Optimal design of chiral metamaterials with prescribed nonlinear properties
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RESEARCH PAPER
Optimal design of chiral metamaterials with prescribed nonlinear properties Kepeng Qiu 1
&
Ruoyao Wang 2 & Zhenpeng Xie 1 & Jihong Zhu 1 & Weihong Zhang 1
Received: 23 June 2020 / Revised: 7 September 2020 / Accepted: 17 September 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this paper, chiral metamaterials (CMM) were optimized from conceptual design to fine design with the effective elastic constants unchanged under finite strain. First, through calculation and comparison of examples, the unit cell method was selected to compute the effective elastic properties of the periodic chiral metamaterials under finite strain. Secondly, the conceptual design of chiral metamaterials with prescribed Poisson’s ratios under finite strain was realized through density-based and feature-driven topology optimization. Then, the method of moving asymptotes (MMA) was used to solve the optimization problems. Based on the optimal configuration, chiral metamaterials with prescribed Poisson’s ratios and Young’s moduli under finite strain were carefully designed through shape optimization. Genetic algorithm was used to solve the optimization problem. Finally, the optimal models were fabricated by 3D printing. The optimal design was validated by tensile test results, i.e., the designed chiral metamaterials can maintain effective elastic properties under large deformation, and the invariance of the effective elastic properties depends on the nonlinearity of the flexible chiral metamaterials. Keywords Chiral metamaterials (CMM) . Optimal design . Finite stain . Effective elastic properties . 3D printing
1 Introduction Metamaterials (MMs) are artificially engineered materials designed to exhibit unconventional physical properties not found in nature (Schurig et al. 2006; Valentine et al. 2008; Grima and Caruana-Gauci 2012; Wang et al. 2016). The properties of metamaterials are mainly determined by the geometric structures of their microstructures rather than their material compositions. Examples of mechanical metamaterials with extraordinary mechanical properties based on their microstructures and mechanisms include negative Poisson’s ratio (NPR), negative compressibility, and negative elasticity (Nicolaou and Motter 2012; Rocklin et al. 2017; Yu et al.
Responsible Editor: Byeng D Youn * Kepeng Qiu [email protected] 1
State IJR Center of Aerospace Design and Additive Manufacturing, School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an, Shaanxi 710072, People’s Republic of China
2
Shanghai Electro-Mechanical Engineering Institute, Shanghai 201109, People’s Republic of China
2018; Bertoldi et al. 2010; Evans and Caddock 1989; Kim and Ju 2015). Auxetic mechanical metamaterials are perhaps the most widely studied mechanical metamaterials, including three main classes of re-entrant, chiral, and rotational rigid structures (Kolken and Zadpoor 2017; Ren et al. 2018). Internally, numerical studies of chiral mechanical metamaterials with multifunctional mechanical prop
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