Modified solution for a harmonic hole in a soft elastic solid under plane deformation

We consider a hole embedded in an elastic solid under plane deformation. The solid undergoes a uniform far-field loading while the boundary of the hole is subjected to a uniform pressure. We revisit the design of a harmonic hole such that the mean stress in the entire solid remains constant. We additionally incorporate the change in the direction of the pressure inside the hole in determining the harmonic shape of the hole in case the deformation around the hole is relatively large. We show that the harmonic shape of the hole remains elliptical but its aspect ratio is different from that predicted by the classical solution. We discuss via several numerical examples the differences between the current modified harmonic shape and the classical counterpart as well as how the directional change of the internal pressure influences the aspect ratio of the elliptical harmonic hole within a soft elastic solid.