On Near-cloaking for Linear Elasticity

Diatta, André; Guenneau, Sébastien; Hutridurga, Harsha

doi:10.1137/20m1333201

Cited by 7 publications

(2 citation statements)

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“…Following [162,307] (and also [514,515] in the context of elastic near-cloaking theory), an elegant way to derive the socalled transformed time-harmonic Navier equation is to multiply (105) by a test function Φ that is infinitely differentiable and vanishes on the boundary ∂Ω of a domain Ω, and to further integrate by parts over the domain Ω with particle location X = (X, Y, Z), which leads to:…”

Section: Transformation Elastodynamics and Cloakmentioning

confidence: 99%

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Mechanical metamaterials

2023

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Mechanical metamaterials, also known as architected materials, are rationally designed composites, aiming at elastic behaviors and effective mechanical properties beyond (“meta”) those of their individual ingredients – qualitatively and/or quantitatively. Due to advances in computational science and manufacturing, this field has progressed considerably throughout the last decade. Here, we review its mathematical basis in the spirit of a tutorial, and summarize the conceptual as well as experimental state-of-the-art. This summary comprises disordered, periodic, quasi-periodic, and graded anisotropic functional architectures, in one, two, and three dimensions, covering length scales ranging from below one micrometer to tens of meters. Examples include extreme ordinary linear elastic behavior from artificial crystals, e.g., auxetics and pentamodes, “negative” effective properties, behavior beyond classical linear elasticity, e.g., arising from local resonances, chirality, beyond-nearest-neighbor interactions, quasi-crystalline mechanical metamaterials, topological band gaps, cloaking based on coordinate transformations and on scattering cancellation, seismic protection, nonlinear and programmable metamaterials, as well as space-time-periodic architectures.

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Section: Transformation Elastodynamics and Cloakmentioning

confidence: 99%

“…One can then approximate the ideal transformed medium with homogenized formulas in section 3.1.1, e.g. making use of Backus's formulae [73], as was done in [515] in order to achieve a layered cylindrical cloak for in-plane elasticity. The symmetrization of the Cossérat tensor was also employed in [564] to design a seismic cloak.…”

Section: Bulk Elastic Wavesmentioning

confidence: 99%