Macroscopic modelling of prestressed microperiodic elastic media

The aim of this contribution is to formulate and apply a macroscopic model for the analysis of the dynamics and stability of prestressed microperiodic elastic media. This modelling problem has been solved by Kolpakov [1] using the asymptotic homogenization method. However, the method used in [1] neglects the effect of the period length on the macroscopic (overall) solid behavior. To eliminate this drawback we propose a nonasymptotic modelling approach which is a certain generalization of the tolerance averaging method recently presented in [2] and a series of papers. The presented general results are illustrated by the analysis of a certain special problem.