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We develop a procedure for the investigation of the phase diagram of materials under strain. This is based on a global structural prediction method where the volume is constrained to predefined values. Our method is more general than other available techniques, and it avoids at the same time numerical instabilities. As a first example, we investigate the phase diagram of two-dimensional carbon as a function of the area per atom. As expected, we find that graphene is stable for a large range of biaxial strains. However, at large areas there appear novel carbon allotropes containing decagons and higher order polygons. These phases are thermodynamically stable for strains below the breaking point of graphene, indicating that they could be accessible experimentally.