LAUSR

Abstract 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.