## 留言板

 引用本文: 崔春丽，徐耀玲. 预测纳米纤维复合材料有效弹性性能的界面模型和界面相模型 [J]. 应用数学和力学，2022，43（8）：877-887
CUI Chunli, XU Yaoling. The Interface Model and the Interphase Model for Predicting the Effective Elastic Properties of Nano-Fiber Composites[J]. Applied Mathematics and Mechanics, 2022, 43(8): 877-887. doi: 10.21656/1000-0887.420231
 Citation: CUI Chunli, XU Yaoling. The Interface Model and the Interphase Model for Predicting the Effective Elastic Properties of Nano-Fiber Composites[J]. Applied Mathematics and Mechanics, 2022, 43(8): 877-887.

• 中图分类号: O31

## The Interface Model and the Interphase Model for Predicting the Effective Elastic Properties of Nano-Fiber Composites

• 摘要:

基于广义自洽法，同时采用Gurtin-Murdoch界面模型和界面相模型研究了纳米纤维复合材料的有效弹性性能，获得了两种模型下有效体积模量的封闭解析解和计算有效面内剪切模量数值解的全部公式。基于界面模型的解答，讨论了有效体积模量和有效面内剪切模量的界面效应。证明了界面模型的解答可由界面相模型的解答退化得到，其中有效体积模量可以实现解析退化，有效面内剪切模量则可以数值退化。以含纳米孔洞的金属铝为例，比较了两种模型计算结果的差异。结果表明，当纳米孔洞半径较小时，两个模型的结果存在很大差异，而当半径较大时两个模型的结果差别不大。

• 图  1  预测纳米纤维复合材料有效性质的两种模型：(a) 界面模型； (b) 界面相模型

Figure  1.  Two models for predicting the effective elastic properties of nano-fiber composites: (a) the interface model; (b) the interphase model

图  2  无量纲有效体积模量和有效面内剪切模量随纤维半径的变化

Figure  2.  Variations of the dimensionless effective bulk modulus and the in-plane shear modulus with the fiber radius

图  3  无量纲有效体积模量和有效面内剪切模量随纤维刚度的变化

Figure  3.  Variations of the dimensionless effective bulk modulus and the in-plane shear modulus with the fiber rigidness

图  4  界面模型和界面相模型的结果对比

Figure  4.  Results comparisons between the interface model and the interphase model

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##### 出版历程
• 收稿日期:  2021-08-05
• 修回日期:  2021-11-24
• 网络出版日期:  2022-07-01
• 刊出日期:  2022-08-01

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