Content: 1. Introduciton: Review of the history of materials failure and fracture mechanics including historial cases and state of the art 2. Fracutre modes and characteristics: mode I, II and III cracks 3. Brittle and ductile fractures in different materials 4. Characterization of frcture toughness 5. Solution of elastic stress around the crack tip: Kolosov-Muskhelishvili formulus and Westergaard solution 6. Stress intensity factor in 2D and 3D problems and crack handbook 7. Computation of Stress intensity factor: J-integral and a general Eshelby’s energy momentum tensor for crack enegy release 8. Computational methods for fractue modelling: meshless methods, XFEM and peridynamics and commercial software for fracture modelling 9. Computational methods for fracture modelling Students are also guided by practical exercises in the computer lab, assigning also specific projects to be solved through the implementation of numerical codes. The codes will be written in Mathematical/Matlab language at the continuum level and in Matlab language when FE discretization are needed. A introduction and examples to using commerical software such as ABAQUS for crack modelling will be demonstrated.