Topology optimization of anisotropic elastic metamaterial with broadband double-negative index

Abstract

Aiming at the promising superlensing for the medical ultrasonic and detection, the double-negative metamaterials which possess the negative mass density and elastic modulus simultaneously can be acted as the ideal superlens for breaking the diffraction limit. In this paper, we use topology optimization to design the two-dimensional single-phase anisotropic elastic metamaterials with broadband double-negative indices and numerically demonstrate the superlensing at the deep-subwavelength scale. We also discuss the impact of several parameters adopted in the objective function and constraints on the optimized results. Unlike all previous reported mechanisms, our optimized structures exhibit the new quadrupolar or multipolar resonances for the negative mass density, negative longitudinal and shear moduli. In addition, we observe the negative refraction of transverse waves in a single-phase material. Most structures can serve as the anisotropic zero-index metamaterials for the longitudinal or transverse wave at a certain frequency. The cloaking effect is demonstrated for both the longitudinal and transverse waves. Moreover, with the particular constraints in optimization, we design a super-anisotropic metamaterial exhibiting the double-negative and hyperbolic dispersions along two principal directions, respectively. Our optimization work provides a robust computational approach to negative index engineering in elastic metamaterials and guides design of other kinds of metamaterials, including the electromagnetic and acoustic metamaterials. The unusual properties of our optimized structures are likely to inspire new ideas and novel applications including the low-frequency vibration attenuation, flat lens and ultrasonography for elastic waves in the future.

arXiv comment37 pages, 18 figures

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• Topology Optimization Methods for 3D Structural Problems: A Comparative Study
• Bridging coupling bandgaps in nonlinear acoustic metamaterials
• Robust 3D multi-polar acoustic metamaterials with broadband double negativity
• Topology optimization of broadband hyperbolic elastic metamaterials with super-resolution imaging
• Generation of smoothly-varying infill configurations from a continuous menu of cell patterns and the asymptotic analysis of its mechanical behaviour
• Locally Resonant Metagrating by Elastic Impedance Modulation
• Regular sloshing modes in irregular cavities using metabathymetry
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