Scattering of elastic waves and dynamic stress in two-particle reinforced composite system

Based on the theory of elastodynamics, applying the addition theorem for spherical Bessel functions, the multiple scattering of elastic waves and dynamic stress in two-particle reinforced composite system is investigated, and the analytical expressions of wave fields in each medium are presented. According to the continuous boundary conditions around the spherical particles, the expansion mode coefficients are determined and the analytical expression of dynamic stress concentration factor in different local coordinate systems is obtained. As an example, the variation of dynamic stress concentration factor around the interface between the particles and the matrix under different parameters is analyzed. Analyses show that when the frequency is different, the effect of the particle center-to-center distance on the dynamic stress varies greatly. Only when the distance is greater than a certain number, the effect can be ignored. When the distance is different, the effect of material properties of the particles and the matrix on the dynamic stress is also examined.