Asymptotic Analysis for a Stiff Variational Problem Arising in Mechanics

A new approach in the theory of homogenization is carried out on the variational boundary value problem of the stiff type that governs the small vibrations of a periodic mixture of an elastic solid and a slightly viscous fluid. A convergence theorem is proved, which gives the behaviour of the solution and points out the role of the connectedness of phases in the mechanics of mixtures.