Homogenization of elasticity equations with contrasting coefficients

Non-stationary problems of linearized elasticity theory in a periodic medium with pores filled with an easily deformable material are considered. The period of the medium is a small positive parameter. It is assumed that the density and the ratio of the minimum and the maximum values of the elasticity moduli of the material are also small positive parameters. Homogenized equations solutions of which approximate the solutions of the problems under consideration are derived. Estimates of the accuracy of this approximation as the parameters approach zero are proved. The form of the homogenized equations and the estimates of the accuracy depend strongly on the geometric properties of the pores and on the asymptotic behaviour of certain expressions containing these small parameters.