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.

Sound and heat revolutions in phononics

Utilizing a multilayered composite approach, we have designed and constructed a new class of artificial materials for thermal conduction. We show that an engineered material can be utilized to control the diffusive heat flow in ways inconceivable with naturally occurring materials. By shielding, concentrating, and inverting heat current, we experimentally demonstrate the unique potential and the utility of guiding heat flux.

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Heat flux manipulation with engineered thermal materials.

The surface effect from surface stress and surface elasticity on the elastic behavior of nanowires in static bending is incorporated into Euler-Bernoulli beam theory via the Young-Laplace equation. Explicit solutions are presented to study the dependence of the surface effect on the overall Young's modulus of nanowires for three different boundary conditions: cantilever, simply supported, and fixed-fixed. The solutions indicate that the cantilever nanowires behave as softer materials when deflected while the other structures behave like stiffer materials as the nanowire cross-sectional size decreases for positive surface stresses. These solutions agree with size dependent nanowire overall Young's moduli observed from static bending tests by other researchers. This study also discusses possible reasons for variations of nanowire overall Young's moduli observed.

Surface Effect on the Elastic Behavior of Static Bending Nanowires

Surface effects often play a significant role in the physical properties of micro- and nanosized materials and structures. In this letter, the authors presented a theoretical model directed towards investigation of the effects of both surface elasticity and residual surface tension on the natural frequency of microbeams. A thin surface layer was introduced on the upper and lower surfaces to rationalize the near-surface material properties that are different from the bulk material. An explicit solution is derived for the natural frequency of microbeams with surface effects. This study might be helpful for the design of microbeam-based sensors and some related measurement techniques.

Effects of surface elasticity and residual surface tension on the natural frequency of microbeams

Metamaterials are rationally designed man-made structures composed of functional building blocks that are densely packed into an effective (crystalline) material. While metamaterials are mostly associated with negative refractive indices and invisibility cloaking in electromagnetism or optics, the deceptively simple metamaterial concept also applies to rather different areas such as thermodynamics, classical mechanics (including elastostatics, acoustics, fluid dynamics and elastodynamics), and, in principle, also to quantum mechanics. We review the basic concepts, analogies and differences to electromagnetism, and give an overview on the current state of the art regarding theory and experiment-all from the viewpoint of an experimentalist. This review includes homogeneous metamaterials as well as intentionally inhomogeneous metamaterial architectures designed by coordinate-transformation-based approaches analogous to transformation optics. Examples are laminates, transient thermal cloaks, thermal concentrators and inverters, 'space-coiling' metamaterials, anisotropic acoustic metamaterials, acoustic free-space and carpet cloaks, cloaks for gravitational surface waves, auxetic mechanical metamaterials, pentamode metamaterials ('meta-liquids'), mechanical metamaterials with negative dynamic mass density, negative dynamic bulk modulus, or negative phase velocity, seismic metamaterials, cloaks for flexural waves in thin plates and three-dimensional elastostatic cloaks.

https://iopscience.iop.org/article/10.1088/0034-4885/76/12/126501/pdf

Metamaterials beyond electromagnetism

In nanoscaled solids, the mathematical behavior of a curved interface between two different phases with interface stress effects can be described by the generalized Young-Laplace equations [T. Young, Philos. Trans. R. Soc. London 95, 65 (1805); P. S. Laplace, Traite de Mechanique Celeste (Gauthier-Villars, Paris, 1805), Vol. 4, Supplements au Livre X]. Here we present a geometric illustration to prove the equations. By considering a small element of the curved thin interface, we model the interface stresses as in-plane stresses acting along its edges, while on the top and bottom faces of the interface the tractions are contributed from its three-dimensional bulk neighborhood. With this schematic illustration, simple force balance considerations will give the Young-Laplace equations across the interface. Similar procedures can be applied to conduction phenomena. This will allow us to reconstruct one type of imperfect interfaces, referred to as highly conducting interfaces.

http://ir.lib.ncku.edu.tw/bitstream/987654321/51156/2/3010600101021.pdf

Derivation of the generalized Young-Laplace equation of curved interfaces in nanoscaled solids

We explore the possibility to cloak a region in curvilinearly anisotropic background materials in the context of conductivity. Materials with curvilinear anisotropy possess constant properties in specific curvilinear coordinate. For cylindrically and spherically anisotropic solids, the cloak center and the origin of material coordinate are generally not collocated. We show that in combination with a rigid-body translation from the cloak center to the material origin, the previous coordinate transformation procedure remains applicable. But now the transformed material specifications depend on the position of cloak center. The validity of the cloak parameters is verified by finite element simulations.

Cloak for curvilinearly anisotropic media in conduction

An invisibility cloak based on transformation optics often requires material with inhomogeneous, anisotropic, and possibly extreme material parameters. In the present study, on the basis of the concept of neutral inclusion, we find that a spherical cloak can be achieved using a layer with finite constant anisotropic conductivity. We show that thermal localization can be tuned and controlled by anisotropy of the coating layer. A suitable balance of the degree of anisotropy of the cloaking layer and the layer thickness provides a cloaking effect. Additionally, by reversing the conductivities in two different directions, we find that a thermal concentrating effect can be simulated. This finding is of particular value in practical implementation as a material with constant material parameters is more feasible to fabricate. In addition to the theoretical analysis, we also demonstrate our solutions in numerical simulations based on finite element calculations to validate our results.

Materials with constant anisotropic conductivity as a thermal cloak or concentrator

We study an invisibility cloak with a twin cavity, simulated by a plane algebraic curve- hippopede. The cloaked region, which looks like eight for some sets of geometric parameters, is expanded from one single point. Using a geometric transformation approach, we demonstrate that the material parameters of cloaking layer can be exactly determined. Numerical simulations show that the incoming rays pass in and out the cloaking region twice, and return to their original trajectory outside the curved cloak. A notable feature is that the cloaking region has two hollow regions in which two objects can be hidden at one time and that they could not perceive each other.

Chung Ning Weng

Papers

Derivation of the generalized Young-Laplace equation of curved interfaces in nanoscaled solids

Cloak for curvilinearly anisotropic media in conduction

Materials with constant anisotropic conductivity as a thermal cloak or concentrator

Invisibility cloak with a twin cavity

Green’s functions and Eshelby tensors for an ellipsoidal inclusion in a non-centrosymmetric and anisotropic micropolar medium