Asymptotic Analysis of Stratified Elastic Media in the Space of Functions with Bounded Deformation

Bellieud, Michel; Cooper, Shane

doi:10.1137/16m107551x

Cited by 2 publications

(1 citation statement)

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“…seismic waves) [217]. This is known as the problem of non-commuting limits for the acoustic band in the physics community [218] and a singularly perturbed problem in the applied mathematics community [132,133,[219][220][221][222][223]. Physicists consider there is a competition between the limits taken for a vanishing Bloch wavenumber in the reciprocal space and an increasing contrast between material parameters within inclusions and surrounding medium when studying the quasi-static limit in a band diagram associated with a periodic structure with clamped inclusions such as in figure 10.…”

Section: Elastic Casementioning

confidence: 99%

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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