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On the mathematical modelling of dynamic problems in a micro‐periodic composite material

The aim of this paper is to propose a certain new 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 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 governing equations. By applying smoothing operation the continuum models are derived directly from the discrete ones.