Directional Control of Rayleigh Wave Propagation in an Elastic Lattice by Gyroscopic Effects

Movchan, A. B.; Carta, G.; Pagneux, Vincent; Brun, Michele

doi:10.3389/fmats.2020.602960

Cited by 11 publications

(5 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…is the composition of elastic structures via periodic lattices [1][2][3][4][5][6][7][8][9]. In these structures, different effects related to out-of-plane or in-plane deformations, the presence of bending moment or prestress have been explored [10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Tensile material instabilities in elastic beam lattices lead to a bounded stability domain

Bordiga

Bigoni

2022

Phil. Trans. R. Soc. A.

View full text Add to dashboard Cite

Homogenization of the incremental response of grids made up of preloaded elastic rods leads to homogeneous effective continua which may suffer macroscopic instability, occurring at the same time in both the grid and the effective continuum. This instability corresponds to the loss of ellipticity in the effective material and the formation of localized responses as, for instance, shear bands. Using lattice models of elastic rods, loss of ellipticity has always been found to occur for stress states involving compression of the rods, as usually these structural elements buckle only under compression. In this way, the locus of material stability for the effective solid is unbounded in tension, i.e. the material is always stable for a tensile prestress. A rigorous application of homogenization theory is proposed to show that the inclusion of sliders (constraints imposing axial and rotational continuity, but allowing shear jumps) in the grid of rods leads to loss of ellipticity in tension so that the locus for material instability becomes bounded . This result explains (i) how to design elastic materials subject to localization of deformation and shear banding for all radial stress paths; and (ii) how for all these paths a material may fail by developing strain localization and without involving cracking. This article is part of the theme issue ‘Wave generation and transmission in multi-scale complex media and structured metamaterials (part 1)’.

show abstract

Section: Introductionmentioning

confidence: 99%

Tensile material instabilities in elastic beam lattices lead to a bounded stability domain

Bordiga

Bigoni

2022

Phil. Trans. R. Soc. A.

View full text Add to dashboard Cite

show abstract

“…For instance, in [29], a lattice model has been employed to describe topologically protected edge modes in microtubules, present in eukaryotic cells, where time-reversal symmetry can be broken by weak magnetic properties of the tubulin proteins. Gyroscopic action can also be used in this framework to create topological insulators, as demonstrated in [30][31][32][33][34][35][36][37] for elastic lattices and in [38,39] for elastic plates.…”

Section: Introductionmentioning

confidence: 99%

Localized waves in elastic plates with perturbed honeycomb arrays of constraints

Haslinger

Frecentese

Carta

2022

Phil. Trans. R. Soc. A.

Self Cite

View full text Add to dashboard Cite

In this paper, we study wave propagation in elastic plates incorporating honeycomb arrays of rigid pins. In particular, we demonstrate that topologically non-trivial band-gaps are obtained by perturbing the honeycomb arrays of pins such that the ratio between the lattice spacing and the distance of pins is less than 3; conversely, a larger ratio would lead to the appearance of trivial stop-bands. For this purpose, we investigate band inversion of modes and calculate the valley Chern numbers associated with the dispersion surfaces near the band opening, since the present problem has analogies with the quantum valley Hall effect. In addition, we determine localized eigenmodes in strips, repeating periodically in one direction, that are subdivided into a topological and a trivial section. Finally, the outcomes of the dispersion analysis are corroborated by numerical simulations, where a time-harmonic point source is applied to a plate with finite arrays of rigid pins to create localized waves immune to backscattering. This article is part of the theme issue ‘Wave generation and transmission in multi-scale complex media and structured metamaterials (part 1)’.

show abstract

“…A design strategy leading to metamaterials capable of effectively filtering and conditioning wave propagation is the composition of elastic structures via periodic lattices [1][2][3][4][5][6][7][8][9]. In these structures, different effects related to out-of-plane or in-plane deformations, presence of bending moment or prestress have been explored [10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Tensile material instabilities in elastic beam lattices lead to a bounded stability domain

Bordiga,

Bigoni,

Piccolroaz

2022

Preprint

View full text Add to dashboard Cite

Homogenization of the incremental response of grids made up of preloaded elastic rods leads to homogeneous effective continua which may suffer macroscopic instability, occurring at the same time in both the grid and the effective continuum. This instability corresponds to the loss of ellipticity in the effective material and the formation of localized responses as, for instance, shear bands. Using lattice models of elastic rods, loss of ellipticity has always been found to occur for stress states involving compression of the rods, as usually these structural elements only buckle under compression. In this way, the locus of material stability for the effective solid is unbounded in tension, i.e. the material is always stable for a tensile prestress. A rigorous application of homogenization theory is proposed to show that the inclusion of sliders (constraints imposing axial and rotational continuity, but allowing shear jumps) in the grid of rods leads to loss of ellipticity in tension, so that the locus for material instability becomes bounded. This result explains (i.) how to design elastic materials passible of localization of deformation and shear banding for all radial stress paths; (ii.) how for all these paths a material may fail by developing strain localization and without involving cracking.

show abstract

Directional Control of Rayleigh Wave Propagation in an Elastic Lattice by Gyroscopic Effects

Cited by 11 publications

References 39 publications

Tensile material instabilities in elastic beam lattices lead to a bounded stability domain

Tensile material instabilities in elastic beam lattices lead to a bounded stability domain

Localized waves in elastic plates with perturbed honeycomb arrays of constraints

Tensile material instabilities in elastic beam lattices lead to a bounded stability domain

Contact Info

Product

Resources

About