Nanoporous materials and structures have attracted widespread attention due to their excellent mechanical properties. Based on the surface elasticity, the effective Young’s moduli are derived for four typical nanoporous structures with periodic unit cells. When the cross-sectional size reduces to nanoscale, the effective Young’s modulus is revealed to be strongly size-dependent. Both the effects of residual surface stress and effective-surface Young’s modulus are examined. The results indicate that negative effective Young’s modulus can be achieved when the residual surface stress is less than zero. The influences of the cross-sectional shape on the relationship between the overall deformation and applied loads are examined. The relative density also plays an important role to the mechanical characteristics not only at macroscales, but also at nanoscales.

中文翻译：

---

表面效应对纳米多孔结构的有效杨氏模量

纳米多孔材料和结构因其优异的力学性能而受到广泛关注。基于表面弹性，推导出四种典型的具有周期性晶胞的纳米多孔结构的有效杨氏模量。当横截面尺寸减小到纳米级时，有效杨氏模量显示出强烈的尺寸依赖性。检查了残余表面应力和有效表面杨氏模量的影响。结果表明，当残余表面应力小于零时，可以获得负的有效杨氏模量。研究了横截面形状对整体变形和施加载荷之间关系的影响。相对密度不仅在宏观尺度上对机械特性也起着重要作用，