基于规则孔型的多孔结构材料等效弹性模量的有限元分析

Finite Element Analysis for the Equivalent Elastic Modulus of Cellular Material with Regular Cell Structure

利用金刚石型多孔结构的代表单元模型,选择圆形支柱截面,从结构的几何关系出发推导出了相对密度公式,并在线弹性范围内,用有限元方法计算出了不同相对密度下的金刚石型多孔结构的等效弹性模量Et及相对弹性模量Et/Es随相对密度的变化曲线。结果表明:在较小相对密度下,相对密度随孔结构尺寸的变化关系与Gibson公式相近,平方项前的系数都接近于1,相对弹性模量随相对密度的变化符合二次多项式的关系。

The relative density of cellular material, having regular diamond-type cells, with circular section, was derived by a representative element model. The equivalent elastic modulus E＇, the variation curve of relative elastic modulus E/E, with relative density, were calculated by the finite element method within the range of linear elastic response. The results show that at low density, the relationship between relative density and cell structure change is close to Gibson model, and the coefficients quadratic term are all close to one. In addition, the variation of relative elastic modulus with relative density accords to relationship of quadratic polynomial.