Many manufactured materials, such as rubbers, are made of several constituents with very different mechanical stiffness. Interestingly, the overall mechanical response of the material exhibits a very particular response under mechanical loads. An accurate theoretical characterization of these materials is of tremendous importance for the traditional industry and the new start-ups in the biomedical sector. The goal of this work is to explore a theoretical model for rubber materials, and soft materials in general, with complex micro-structural properties.