Pentamode metamaterials (PMMs) are a new class of three-dimensional (3D) mechanical metamaterials, engineered to have unusual elastic property of vanishing shear modulus. Here ‘penta’ denotes five, referring to only one non-zero but five vanishing eigenvalues in the elasticity tensor of isotropic materials. PMMs gain their properties from their rationally designed structural architecture rather than their composition, mimicking the behavior of fluids but are solid, hard to compress yet easy to deform. Compared to most up-to-date design methods based on rigid-body double-cone concept, this paper is to propose, for the first time, a new generative design method using topology optimization to find novel micro-lattice architectures, to enable pentamode properties through the overall elastic deformation of the micro-lattice. The design problem is then formulated to make the micro-lattice have a large but realistically attainable ratio of effective bulk modulus compared to the shear modulus, corresponding to the isotropic microstructure with the effective Poisson’s ratio close to 0.5. The larger of the ratio, the better of the PMM solids to simulate liquids. Several numerical cases with the additive manufacture technique (SLM: selective laser melting) are used to demonstrate the effectiveness of the proposed topological design method in this paper.

五模超材料（PMM）是一类新型的三维（3D）机械超材料，其工程设计具有不寻常的剪切模量弹性特性。在这里，“五边形”表示五个，仅表示各向同性材料弹性张量中的一个非零但五个消失的特征值。PMM通过合理设计的结构结构而不是其成分来获得其特性，从而模仿流体的行为，但它们是固体，难以压缩且易于变形。与基于刚体双锥概念的最新设计方法相比，本文首次提出了一种新的生成设计方法，该方法使用拓扑优化来找到新颖的微晶格体系结构，以实现五模态通过微晶格的整体弹性变形来实现其特性。然后提出设计问题，以使微晶格具有比剪切模量大但实际上可达到的有效体积模量比，对应于有效泊松比接近0.5的各向同性微观结构。比例越大，模拟液体的PMM固体越好。本文使用增材制造技术（SLM：选择性激光熔化）的几个数值案例来证明本文提出的拓扑设计方法的有效性。