The fracture strength of materials depends in a non trivial manner on the characteristic length-scales of the specimen and represents a fundamental open problem of science and engineering. This size effect can be understood considering that some form of disorder, such as dislocations, grains or microcracks, is always present in materials. Hence, different parts of the sample should have a different strength depending of the local microstructure. The strength is not a self-averaging quantity since it is dominated by the weakest spot, where global failure is likely to initiate. Larger samples will in general contain more weak parts and are thus bound to fail earlier on average. While the physical mechanism behind this extreme-value based statistical size effect is clear, obtaining mathematical laws in realistic situations is still a formidable task. For instance in quasi-brittle materials, such as concrete and many other composites, size effects are particularly complicated because of the significant damage accumulation preceding sample failure. Other problems arise because cracks are interacting and it is not clear how to take this into account in the framework of extreme value theory. Other intriguing aspects of fracture are associated with intense and widely fluctuating acoustic activity and by the formation of self-affine fracture surfaces. To tackle these issues, we studied fracture from the point of view of statistical mechanics, using lattice models of fracture and breakdown. Our contributions concern the use of continuous damage to model ductile failure, an understanding of the relation between fracture and phase transitions and of the role of disorder for size effects. We wrote an extensive review on statistical models for fracture published in Advanced in Physics. Our current research in this field is devoted to understand the fundamental aspects of fracture size effects and elucidate the origin of the failure distribution from nanoscale materials like graphene to large scale disordered media.

**Key publications:**

Z. Budrikis, S. Zapperi, “Temperature-Dependent Adhesion of Graphene Suspended on a Trench” Nano Letters Article ASAP, DOI: 10.1021/acs.nanolett.5b03958 (2015).

A. L. Sellerio, A. Taloni, and S. Zapperi, “Fracture Size Effects in Nanoscale Materials: The Case of Graphene” Phys. Rev. Applied 4, 024011 (2015).

C. Manzato, A. Shekhawat, P. K. V. V. Nukala, M. J. Alava, J. P. Sethna, and S. Zapperi, “Fracture Strength of Disordered Media: Universality, Interactions, and Tail Asymptotics”, Phys. Rev. Lett. 108, 065504 (2012).