Kelvin结构多孔材料弹性模量分析

Elastic Modulus Analysis for Cellular Materials of Kelvin Structure

Kelvin模型是由六个正四边形和八个正六边形组成的十四面体结构，可与在金属中观察到的晶粒和在一些生物组织中观察到的细胞形状相媲美。本文根据线弹性均匀化理论，结合有限元方法给出了三维周期性Kelvin结构的均匀化有限元列式。并利用ANSYS平台和二次开发工具，建立了Kelvin结构实体表示和有限元计算模型，预测出不同相对密度下规则闭孔Kelvin结构的等效弹性系数E1111^H,E1122^H，E1212^H和等效泊松比μ12^H。计算结果表明，Kelvin结构的刚度一质量比随着相对密度增大而增大，剪切刚度一质量比在相对密度3％左右出现极小值点。

The Kelvin model is a 14 -sided polyhedral structure containing six squares and eight hexagons, and can be compared favorably with crystalline grains observed in the metal and with cells observed in some biological structures. According to the homogenization theory, this paper firstly describes a finite element method for predicting the equivalent elastic modulus of 3 - D periodic structures. And then by using ANSYS software, the Kelvin model of solid is developed, and the equivalent elastic modulus , , and equivalent Poisson＇s ratio of a regular close Kelvin structure are computed in accordance with various relative densities. The results show that the range of stiffness - mass ratio increases with the relative densities, and the minimum of shear stiffness - mass ratio is found at the relative density of 3%.