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Two-node method for the effective elastic modulus of periodic cellular truss materials and experiment verification via stereolithography
European Journal of Mechanics - A/Solids ( IF 4.1 ) Pub Date : 2020-12-25 , DOI: 10.1016/j.euromechsol.2020.104201
Shuheng Wang , Yongbin Ma , Zichen Deng

A two-node method is proposed in this paper based on the traditional representative volume element (RVE) method to predict the effective elastic modulus of periodic cellular truss materials. Through this method, the original unit cell with more than two nodes on the connecting boundary is converted to a new unit cell with only two nodes on the boundary, and the effective elastic modulus is indirectly obtained by the new unit cell. The accuracy of the present method is validated by using the traditional homogenization method numerically and by the static compression tests of the 3D printed cellular structures experimentally. Numerical results show that the present two-node method is more accurate and easier than the traditional RVE method and the asymptotic homogenization (AH) method when the size of the unit cell is negligible relative to the macrostructure size. For periodic cellular materials with rod elements, the present method can provide results with the same accuracy as the AH method but with more efficiency. For periodic cellular materials with beam elements, the present method can provide more accurate lower bound of the effective elastic modulus than the traditional RVE method. The compression tests results show that the elastic modulus of the structure obtained by the two-node method is almost the same as the original structure and is in good agreement with the numerical results.



中文翻译:

周期性单元格桁架材料有效弹性模量的两节点法和立体光刻实验验证

在传统的代表性体积元(RVE)方法的基础上,本文提出了一种两节点法来预测周期性蜂窝桁架材料的有效弹性模量。通过这种方法,将在连接边界上具有两个以上节点的原始单位单元转换为在边界上仅具有两个节点的新单位单元,并通过新的单位单元间接获得有效弹性模量。通过数值上使用传统的均质化方法并通过实验对3D打印的细胞结构进行静态压缩测试,可以验证本方法的准确性。数值结果表明,当单位晶胞的尺寸相对于宏观结构尺寸可忽略不计时,本发明的两节点方法比传统的RVE方法和渐近均匀化(AH)方法更准确,更容易。对于具有杆元件的周期性多孔材料,本方法可以提供与AH方法相同的精度但效率更高的结果。对于具有梁单元的周期性蜂窝材料,本方法可以提供比传统RVE方法更准确的有效弹性模量下限。压缩试验结果表明,采用两节点法得到的结构的弹性模量与原始结构几乎相同,与数值结果吻合良好。本方法可以提供与AH方法相同的准确性但效率更高的结果。对于具有梁单元的周期性蜂窝材料,本方法可以提供比传统RVE方法更准确的有效弹性模量下限。压缩试验结果表明,采用两节点法得到的结构的弹性模量与原始结构几乎相同,与数值结果吻合良好。本方法可以提供与AH方法相同的准确性但效率更高的结果。对于具有梁单元的周期性蜂窝材料,本方法可以提供比传统RVE方法更准确的有效弹性模量下限。压缩试验结果表明,采用两节点法得到的结构的弹性模量与原始结构几乎相同,与数值结果吻合良好。

更新日期:2020-12-25
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