Quasi-circular cylindrical pore in an elastic solid incorporating surface stresses

Abstract

Within the framework of continuum mechanics, the 2-D problem of an elastic field arising around a quasi-circular cylindrical pore under the action of a remote load and surface stresses is considered incorporating the Gurtin-Murdoch surface elasticity model. Two approaches to solving the problem are presented. One is based on conformal mapping, the other on the boundary perturbation method. In both cases, Goursat–Kolosov’s complex potentials and special Muskhelishvili’s technique are used. In the first approach, the solution to the problem is reduced to a hypersingular integro-differential equation, and in the second, to a sequential solution of integral equations similar to the equation of the first approach. Using the first-order approximation of the perturbation method, the effect of surface stresses on the stress state of the pore surface was investigated depending on the magnitude of the deviation from the circular, the magnitude of the uniaxial load and the size of the cross-section of the pore. At low load values, a significant influence of residual surface stress on the elastic field is observed.