Customized broadband pentamode metamaterials by topology optimization

Pentamode metamaterials (PMs), a kind of metafluids composed of complex solid medium, have shown enormous potential for both elastic wave and underwater acoustic wave manipulation. However, due to the lack of thorough understanding of the formation mechanism, most reported artificial and empirical PMs share very similar topological features, thus depriving the possibility of obtaining rigorous combination of wave parameters that are required to deliver desirable and prescribed properties and functionalities. To tackle this challenge, with the assumption of C_2v, C_4v and C_6v symmetries in both square and triangle lattices, we propose a unified inverse strategy to systematically design and explore a series of novel isotropic or anisotropic PM microstructures through bottom-up topology optimization. Optimized PM microstructures are designed to provide customized effective mass density, elastic modulus, anisotropy degree and pentamode features on demand. We demonstrate that most optimized microstructures possess broadband single-mode range of exclusive longitudinal waves; some even feature record-breaking relative single-mode bandwidths exceeding 150%. Upon shielding lights on the beneficial topological features of the broadband PMs, we extract the main topological features to form simplified PM configurations, i.e., multiple symmetric solid blocks with slender rods, which can induce the multiform multiple-order rotational vibrations or the integration of the low-order rotational vibrations and anisotropic local resonances for the broadband single-mode nature. At a higher design level, we establish a dedicated inverse-design strategy, under the function-macrostructure-microstructure paradigm, to conceive a novel broadband subwavelength underwater pentamode shielding device, which enables the conversion of propagating acoustic wave to the evanescent surface wave mode within the frequency range [1000 Hz, 4000 Hz]. Our study offers new possibilities for the practical realization of broadband PMs and underwater pentamode devices with rigorously tailored effective parameters, thus bring the PM-based technology within reach for practical applications.