Application of approximation model and boundary element method in solving effective properties of composites with imperfect interface

Based on the interphase model, the three-layer built-in model was established to describe the multi-inclusion composites with imperfect interface. Firstly, the formulations for predicting effective elastic properties of multi-inclusion composites were presented. Then, by separating the three-layer built-in model into two solving systems, the micromechanical approximation model was obtained. Secondly, the basic formulations of fast multipole boundary element method were developed according to the interphase model. Finally, these two methods were compared with each other to verify the correctness and effectiveness, and the effect of imperfect interface on the macromechanical behavior of composites was further investigated. It has been shown that the micromechanical approximation method is quite easy to perform and suitable to fast predict the effective elastic properties of composites with imperfect interface, while the numerical algorithm is able to fast and directly observe the stress distribution in the composites under the influence of the interface imperfection. Based on the analysis, it can be also observed that a stiff inclusion surrounded by a weak interphase (with thicker thickness and lower elastic modulus) behaves as a soft inclusion, and the matrix will take on more stress with the increase of the thickness of interphase, which will easily result in the failure occurred at the interphase.