Homogenization of elastic materials containing self-similar rigid micro-inclusions

We consider elastic materials containing rigid micro-inclusions located along self-similar fractals. We use Γ -convergence methods in order to study the asymptotic behaviour of the structure with respect to vanishing parameters describing the thickness of the inclusions. We derive effective elastic behaviours of the elastic materials with boundary conditions describing discontinuities in the tractions across the self-similar fractal interfaces.