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.

五元超材料（PMs）是一种由复杂固体介质组成的超流体，在弹性波和水下声波操纵方面都显示出巨大的潜力。然而，由于缺乏对形成机理的透彻了解，大多数报道的人工和经验性PM都具有非常相似的拓扑特征，因此剥夺了获得传递理想参数和预定特性和功能所需的波参数的严格组合的可能性。为了应对这一挑战，假设C _{2 v}，C _{4 v}和C _{6 v}在正方形和三角形晶格中的对称性方面，我们提出了一种统一的逆策略，以通过自下而上的拓扑优化系统地设计和探索一系列新颖的各向同性或各向异性的PM微结构。经过优化的PM微结构可按需提供定制的有效质量密度，弹性模量，各向异性度和五模态特征。我们证明，最优化的微结构拥有排他性纵波的宽带单模范围；有些甚至具有破纪录的相对单模带宽超过150％。在对宽带PM的有益拓扑特征进行屏蔽后，我们提取主要拓扑特征以形成简化的PM配置，即带有细长杆的多个对称实心块，对于宽带单模性质，它可以引起多形式的多阶旋转振动或低阶旋转振动和各向异性局部共振的积分。在更高的设计水平上，我们根据功能-宏结构-微结构范式建立了专门的逆设计策略，以构想出一种新型的宽带亚波长水下五模屏蔽装置，该装置能够将传播的声波转换为内的surface逝面波模式。频率范围[1000 Hz，4000 Hz]。我们的研究为宽带PM和具有严格定制的有效参数的水下五模设备的实际实现提供了新的可能性，从而使基于PM的技术可用于实际应用。