Influence of hole shape and surface elasticity on anti-plane shear properties of porous structures with periodic holes

Abstract

This work presents a complex variable-based scheme to calculate the anti-plane shear properties of a porous structure containing periodic holes under uniform (anti-plane shear) loadings. The scheme is featured by practically arbitrary shapes of the holes and the surface effects (resulting from surface elasticity) incorporated on each hole’s boundary. Numerical examples are given to verify the feasibility of our scheme and to study the influence of the hole shape and surface effects on the stress concentration around the holes and the effective (longitudinal) shear moduli of the structure. It is shown that the stress concentration around periodic holes can be treated approximately as that around a single hole (for the same hole size and surface shear modulus) when the hole volume fraction is less than 7%. It is also found that for (reasonably) given surface shear modulus, hole volume fraction and hole size, the structure containing periodic circular holes can achieve larger effective shear moduli but lower sensitivity of effective shear moduli to the surface effects, as compared with those containing periodic regular polygonal holes.