https://hal.archives-ouvertes.fr/jpa-00239583/document

Il nuovo cimento

Three-dimensional Problems of the Theory of Elasticity. By A. I. Lur’e.1964. (Interscience Publishers)

We report a new type of phononic crystals with topologically nontrivial band gaps for both longitudinal and transverse polarizations, resulting in protected one-way elastic edge waves. In our design, gyroscopic inertial effects are used to break the time-reversal symmetry and realize the phononic analogue of the electronic quantum (anomalous) Hall effect. We investigate the response of both hexagonal and square gyroscopic lattices and observe bulk Chern numbers of 1 and 2, indicating that these structures support single and multimode edge elastic waves immune to backscattering. These robust one-way phononic waveguides could potentially lead to the design of a novel class of surface wave devices that are widely used in electronics, telecommunication, and acoustic imaging.

Topological Phononic Crystals with One-Way Elastic Edge Waves

Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods

Rationally designed artificial materials, called metamaterials, allow for tailoring effective material properties beyond ("meta") the properties of their bulk ingredient materials. This statement is especially true for chiral metamaterials, as unlocking certain degrees of freedom necessarily requires broken centrosymmetry. While the field of chiral electromagnetic/optical metamaterials has become rather mature, the field of elastic/mechanical metamaterials is just emerging and wide open. This research news reviews recent theoretical and experimental progress concerning 3D chiral mechanical and optical metamaterials, with special emphasis on work performed at KIT.

https://onlinelibrary.wiley.com/doi/epdf/10.1002/adma.201807742

New Twists of 3D Chiral Metamaterials

Systematic step-by-step approach to asymptotic algorithms that enables the reader to develop an insight to compound asymptotic approximations Presents a novel, well-explained method of meso-scale approximations for bodies with non-periodic multiple perforations Contains illustrations and numerical examples for a range of physically realisable configurationsThere are a wide range of applications in physics and structural mechanics involving domains with singular perturbations of the boundary Examples include perforated domains and bodies with defects of different types The accurate direct numerical treatment of such problems remains a challenge Asymptotic approximations offer an alternative, efficient solution Green’s function is considered here as the main object of study rather than a tool for generating solutions of specific boundary value problems The uniformity of the asymptotic approximations is the principal point of attention We also show substantial links between Green’s functions and solutions of boundary value problems for meso-scale structures Such systems involve a large number of small inclusions, so that a small parameter, the relative size of an inclusion, may compete with a large parameter, represented as an overall number of inclusionsThe main focus of the present text is on two topics: (a) asymptotics of Green’s kernels in domains with singularly perturbed boundaries and (b) meso-scale asymptotic approximations of physical fields in non-periodic domains with many inclusions The novel feature of these asymptotic approximations is their uniformity with respect to the independent variablesThis book addresses the needs of mathematicians, physicists and engineers, as well as research students interested in asymptotic analysis and numerical computations for solutions to partial differential equations

Green's Kernels and Meso-Scale Approximations in Perforated Domains

For the first time, a design of a “deflecting elastic prism” is proposed and implemented for waves in a chiral medium. A novel model of an elastic lattice connected to a non-uniform system of gyroscopic spinners is designed to create a unidirectional wave pattern, which can be diverted by modifying the arrangement of the spinners within the medium. This important feature of the gyro-system is exploited to send a wave from a point of the lattice to any other point in the lattice plane, in such a way that the wave amplitude is not significantly reduced along the path. We envisage that the proposed model could be very useful in physical and engineering applications related to directional control of elastic waves.

/pdf/deflecting-elastic-prism-and-unidirectional-localisation-for-3mp9d5p4by.pdf

"Deflecting elastic prism" and unidirectional localisation for waves in chiral elastic systems.

We present uniform asymptotic approximations of Green's kernels for boundary value problems of elasticity in singularly perturbed domains containing a small hole. We consider the cases of two and t ...

https://users.mai.liu.se/vlama82/pdf/Greenstensors2nddraft.pdf

Uniform asymptotic formulae for Green's tensors in elastic singularly perturbed domains

We demonstrate a new method of achieving topologically protected states in an elastic hexagonal system of trusses by attaching gyroscopic spinners, which bring chirality to the system. Dispersive features of this medium are investigated in detail, and it is shown that one can manipulate the locations of stop-bands and Dirac points by tuning the parameters of the spinners. We show that, in the proximity of such points, uni-directional interfacial waveforms can be created in an inhomogeneous lattice and the direction of such waveforms can be controlled. The effect of inserting additional soft internal links into the system, which is thus transformed into a heterogeneous triangular lattice, is also investigated, as the hexagonal lattice represents the limit case of the heterogeneous triangular lattice with soft links. This work introduces a new perspective in the design of periodic media possessing non-trivial topological features.

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2018.0132

Interfacial waveforms in chiral lattices with gyroscopic spinners

The paper presents a model of a chiral multi-structure incorporating gyro-elastic beams. Floquet–Bloch waves in periodic chiral systems are investigated in detail, with the emphasis on localization and the formation of standing waves. It is found that gyricity leads to low-frequency standing modes and generation of stop-bands. A design of an earthquake protection system is offered here, as an interesting application of vibration isolation. Theoretical results are accompanied by numerical simulations in the time-harmonic regime.

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2017.0136

Michael Nieves

Papers

Green's Kernels and Meso-Scale Approximations in Perforated Domains

"Deflecting elastic prism" and unidirectional localisation for waves in chiral elastic systems.

Uniform asymptotic formulae for Green's tensors in elastic singularly perturbed domains

Interfacial waveforms in chiral lattices with gyroscopic spinners

Gyro-elastic beams for the vibration reduction of long flexural systems.