The increasing applications of nanoporous materials in engineering structures call for robust strength criteria that are able to model the size effects of multiscale voids inherent to these materials. Many literature works have devoted to this line of research by either employing the classical homogenization approach or extending Gurson’s model to incorporate the nanovoid surface mechanics. However, few studies are able to simultaneously account for the multiscale effects of both nanovoid and microvoid porosities. This work presents a two-level hierarchical strength theory for nanoporous materials accommodating the effects of nanovoid surface and multiscale porosities. No surface effects exist for microvoids because of their sufficiently large length scale. The lower level representative volume element (RVE) is modeled as a homogeneous, incompressible and rigid-perfectly plastic matrix embedded with multiple nanovoids of similar size. The lower level RVE is then treated as a material point in the upper level RVE made by a hollow sphere. By the coupling of homogenization method for the lower level RVE and the limit analysis of Gurson type at the upper level, an implicit closed-form macroscopic strength criterion is derived. Parametric studies about the significance of nanovoid surface properties, nanovoid size, nanovoid porosity and microvoid porosity on yield loci reveal that the proposed two-level hierarchical model is a substantial reinforcement to the conventional single level strength criteria available in the open literature.

纳米多孔材料在工程结构中的日益增长的应用要求具有鲁棒的强度标准，该标准能够模拟这些材料固有的多尺度空隙的尺寸效应。通过采用经典的均质化方法或扩展Gurson模型以纳入纳米空隙表面力学，许多文献作品致力于这一研究领域。但是，很少有研究能够同时解释纳米空隙和微空隙孔隙率的多尺度影响。这项工作提出了一种针对纳米多孔材料的两级分层强度理论，以适应纳米空隙表面和多尺度孔隙的影响。由于微孔的长度尺度足够大，因此不存在表面效应。下层代表体积元素（RVE）建模为均质，不可压缩且完全刚性的塑料基质，其中嵌入了多个大小相似的纳米空隙。然后将下层RVE视为由空心球制成的上层RVE的实质点。通过对较低水平RVE的均质化方法和较高水平的Gurson类型的极限分析的耦合，得出了隐式的封闭形式宏观强度准则。关于纳米空隙表面性质，纳米空隙尺寸，纳米空隙孔隙率和微空隙孔隙率对屈服位点的重要性的参数研究表明，所提出的两级分层模型是对公开文献中常规单级强度标准的实质性增强。然后将下层RVE视为由空心球制成的上层RVE的实质点。通过对较低水平RVE的均质化方法和较高水平的Gurson类型的极限分析的耦合，得出了隐式的封闭形式宏观强度准则。关于纳米空隙表面性质，纳米空隙尺寸，纳米空隙孔隙率和微空隙孔隙率对屈服位点的重要性的参数研究表明，所提出的两级分层模型是对公开文献中常规单级强度标准的实质性增强。然后将下层RVE视为由空心球制成的上层RVE的实质点。通过对较低水平RVE的均质化方法和较高水平的Gurson类型的极限分析的耦合，得出了隐式的封闭形式宏观强度准则。关于纳米空隙表面性质，纳米空隙尺寸，纳米空隙孔隙率和微空隙孔隙率对屈服位点的重要性的参数研究表明，所提出的两级分层模型是对公开文献中常规单级强度标准的实质性增强。