Combined bending-tension/compression deformation of micro-bars accounting for strain-driven long-range interactions

Abstract

The paper aims to investigate combined bending-tension/compression deformation of a micro-bar. The strain-driven nonlocal differential model which involves information about long-range interactions between atoms is used to develop the mechanical model and theoretical formulations. Subsequently, effects of internal long-range scale parameter, length of micro-bar, external loads and bending rigidity on combined deformation are shown and discussed. In particular, the upper bound of internal longrange scale parameter and the buckling load are achieved during bending-compression analyses. It is demonstrated that the existence of internal scale parameter or axial tensile load decreases combined deformation. The deflection at the midpoint reduces with increasing bending rigidity, while it rises with increasing length of the microbar. Additionally, an effect of the acting position of transverse load on combined deformation is discussed and deflection at the symmetry point of transverse acting position is achieved. When the long-range interaction is taken into consideration, the equivalent stiffness of the micro-bar subjected to combined bending-tension is stiffer than that predicted by classical mechanics, and it validates the existing nonlocal hardening model. The combined bending-compression of the micro-bar reveals that the deflection may increase or decrease with an increase in the long-range scale or structural length, which verifies both the nonlocal softening and hardening models.