Torsion Effects in Elastic Composites with High Contrast

We establish a homogenization result and a corrector result for a vibration problem of elasticity. We assume that the data depend in a periodic way on a small parameter ε. We assume also that the Lamé coefficients take possibly high values in a periodical set of disconnected inclusions and take values of the order ε2 elsewhere. In the fibered case, torsional vibrations take place at an infinitesimal scale and give rise to non-local effects.