Coordination-dependent surface strain and rational construction of robust structures.

A surface relaxation model is established to study the elastic properties of nanoscale structures. This model predicts coordination-dependent strain at the surface and thickness-dependent stiffness of a material. Several atomic layers at the surface endure a significant strain gradient, which is dominated by the intrinsic properties of the material. The stiffness of low-dimensional materials is enhanced by surface relaxation effect. Surface effects on strong structures, including honeycomb structure and octet-truss structure with a high stiffness-to-weight ratio, are discussed. For these structures assembled with nanobeams, the Young's modulus decreases with decreasing size of the struts. The coupling between Young's modulus and relative density can be scaled down by engineering tensile strain on the struts.