High-frequency homogenisation in periodic media with imperfect interfaces

International audienceIn this work, the concept of high-frequency homoge-nisation is extended to the case of one-dimensional periodic media with imperfect interfaces of the spring-mass type. In other words, when considering the propagation of elastic waves in such media, displacement and stress discon-tinuities are allowed across the borders of the periodic cell. As is customary in high-frequency homogenisation, the homogenisation is carried out about the periodic and antiperiodic solutions corresponding to the edges of the Brillouin zone. Comparisons are made with the exact solutions obtained by the Bloch-Floquet approach for the particular examples of monolayered and bilayered materials. Asymptotic approximations are provided for both the higher branches of the dispersion diagram (second-order) and the resulting wave field (leading-order). In these two cases, convergence measurements are carried out to validate the approach. The special case of two branches of the dispersion diagram intersecting with a non-zero slope at an edge of the Brillouin zone (occurrence of a so-called Dirac point) is also considered in detail and illustrated numerically