A simplicial model for dynamic problems in periodic media

The aim of contribution is to specify a class of periodic mass-point systems with ternary interactions which can be interpreted as discrete models of plane dynamic problems in linear-elastic composite materials. The obtained results yield a new mathematical tool for the analysis of wave propagation problems in heterogeneous periodic material structures, which can be carried out on different levels of accuracy. An application of the proposed model to the analysis of a plane wave propagating in the homogeneous medium with prizmatic rigid inclusions is shown.