Design of Porous Metamaterials via GA-based Optimization Incorporating Geometry Constraints

Abstract

Acoustic metamaterials exhibit unique bandgap characteristics that enable the manipulation of elastic waves at specific frequencies. The properties of these periodic metamaterials can be tailored by optimizing the material layout within the design domain. Many optimization methods have been proposed consisting of gradient_based and non_gradient_based methods. For gradient_based methods, establishing explicit mathematical formulas for optimization problems of acoustic wave propagation is usually challenging due to complex microstructures. In comparison, these explicit relationships are not required in non_gradient_based methods. Accordingly, genetic algorithms have become the most popular techniques. However, the major problem regarding this method is the enormous search space. This dramatically decreases the possibility of finding desired solutions in limited computational power. Additionally, ignoring the correlation information between elements gives rise to redundancy in searching. To cope with these drawbacks, a geometric_constrained strategy regarding connection of unit cell structure is proposed. The proposed framework has been proven effective in significantly decreasing the search space. The bandgap widths of optimized 2D structures employing the developed method under even 12*12 grids are much wider than those under 32*32 and 60*60 grids in conventional topology optimization. Three dimensional (3D) porous PnCs hold practical significance due to their omnidirectional absorption of acoustic waves. However, the increase in dimensionality results in a substantially larger search space and more complex connectivity issues. To address these challenges, the geometric constraint method developed for porous 2D PnCs is modified for designing porous 3D metamaterials. Besides, a pyramid symmetry is proposed for reducing the number of design variables. The effectiveness of the developed optimization framework has been demonstrated. Notably, optimization results have revealed that certain 3D structures, featuring only one type of mass lump, exhibit outstanding performance. These ultimately optimized structures are intricately linked to specific sequences of bandgaps. Compared with porous 3D single_phase PnCs, the increased configuration flexibility of porous 3D two_material PnCs indicates a broader range of potential for desired structures. However, the introduction of two materials in 3D PnCs leads to a significant search space than those with only one material. Meanwhile, there may be bonding issues at the boundary between two_material regions. To overcome these challenges, a method of 3D PnC construction by 2D mapping is proposed for reducing the number of design variables, and additional enclose constraints are proposed to handle different material property disparity. By incorporating these proposals into a genetic algorithm, the effectiveness of the optimization framework is demonstrated, showcasing its capability to reduce design variables and its applicability to two materials with various disparities. Hybrid metamaterials by combining acoustic and negative Poisson's ratio performance can offer multifunctionalities, making them adaptable to more application scenarios. Existing hybrid structures, however, usually exhibit narrow bandgaps that greatly restrict their potential engineering applications. Additionally, error_and_trial approaches commonly used are inefficient. Furthermore, widely utilized finite element analysis (FEA) renders high consumption of computational power due to its heavy reliance on mesh. To address these problems, an NSGA_ANN_based optimization framework is developed. The effectiveness and efficiency of the optimization framework have been verified. Compared to traditional FEA optimization, time consumption using ANN_based optimization is significantly decreased by 76%.