The stiffening or softening of nanomaterials determined by a quantitative model

A quantitative model for the size-dependent Young's modulus Y(D) of nanomaterials is established in this work by considering the modulus of single bond and bond number in nanomaterials. Due to bond relaxation, the single bond strength and it's elastic modulus are enhanced as size drops, while bond number is decreased. This makes the Young's moduli of nanomaterials possess different change with size. If compared with bulk Young's modulus Y0, both the stiffer with Y(D) > Y0 and the softer with Y(D) < Y0 for different nanomaterials are predicted. The corresponding experimental or simulation results show their good consistence with the model predictions, which greatly confirms the reasonability of the established model.