The Principle of Virtual Power (PVP): Application to Complex Media, Extension to Gauge and Scale Invariances, and Fundamental Aspects

Hirsinger, Laurent; Daher, Naoum; Devel, M.; Lecoutre, Gautier

doi:10.1007/978-3-319-77504-3_2

Cited by 1 publication

(1 citation statement)

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“…It means that there is no length scale to start with. This theory makes sense if and only if the considered samples consist of a large number of atoms [22,23]. If the sample size is even remotely comparable to the constituent atomic size, such a model is not truly valid and then atomistic mechanics or molecular dynamics [24,25] approaches are more suitable; we will return to this aspect in section 2.…”

Section: Classical Elasticity 221 Cauchy Elasticitymentioning

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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Section: Classical Elasticity 221 Cauchy Elasticitymentioning

confidence: 99%