Optimal design of two-dimensional band-gap materials for uni-directional wave propagation

New configurations and new properties of materials used in engineering components can be developed by introducing band-gap materials for which a two-dimensional design domain is optimized for uni-directional wave propagation. In this paper, uni-directional band-gap materials with periodic two-dimensional appearances are designed for in-plane waves. By using the Finite Element Method to solve the dynamic behavior of the representative unit cell, the dispersion relation of wave propagation is built up based on Floquet-Bloch theory. With the goal of maximizing the width of band gaps for a certain direction, the distribution of two material phases in a two-dimensional unit cell is determined by a gradient-based topology optimization method. The numerical results show that the proposed periodic hierarchical laminates and the corresponding periodic layered material with homogenized anisotropic layers exhibit wider band gaps than multilayered materials optimized by a one-dimensional design domain. Meanwhile, the influence of the anisotropic property of combined layers and homogenized layers on the band-gap characteristics is analyzed.