the largely unexplored phase space of multi-functional metastructures, with a
wide variety of potential applications to electrical, magnetic, acoustic, and
thermal scenarios.
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We present an overview of results from our recent and ongoing research in the field of metamaterials. In particular, we focus on the recently emerged concepts of parity-time-symmetric metamaterials, metamaterial analog computing, and transformation multiphysics.
We present the first experimental demonstration of a dc electric cloak for steady current fields. Using the analogy between electrically conducting materials and resistor networks, a dc invisibility cloak is designed, fabricated, and tested using the circuit theory. We show that the dc cloak can guide electric currents around the cloaked region smoothly and keep perturbations only inside the cloak. Outside the cloak, the current lines return to their original directions as if nothing happens. The measurement data agree exceptionally well with the theoretical prediction and simulation result, with nearly perfect cloaking performance. The proposed method can be directly used to realize other dc electric devices with anisotropic conductivities designed by the transformation optics. Manipulation of steady currents with the control of anisotropic conductivities has a lot of potential applications, such as electric impedance tomography, graphene, natural resource exploration, and military camouflage.
We discuss the conductivity of two-dimensional media with coated neutral inclusions of finite conductivity. Such an inclusion when inserted in a matrix, does not disturb the uniform external field. We are looking for shapes of the core and coatin in terms of the conformal mapping ω(z) of the unit disc onto coated inclusions. The considered inverse problem is reduced to an eigenvalue problem for an integra equation containing singular integrals over a closed curve L1 on the transformed complex plane. The conformal mapping ω(z) is constructed via eigenfunctions of the integral equation. For each fixed curve L1, the boundary of the core is given by the curve ω(L1). The boundary of the coating is obtained by the mapping of the unit circle. It is justified that any shaped inclusion wit a smooth boundary can be made neutral by surrounding it with an appropriate coating. Shapes of the neutral inclusions ar obtained in analytical form when L1 is an ellipse.
It was recently shown theoretically that the time-dependent heat conduction equation is form invariant under curvilinear coordinate transformations. Thus, in analogy to transformation optics, fictitious transformed space can be mapped onto (meta)materials with spatially inhomogeneous and anisotropic heat-conductivity tensors in the laboratory space. On this basis, we design, fabricate, and characterize a microstructured thermal cloak that molds the flow of heat around an object in a metal plate. This allows for transient protection of the object from heating while maintaining the same downstream heat flow as without object and cloak.
The theory of composite materials is the study of partial differential equations with rapid oscillations in their coefficients. Although extensively studied for more than a hundred years, an explosion of ideas in the past four decades has dramatically increased our understanding of the relationship among the properties of the constituent materials, the underlying microstructure of a composite, and the overall effective moduli that govern the macroscopic behavior. This renaissance has been fueled by the technological need for improving our knowledge base of composites, by the advance of the underlying mathematical theory of homogenization, by the discovery of new variational principles, by the recognition of how important the subject is to solving structural optimization problems, and by the realization of the connection with the mathematical problem of quasiconvexification. This book surveys these exciting developments at the frontier of mathematics and presents many new results.
In this paper, we investigate how the form of the conventional elastodynamic equations changes under curvilinear transformations. The equations get mapped to a more general form in which the density is anisotropic and additional terms appear which couple the stress not only with the strain but also with the velocity, and the momentum gets coupled not only with the velocity but also with the strain. These are a special case of equations which describe the elastodynamic response of composite materials, and which it has been argued should apply to any material which has microstructure below the scale of continuum modelling. If composites could be designed with the required moduli then it could be possible to design elastic cloaking devices where an object is cloaked from elastic waves of a given frequency. To an outside observer it would appear as though the waves were propagating in a homogeneous medium, with the object and surrounding cloaking shell invisible. Other new elastodynamic equations also retain their form under curvilinear transformations. The question is raised as to whether all equations of microstructured continua have a form which is invariant under curvilinear space or space-time coordinate transformations. We show that the non-local bianisotropic electrodynamic equations have this invariance under space-time transformations and that the standard non-local, time-harmonic, electromagnetic equations are invariant under space transformations.
The theoretical design and the first experimental verification of an exterior dc invisibility cloak that can hide an object from dc detection at a distance are presented. Based on the transformation optics theory, the exterior dc cloak requires negative conductivity material to create folded geometry, which will cancel the real geometry of detected object in distance and make it invisible. Negative conductivities are designed and realized using active devices, together with resistor networks, to generate the equivalent conductivity materials required by the exterior dc cloak. An experimental sample of the dc cloak is fabricated on the printed circuit board and the measured result has excellent agreement with numerical and circuit simulations, showing very good cloaking performance at a distance.
The phonon is the physical particle representing mechanical vibration and is responsible for the transmission of everyday sound and heat. Understanding and controlling the phononic properties of materials provides opportunities to thermally insulate buildings, reduce environmental noise, transform waste heat into electricity and develop earthquake protection. Here I review recent progress and the development of new ideas and devices that make use of phononic properties to control both sound and heat. Advances in sonic and thermal diodes, optomechanical crystals, acoustic and thermal cloaking, hypersonic phononic crystals, thermoelectrics, and thermocrystals herald the next technological revolution in phononics.
The concept of the electromagnetic wave transparency is introduced into the thermal field. The conditions of the thermal transparency for a multilayered sphere with isotropic coatings, a coated spheroid with an isotropic coating, and a coated sphere with a radial anisotropic core or a radial anisotropic coat are deduced with the help of the idea of the neutral inclusion. The thermal transparency can be achieved by making the effective thermal conductivity of the composite inclusion equal to the thermal conductivity of the surrounding matrix. The validity of the theoretical analysis is checked by the corresponding simulated results, which indicate that the designed neutral inclusion can be transparent perfectly. A specific case of interest of the thermal transparency is its application to cancel the thermal stress concentration resulting from the existence of the inclusions in the particle (even the thermal-insulated particle) -reinforced composites.
It is shown that, in a plane sheet under any particular loading system, acting in the plane of the sheet, certain reinforced holes may be made which do not alter the stress distribution in the main body of the sheet. These reinforced holes (hereafter called neutral holes) necessarily have exactly the same stiffness and at least the same strength as the portion of the sheet that has been cut out. The weight of the reinforcement is usually greater than the weight of the sheet that has been cut out, though there are cases where it is less.
Mathematical formulae are developed to determine both the shape of a neutral hole and the variation along the hole boundary of the cross-sectional area of the reinforcement.