中文摘要：

利用推广的五相球模型得到了含涂层空心微球填充复合材料的有效体积模量、剪切模量和杨氏模量预测的理论公式。分析了复合材料有效模量同空心微球壁的厚度、填充体积分数、涂层厚度等参数的关系。为了说明本文结果的有效性，将五相球模型退化为不含涂层空心球填充复合材料的情况，并与文献中的实验数据进行对比。算例计算表明：涂层较薄时，填料体积分数越大，空心微球壁相对越厚，弹性模量就越大。当填料体积分数最大时，在空心微球壁相对最薄处，弹性模量最低。

英文摘要：

The theoretical formulas are worked out to predict the effective bulk moduli, shear moduli and Young＇s moduli of the composite reinforced by hollow coating spheres using the developed five phase spherical model. The relations of the effective moduli of the composite, the thickness of the hollow sphere wall, volume fraction of the filler, and thickness of the coating were investigated. In order to illustrate the validity of the present results, the five phase model can be reduced to the case of hollow noncoating spheres filled into the matrix, and the reduced results were compared with the experimental data. The calculating example shows that the greater filler volume fraction and relatively thicker wall lead to the bigger elastic moduli, and the smallest elastic moduli appear in the case of the greatest filler volume fraction and the relative thinnest wall when the thickness of the coating is very thin.