In recent years, nanostructures have been used in a vast number of applications, making the study of the mechanical behaviour of such structures important. In this paper, two different constitutive equations including first-order strain gradient and simplified differential non-local are employed to model the buckling behaviour of skew nanoplates. The Galerkin method is used for solving the equations in order to obtain buckling load. Using this method, the influence of different parameters consisting of non-classical properties, boundary conditions, and geometrical parameters such as length and angle on the buckling load, are studied. The results showed that small-scale effects are very important in skew graphene sheets and their inclusion results in smaller buckling loads.

To evaluate the influence of strain rate on mechanical behavior of nanocrystalline (NC) materials, a phase mixture constitutive model composed of ordered grain interior phase and plastically softer grain boundary dislocation pile up zone phase was built. Because of dissimilar properties and mismatch between the two phases, dislocation density evolution controlling mechanism based on statistically stored dislocations and geometrically necessary dislocations was analyzed and extended to NC regime to consider their disparate effects. Based on the composite model, a new stress–strain constitutive relation for strain rate-dependent behaviors was firstly established based on dislocation density evolution and strain gradient theory. The calculated data were then compared with corresponding experimental curves and strong strain rate-dependent behaviors were exhibited, which indicated that the predictions kept in good agreement with experiments. Further discussions were presented for calculations of strain rate sensitivity and activation volume for NC Ni through the proposed model.