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基于中间层模型,建立了用于描述具有弱界面的多夹杂复合材料的三层嵌入式模型。首先,给出了计算多夹杂复合材料有效性能的公式,随后将三层嵌入式模型分成两种体系得到了相应的细观力学近似方法。此外,针对中间层模型进一步给出了快速多极边界元的基本列式。最后,通过算例验证所提出的两种方法的正确性及有效性,并进一步考察了界面性能对复合材料整体宏观性能的影响。比较结果发现,细观力学近似模型形式简单,易于编程计算,适用于快速预测具有弱界面的复合材料有效弹性性能。而数值算法能够快速有效直观的考察复合材料内部受弱界面影响后的应力分布。算例分析结果表明,当中间层厚度较大而弹性模量较低时,会使得夹杂不再具有增强效果。并且,随着中间层厚度的增加,基体内承担的最大应力也随之增加,从而容易导致复合材料在界面处产生破坏。
Based on the middle layer model, a three-layer embedded model for describing multi-inclusion composites with weak interfaces was established. First, the formula to calculate the effective performance of multi-inclusion composite is given. Then the three-layer embedded model is divided into two systems to get the corresponding meso-mechanics approximation method. In addition, the basic formulation of fast multipole BEM is given for the middle layer model. Finally, the correctness and validity of the proposed two methods are validated by an example, and the influence of interfacial properties on the macroscopic properties of the composites is further investigated. The results show that the approximate model of meso - mechanics is simple and easy to program and calculate, which is suitable for the rapid prediction of the effective elastic properties of composites with weak interface. The numerical algorithm can quickly and effectively investigate the stress distribution in the composites under the influence of the weak interface. The results of the example analysis show that when the thickness of the middle layer is large and the elastic modulus is low, the inclusion will no longer have the enhancement effect. And, with the increase of the thickness of the middle layer, the maximum stress in the matrix also increases, which easily leads to the destruction of the composite at the interface.