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).

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

Within a time span of 15 years, acoustic metamaterials have emerged from academic curiosity to become an active field driven by scientific discoveries and diverse application potentials. This review traces the development of acoustic metamaterials from the initial findings of mass density and bulk modulus frequency dispersions in locally resonant structures to the diverse functionalities afforded by the perspective of negative constitutive parameter values, and their implications for acoustic wave behaviors. We survey the more recent developments, which include compact phase manipulation structures, superabsorption, and actively controllable metamaterials as well as the new directions on acoustic wave transport in moving fluid, elastic, and mechanical metamaterials, graphene-inspired metamaterials, and structures whose characteristics are best delineated by non-Hermitian Hamiltonians. Many of the novel acoustic metamaterial structures have transcended the original definition of metamaterials as arising from the collective manifestations of constituent resonating units, but they continue to extend wave manipulation functionalities beyond those found in nature.

/pdf/acoustic-metamaterials-from-local-resonances-to-broad-4s4297ihw6.pdf

Acoustic metamaterials: From local resonances to broad horizons.

A topological insulator, as originally proposed for electrons governed by quantum mechanics, is characterized by a dichotomy between the interior and the edge of a finite system: The bulk has an energy gap, and the edges sustain excitations traversing this gap. However, it has remained an open question whether the same physics can be observed for systems obeying Newton’s equations of motion. We conducted experiments to characterize the collective behavior of mechanical oscillators exhibiting the phenomenology of the quantum spin Hall effect. The phononic edge modes are shown to be helical, and we demonstrate their topological protection via the stability of the edge states against imperfections. Our results may enable the design of topological acoustic metamaterials that can capitalize on the stability of the surface phonons as reliable wave guides.

https://science.sciencemag.org/content/sci/349/6243/47.full.pdf

Observation of phononic helical edge states in a mechanical topological insulator

The English-language dictionary defines wrinkles as "small furrows, ridges, or creases on a normally smooth surface, caused by crumpling, folding, or shrinking". In this paper we review the scientific aspects of wrinkling and the related phenomenon of buckling. Specifically, we discuss how and why wrinkles/buckles form in various materials. We also describe several examples from everyday life, which demonstrate that wrinkling or buckling is indeed a commonplace phenomenon that spans a multitude of length scales. We will emphasize that wrinkling is not always a frustrating feature (e.g., wrinkles in human skin), as it can help to assemble new structures, understand important physical phenomena, and even assist in characterizing chief material properties.

Soft matter with hard skin : From skin wrinkles to templating and material characterization

Phononic properties of hexagonal chiral lattices

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

Acoustic lenses are employed in a variety of applications, from biomedical imaging and surgery to defense systems and damage detection in materials. Focused acoustic signals, for example, enable ultrasonic transducers to image the interior of the human body. Currently however the performance of acoustic devices is limited by their linear operational envelope, which implies relatively inaccurate focusing and low focal power. Here we show a dramatic focusing effect and the generation of compact acoustic pulses (sound bullets) in solid and fluid media, with energies orders of magnitude greater than previously achievable. This focusing is made possible by a tunable, nonlinear acoustic lens, which consists of ordered arrays of granular chains. The amplitude, size, and location of the sound bullets can be controlled by varying the static precompression of the chains. Theory and numerical simulations demonstrate the focusing effect, and photoelasticity experiments corroborate it. Our nonlinear lens permits a qualitatively new way of generating high-energy acoustic pulses, which may improve imaging capabilities through increased accuracy and signal-to-noise ratios and may lead to more effective nonintrusive scalpels, for example, for cancer treatment.

https://www.pnas.org/content/pnas/107/16/7230.full.pdf

Generation and control of sound bullets with a nonlinear acoustic lens

This paper investigates complex composite cellular structures featuring a chiral topology with the ability to undergo large overall displacements with limited straining of its components. Numerical analyses are performed to exploit such properties in the design of a morphing airfoil. The advantages associated with the use of composites are investigated by comparing the numerical results with those obtained with a metallic structure. A manufacturing process is then developed to assemble the considered structural configurations using composite materials. The novel process developed is described as applied to the manufacturing of macro chiral components that are tested to evaluate their ability to undergo large deformations. Finally, detailed numerical models of the manufactured structures are presented as a possible approach to evaluate the strength of the proposed configuration.

Composite chiral structures for morphing airfoils: Numerical analyses and development of a manufacturing process

Periodic arrays of shunted, piezoelectric patches are employed to control waves propagating over the surface of plate structures, and corresponding vibrations. The shunted, piezoelectric patches act as sources of impedance mismatch, which gives rise to interference phenomena resulting from the interaction between incident, reflected and transmitted waves. Periodically distributed mismatch zones, i.e., the piezo patches, produce frequency dependent, wave-dynamic characteristics, which include the generation of band gaps, or stop bands in the frequency domain. The extent of induced band gaps depends on the mismatch in impedance generated by each patch. The total impedance mismatch, in turn, is determined by the added mass and stiffness of each patch as well as the shunting electrical impedance. Proper selection of the shunting electric-circuit thus provides control over the attenuation capabilities of the piezo-plate structure, as well as the ability to adapt to changing excitation conditions. Control of wave-propagation attenuation and vibration reduction for plates with periodic, shunted, piezoelectric patches is demonstrated numerically, employing finite-element models of the considered structures.

/pdf/vibration-and-wave-propagation-control-of-plates-with-2fjjm1bqci.pdf

Alessandro Spadoni

Papers

Phononic properties of hexagonal chiral lattices

Elasto-static micropolar behavior of a chiral auxetic lattice

Generation and control of sound bullets with a nonlinear acoustic lens

Composite chiral structures for morphing airfoils: Numerical analyses and development of a manufacturing process

Vibration and Wave Propagation Control of Plates with Periodic Arrays of Shunted Piezoelectric Patches