Topological design of pentamode lattice metamaterials using a ground structure method

Pentamode metamaterials are a new class of artificially engineering three-dimensional lattice composites. There exist a few types of pentamode metamaterials that are dominated by ad hoc design motifs, while a systematic design approach is still missing. This paper will present an efficient topological optimization methodology to discover a series of novel pentamode lattice microarchitectures over a range of effective material properties. Firstly, the necessary and sufficient condition that is required for elasticity constants of pentamode micro lattices with at least elastically orthotropic symmetry is derived. Secondly, a general mathematical formulation for design optimization of such pentamode micro lattices is developed. Thirdly, a truss-based three-dimensional ground structure with geometrically orthotropic symmetry is generated, with geometric constraints to avoid intersection and overlap of truss bars within the ground structure. The genetic algorithm is then used to solve the topology optimization problem described by the ground structure. Finally, twenty-four pentamode lattices are designed to demonstrate the effectiveness of the proposed method.