Stress Concentration of One Microvoid Embedded in an Adhesive Layer under Harmonic Load

Abstract

This paper investigates the stress concentration of an adhesive material containing a micro air void subjected to a harmonic dynamic surface load. The elastodynamic Green’s function was used to derive the elastic field and take into account the boundary effect. Using the equivalent inclusion method, the micro air void was replaced by the matrix but an eigenstrain and fictitious force were introduced to simulate the material mismatch. Coupling with the boundary element method, one can assemble a linear equation system from which the microvoid and boundary effect are fully taken into account and the eigenstrain, fictitious force, and unknown boundary responses can be calculated. Therefore, the elastodynamic field can be obtained from the equivalent inclusion problem with the prescribed boundary conditions for any bounded domain. The results have been verified and compared with the finite-element simulation for a static case, the classic Eshelby solution for a low-frequency case, and the traditional boundary element method for a full time-harmonic case. A parametric study of stress concentration factors in the adhesive for one void with various depths and frequencies was performed. This method can be extended to general cases of many particles embedded in a matrix with arbitrary boundary conditions.