Abstract
AbstractMetamaterials are man-made designer matterthat obtains its unusual effective properties by structure rather than chemistry. Building upon the success of electromagnetic and acoustic metamaterials, researchers working on mechanical metamaterials strive at obtaining extraordinary or extreme elasticity tensors and mass-density tensors to thereby mold static stress fields or the flow of longitudinal/transverse elastic vibrations in unprecedented ways. In this prospective paper, we focus on recent advances and remaining challenges in this emerging field. Examples are ultralight-weight, negative mass density, negative modulus, pentamode, anisotropic mass density, Origami, nonlinear, bistable, and reprogrammable mechanical metamaterials.
Highlights
When considering general mechanical materials under arbitrary compression, stretching, and shearing, Hooke’s law translates into rank-two tensors for stress and strain, which are connected via the rank-four elasticity tensor (Box 1)
For mass-and-spring resonances with eigenfrequencies Ωi inside of the mechanical metamaterial unit cells, the effective behavior can be described by a mass-density tensor with components rii(v) = r + Dri
By combining dipolar-like and rotational resonances of the oscillating chiral center piece, a collective mode is induced that exhibits both negative effective mass density and negative longitudinal modulus
Summary
For mass-and-spring resonances with eigenfrequencies Ωi inside of the mechanical metamaterial unit cells, the effective behavior can be described by a mass-density tensor with components rii(v) = r + Dri Spherical metal cores coated with a compliant rubber shell, packed to a simple-cubic lattice in a host material have been considered early on as depicted in Fig. 1(c).[19] Each core–shell unit forms a simple mass- and spring model, which can exhibit a Mie-type resonance frequency far below the Bragg resonance frequency of the lattice.[19,20] Depending of the order of these resonances, negative effective values of the mass density and/or of the elastic moduli can be accomplished.
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