基于均匀化理论的功能梯度材料力学性质的研究

Studyon themechanicpropertiesoffunctionalgradient materialbased on homogenization theory

目的利用均匀化理论讨论了功能梯度材料的细观结构形式对其宏观性能的影响。方法利用均匀化理论,研究组分材料泊松比、表观密度、弹性模量及分布的影响。结果组分材料的泊松比对功能梯度材料的弹性模量的影响不仅与泊松比的大小有关,而且与组分材料的分布形式有关;组分材料的表观密度对功能梯度材料弹性模量的影响可用指数函数模拟;组分材料的弹性模量对功能梯度材料弹性模量的影响可用线性函数模拟;组分材料的分布对功能梯度材料弹性模量的影响甚微。结论功能梯度材料的弹性模量是受组分材料的泊松比影响的。

Objective To study the effect of microstrueture on the macroscopic characteristics of functional gradient material with homogenization theory. Methods The homogenization theory was applied for study the Poisson＇s ratio, apparent density , elastic modulus and distribution of constituent materials. Results The effect of Poisson＇s ratio on elastic modulus of functional gradient material was not only related to the value of Poisson ratio but also to the distribution patterns of constituent materials. The relation of elastic modulus of the functional gradient material with apparent density of constituent material might be simulated by exponential function while the relation of elastic modulus of the functional gradient material with elastic modulus of constituent material might be simulated by linear function. But the effect of distribution of constituent materials on the elastic modulus of the functional gradient material was very little. Conclusion The elastic modulus of functional gradient material is influenced by Poisson＇s ratio of constituent material.