Simulation of Residual Stress Around Nano-Perforations in Elastic Media: Insights for Porous Material Design

The mechanical integrity of advanced porous materials and perforated structures at the nanoscale is critically governed by the interaction of surface effects and stress concentration around pore architectures. This paper investigates the residual stress field induced by surface tension around two arbitrarily shaped nano-perforations within an infinite elastic matrix, a configuration highly relevant to nanoporous metals and functional composites. By leveraging the complex variable method and conformal mapping techniques, the physical domains of the perforations (approximated as triangular and square shapes, paired with an elliptical perforation) are transformed into unit circles. This transformation allows for the derivation of semi-analytical solutions for the complex potentials and the subsequent stress field. Systematic numerical case studies reveal that a reduced inter-perforation distance dramatically intensifies the hoop stress concentration at the adjacent vertices, identifying these sites as potential initiation points for mechanical failure. Conversely, an increase in the size of one perforation can effectively shield its neighbor and reduce the overall stress level. These findings provide quantitative, physics-based guidelines for the microstructural design of nanoporous materials. By consciously tailoring the spatial distribution, size, and shape of perforations, the mechanical reliability of nanomaterials can be rationally optimized for applications in nanoscale systems.