Fracture is a free discontinuity problem, and homogenization and optimal design of such problems is a long-standing intellectual challenge. In this project, new theoretical and computational approaches addressing this challenge will be pursued. This project brings together an interdisciplinary team with the vision of exploiting digital manufacturing methods, including 3D printing and ink-jet printing, to synthesize structural materials with exceptional mechanical properties. It has long been understood that the fine-scale structure of materials -- the microstructure -- can affect mechanical properties, and this has been exploited in both materials processing and in creating composite materials. However, such effort has historically been limited in the range of microstructures that could be explored. The vision here is to overcome this limitation by adapting methods of digital and additive manufacturing -- which emerged and have largely been used as tools for prototyping -- to make structural materials with superior mechanical performance. The investigators specifically focus on fracture because of its existential engineering importance and because it raises deep scientific questions. This project will provide for the training through research involvement of doctoral students as well as undergraduate researchers in an interdisciplinary setting, and a new opportunity for engaging K-12 students and for promoting STEM education amongst underrepresented groups.