The motivation for the extension of the theory to heterogeneous materials comes from the observation that many natural as well as man-made composite materials may exhibit peculiar mechanical properties and high resistance to fracture propagation. The general goal of the research project is the advance in the fundamental understanding of crack propagation, localization and damage progression in complex heterogeneous materials. In this context, a special effort will be devoted to the analytical solution of still unsolved fundamental mathematical problems in view of the application to the description of material failure in composite solids.