Ripples, present in free standing graphene, have an important influence in the mechanical behavior of this two-dimensional material. In this work we show through nanoindentation simulations, how out-of-plane displacements can be modified by strain resulting in softening of the membrane under compression and stiffening under tension. Irradiation also induces changes in the mechanical properties of graphene. Interestingly, compressed samples, irradiated at low doses are stiffened by the irradiation while samples under tensile strain do not show significant changes in their mechanical properties. These simulations indicate that vacancies, produced by the energetic ions, cannot be the ones directly responsible for this behavior. However, changes in roughness induced by the momentum transferred from the energetic ions to the membrane, can explain these differences. These results provide an alternative explanation to recent experimental observations of stiffening of graphene under low dose irradiation, as well as paths to tailor the mechanical properties of this material via applied strain and irradiation.This work is supported by the Generalitat Valenciana through grant reference PROMETEO2012/011 and the Spanish government through grant FIS2010-21883. CJR and EMB thanks support from SeCTyP-UNCuyo grant M003, and ANPCyT grant PICT-2014-0696. CJR thanks CONICET and the 310 Group at FCEN-UNCuyo
