Representative unit cell model of elastic spherical particle composite with interphase and/or general imperfect interface

We consider the representative unit cell (RUC) model of the elastic spherical particle composite with (a) interphase layer and (b) general imperfect interface in the form proposed by Bovik (1994). The rigorous analytical solution to both RUC model problems is obtained by the multipole expansion method in a unified manner. Fulfillment of the matrix-to-inhomogeneity elastic contact conditions reduces the boundary value problem to the linear algebraic system for multipole strengths and provides a highly efficient algorithm for numerical study. The proposed approach applies to all physically consistent models of imperfect interface including the nonlinear ones. In so doing, use of the vector spherical harmonics makes the solving procedure simple and straightforward. Comparison of the accurate numerical data obtained from the interphase and interface models confirms correctness of the Bovik model and illustrates its applicability limits in the multi particle environment. The developed RUC model enables consideration of composite with the spherical particles of diverse size, properties, interphases and interface bonding, with an adequate account of interaction between the inhomogeneities. Comparison with the laboratory test data for syntactic foam shows that a careful modeling of microstructure is a prerequisite for reliable prediction of the effective elastic properties of composite.

Automated summary

This study examines the representative unit cell (RUC) model of elastic spherical particle composite, obtaining rigorous analytical solutions using the multipole expansion method in a unified manner. The use of vector spherical harmonics simplifies the solving procedure, while comparison of experimental and model data confirms the correctness and applicability of the model.