周期性多孔金属材料宏观有效模量和细观局部应力的预测  

Homogenized Moduli and Localized Stresses of Periodically⁃Arranged Porous Metallic Materials

作　　者：董伟伟 刘承 DONG Weiwei;LIU Cheng(The Architectural Design&Research Institute of Zhejiang University Co.,Ltd.,Hangzhou 310028,Zhejiang,China;Department of Civil Engineering,Zhejiang College of Construction,Hangzhou 311231,Zhejiang,China)

机构地区：[1]浙江大学建筑设计研究院有限公司,浙江杭州310028 [2]浙江建设职业技术学院建筑工程学院,浙江杭州311231

出　　处：《力学季刊》2024年第2期483-492,共10页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(12002303);国家优秀青年科学基金(12322206)。

摘　　要：通过材料内侧孔壁的边界条件和单胞的周期性边界条件,可以得到材料的细观性能,并通过材料的总体均匀化本构关系得到材料在面内和面外的宏观均匀化模量参数.所计算的均匀化模量与其他数值及解析模拟得到的结果非常吻合.由于省去了有限元法中对于细观结构的网格划分和前后处理等过程,本文提出的方法在计算效率方面有了明显的提高.此外,对于含有两种不同孔隙体积比的多孔金属材料的初始屈服面进行了预测.以上结果显示,本文所提供的方法可以为工程人员进行多孔材料的模拟和设计提供有效的理论依据.The micromechanical property of the porous material can be obtained through applying the boundary conditions at the inner side of each porosity as well as the outer periodic boundary conditions.The macroscopic in-plane and out-of-plane effective moduli can be finally obtained through the homogenized constitutive equations.The obtained homogenized moduli are highly consistent with those from the finite volume simulations and Kirsch solutions.More importantly,the computational efficiency of the proposed approach is significantly improved by avoiding the mesh discretization of each unit cell,as well as the pre-and postprocessing of other numerical techniques.The initial yield surfaces are also predicted for the porous aluminum materials with two different porosity volume fractions.The proposed method is demonstrated to be able to provide theoretical guidance for the engineers in the simulation and design of porous materials.

关 键 词：多孔金属材料 多尺度模拟 正方形和六边形晶胞 周期性边界条件 Trefftz方法 初始屈服面 

分 类 号：O341[理学—固体力学]