Discrete and continuum models in elastodynamics of micro-periodic solids

The aim of this paper is to propose a new alternative approach to the formulation of both discrete and continuum models for the analysis of dynamic problems in elastic composite solids with a periodic microstructure. The proposed approach is based on a periodic simplicial division of the unit cell, [1], and on the assumption of a uniform strain in every simplex. The main feature of the obtained discrete model is the finite-difference form of the governing equations. The proposed discrete model can be formulated on different levels of accuracy. Considerations are restricted to problems in which the typical wavelength of the macroscopic deformation pattern is sufficiently large when compared to the unit cell diameter By applying smoothing operation the continuum models are derived directly from the discrete ones. The general equations obtained in the models proposed here are applied in order to investigate dispersion phenomena in the wave propagation problems.