Design of material microstructures for maximum effective elastic modulus and macrostructures

• Published in: Engineering computations 2018-04, Vol.35 (2), p.622-640
• Main Authors: Da, Daicong, Cui, Xiangyang, Long, Kai, Huang, Guanxin, Li, Guangyao
• Format: Article
• Language: English
• Subjects: Compliance; Composite materials; Computation; Density; Design; Design optimization; Elastic properties; Elasticity; Energy; Energy consumption; Evolutionary algorithms; Heat treating; Homogenization; Macrostructure; Microstructure; Modulus of elasticity; Optimization algorithms; Permeability; Porous materials; Sensitivity analysis; Topology optimization; Two dimensional composites; Variables; Viscoelasticity
• ISSN: 0264-4401; 1758-7077
• DOI: 10.1108/EC-09-2016-0323

Purpose In pure material design, the previous research has indicated that lots of optimization factors such as used algorithm and parameters have influence on the optimal solution. In other words, there are multiple local minima for the topological design of materials for extreme properties. Therefore, the purpose of this study is to attempt different or more concise algorithms to find much wider possible solutions to material design. As for the design of material microstructures for macro-structural performance, the previous studies test algorithms on 2D porous or composite materials only, it should be demonstrated for 3D problems to reveal numerical and computational performance of the used algorithm. Design/methodology/approach The presented paper is an attempt to use the strain energy method and the bi-directional evolutionary structural optimization (BESO) algorithm to tailor material microstructures so as to find the optimal topology with the selected objective functions. The adoption of the strain energy-based approach instead of the homogenization method significantly simplifies the numerical implementation. The BESO approach is well suited to the optimal design of porous materials, and the generated topology structures are described clearly which makes manufacturing easy. Findings As a result, the presented method shows high stability during the optimization process and requires little iterations for convergence. A number of interesting and valid material microstructures are obtained which verify the effectiveness of the proposed optimization algorithm. The numerical examples adequately consider effects of initial guesses of the representative unit cell (RUC) and of the volume constraints of solid materials on the final design. The presented paper also reveals that the optimized microstructure obtained from pure material design is not the optimal solution any more when considering the specific macro-structural performance. The optimal result depends on various effects such as the initial guess of RUC and the size dimension of the macrostructure itself. Originality/value This paper presents a new topology optimization method for the optimal design of 2D and 3D porous materials for extreme elastic properties and macro-structural performance. Unlike previous studies, the presented paper tests the proposed optimization algorithm for not only 2D porous material design but also 3D topology optimization to reveal numerical and computational performance o