Dynamic stress response analysis of inhomogeneous medium containing inhomogeneous inclusions under action of SH waves

This paper proposes an analytical method for studying the propagation of elastic waves in shear modulus- and density-inhomogeneous substrates containing shear modulus- and density-inhomogeneous inclusions based on theories and methods regarding elastic wave propagation in a homogeneous medium. This method provides research ideas and theoretical references to analyze the dynamic stress concentration and interface displacement problems in functionally graded material (FGM) composites. Taking an inhomogeneous substrate, with power-law variations in both shear modulus and density, containing inhomogeneous circular inclusions under the action of SH waves as an example, the dynamic stress responses caused by the circular inclusions, whose shear modulus and density vary with exponential gradients, are analyzed. The effects of the reference wavenumber in the substrate, the inclusion-to-substrate wavenumber ratio, and the inhomogeneous variations of the substrate and inclusions on the peripheral dynamic stress concentration factor distribution of the inclusions are analyzed using calculation examples. The results suggest that circular inclusion-induced dynamic stress concentration is sensitive to changes in substrate heterogeneity. When the inhomogeneous parameter of the substrate increases, the dynamic stress concentration around a circular inclusion increases sharply. Finally, the dynamic stress concentration can be somewhat reduced by regulating the inclusion heterogeneity.