to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

The term photonic crystals appears because of the analogy between electron waves in crystals and the light waves in artificial periodic dielectric structures. During the recent years the investigation of one-, two-and three-dimensional periodic structures has attracted a widespread attention of the world optics community because of great potentiality of such structures in advanced applied optical fields. The interest in periodic structures has been stimulated by the fast development of semiconductor technology that now allows the fabrication of artificial structures, whose period is comparable with the wavelength of light in the visible and infrared ranges.

http://ieeexplore.ieee.org/iel5/6354/16969/00781867.pdf

Photonic crystals

Staff members at Los Alamos National Laboratory (LANL) produced a summary of the structural health monitoring literature in 1995. This presentation will summarize the outcome of an updated review covering the years 1996 2001. The updated review follows the LANL statistical pattern recognition paradigm for SHM, which addresses four topics: 1. Operational Evaluation; 2. Data Acquisition and Cleansing; 3. Feature Extraction; and 4. Statistical Modeling for Feature Discrimination. The literature has been reviewed based on how a particular study addresses these four topics. A significant observation from this review is that although there are many more SHM studies being reported, the investigators, in general, have not yet fully embraced the well-developed tools from statistical pattern recognition. As such, the discrimination procedures employed are often lacking the appropriate rigor necessary for this technology to evolve beyond demonstration problems carried out in laboratory setting.

A review of structural health monitoring literature 1996-2001

Acoustic metamaterials can manipulate and control sound waves in ways that are not possible in conventional materials. Metamaterials with zero, or even negative, refractive index for sound offer new possibilities for acoustic imaging and for the control of sound at subwavelength scales. The combination of transformation acoustics theory and highly anisotropic acoustic metamaterials enables precise control over the deformation of sound fields, which can be used, for example, to hide or cloak objects from incident acoustic energy. Active acoustic metamaterials use external control to create effective material properties that are not possible with passive structures and have led to the development of dynamically reconfigurable, loss-compensating and parity–time-symmetric materials for sound manipulation. Challenges remain, including the development of efficient techniques for fabricating large-scale metamaterial structures and converting laboratory experiments into useful devices. In this Review, we outline the designs and properties of materials with unusual acoustic parameters (for example, negative refractive index), discuss examples of extreme manipulation of sound and, finally, provide an overview of future directions in the field. Acoustic metamaterials can be used manipulate sound waves with a high degree of control. Their applications include acoustic imaging and cloaking. This Review outlines the designs and properties of these materials, discussing transformation acoustics theory, anisotropic materials and active acoustic metamaterials.

Controlling sound with acoustic metamaterials

Dynamics of Phononic Materials and Structures: Historical Origins, Recent Progress, and Future Outlook

Phononic properties of hexagonal chiral lattices

We investigate elastic periodic structures characterized by topologically nontrivial bandgaps supporting backscattering suppressed edge waves. These edge waves are topologically protected and are obtained by breaking inversion symmetry within the unit cell. Examples for discrete one and two-dimensional lattices elucidate the concept and illustrate parallels with the quantum valley Hall effect. The concept is implemented on an elastic plate featuring an array of resonators arranged according to a hexagonal topology. The resulting continuous structures have non-trivial bandgaps supporting edge waves at the interface between two media with different topological invariants. The topological properties of the considered configurations are predicted by unit cell and finite strip dispersion analyses. Numerical simulations demonstrate edge wave propagation for excitation at frequencies belonging to the bulk bandgaps. The considered plate configurations define a framework for the implementation of topological concepts on continuous elastic structures of potential engineering relevance.

https://robots.iopscience.iop.org/article/10.1088/1367-2630/aa56a2/pdf

Edge waves in plates with resonators: an elastic analogue of the quantum valley Hall effect

Auxetic materials expand when stretched, and shrink when compressed. This is the result of a negative Poisson's ratio ν. Isotropic configurations with ν≈−1 have been designed and are expected to provide increased shear stiffness G. This assumes that Young's modulus and ν can be engineered independently. In this article, a micropolar-continuum model is employed to describe the behavior of a representative auxetic structural network, the chiral lattice, in an attempt to remove the indeterminacy in its constitutive law resulting from ν=−1. While this indeterminacy is successfully removed, it is found that the shear modulus is an independent parameter and, for certain configurations, it is equal to that of the triangular lattice. This is remarkable as the chiral lattice is subject to bending deformation of its internal members, and thus is more compliant than the triangular lattice which is stretch dominated. The derived micropolar model also indicates that this unique lattice has the highest characteristic length scale lc of all known lattice topologies, as well as a negative first Lame constant without violating bounds required for thermodynamic stability. We also find that hexagonal arrangements of deformable rings have a coupling number N=1. This is the first lattice reported in the literature for which couple-stress or Mindlin theory is necessary rather than being adopted a priori.

Elasto-static micropolar behavior of a chiral auxetic lattice

Cellular structures like honeycombs or reticulated micro-frames are widely used in sandwich construction because of their superior structural static and dynamic properties. The aim of this study is to evaluate the dynamic behavior of two-dimensional cellular structures, with the focus on the effect of the geometry of unit cells on the dynamics of the propagation of elastic waves within the structure. The characteristics of wave propagation for the considered class of cellular solids are analyzed through the finite element model of the unit cell and the application of the theory of periodic structures. This combined analysis yields the phase constant surfaces, which define the directions of waves propagating in the plane of the structure for the assigned frequency values. The analysis of iso-frequency contour lines in the phase constant surfaces allows the prediction of the location and extension of angular ranges, and therefore regions within the structures where waves do not propagate. The performance of honeycomb grids of regular hexagonal topology is compared with that of grids of various geometries, with the emphasis on configurations featuring a negative Poisson's ratio behavior. The harmonic response of the considered structures at specified frequencies confirms the predictions from the analysis of the phase constant surfaces and demonstrates the strongly spatially-dependent characteristics of periodic cellular structures. The numerical results presented indicate the potentials of the phase constant surfaces as tools for the evaluation of the wave propagation characteristics of this class of two-dimensional periodic structures. Optimal design configurations can be identified in order to achieve the desired transmissibility levels in specified directions and to obtain efficient vibration isolation capabilities. The findings from the presented investigations and the described analysis methodology will provide invaluable guidelines for the prototyping of future concepts of honeycombs or cellular structures with enhanced vibro-acoustics performance.

https://iopscience.iop.org/article/10.1088/0964-1726/12/3/307/pdf

Massimo Ruzzene

Papers

Dynamics of Phononic Materials and Structures: Historical Origins, Recent Progress, and Future Outlook

Phononic properties of hexagonal chiral lattices

Edge waves in plates with resonators: an elastic analogue of the quantum valley Hall effect

Elasto-static micropolar behavior of a chiral auxetic lattice

Wave beaming effects in two-dimensional cellular structures