On complete and micropolar-based incomplete strain gradient theories for periodic lattice structures

作     者：Zeyang CHI Jinxing LIU A.K.SOH Zeyang CHI;Jinxing LIU;A.K.SOH

作者机构：Faculty of Civil Engineering and MechanicsJiangsu UniversityZhenjiang 212013Jiangsu ProvinceChina School of EngineeringMonash University MalaysiaJalan Lagoon SelatanBandar SunwaySelangor Darul Ehsan 47500Malaysia 

出 版 物：《Applied Mathematics and Mechanics(English Edition)》 (应用数学和力学（英文版）)

年 卷 期：2023年第44卷第10期

页      面：1651-1674页

核心收录：

学科分类：08[工学] 080102[工学-固体力学] 0801[工学-力学（可授工学、理学学位）] 

基　　金：Project supported by the National Natural Science Foundation of China (No. 11972174) 

主　　题：periodic lattice metamaterial energy principle homogenization micropolar(MP) strain gradient(SG)theory 

摘      要：The micropolar(MP) and strain gradient(SG) continua have been generally adopted to investigate the relations between the macroscopic elastic constants and the microstructural geometric parameters. Owing to the fact that the microrotation in the MP theory can be expressed in terms of the displacement gradient components, we may regard the MP theory as a particular incomplete SG theory called the MPSG theory,compared with the existing SG theories which are deemed complete since all the SGs are included. Taking the triangular lattice comprising zigzag beams as an example, it is found that as the angle of the zigzag beams increases, the bending of the beams plays a more important role in the total strain energy, and the difference between the results by the two theories gradually decreases. Finally, the models are verified with the pure bending and simple shear of lattices by comparing with the results obtained by the finite element method(FEM)-based structure analyses.