Image Charges in 2D Linear Elasticity

The analogy between electrostatics and 2D linear elasticity enables us to describe the deformation of two dimensional solid structures with holes (or inclusions) in terms of “elastic multipoles”. Just like external electric field induces polarization (dipoles, quadrupoles, etc.) of conductive objects, external stress induces elastic multipoles inside holes. Previously, we demonstrated how one can predict complex deformation patterns of structures with many holes that are far away from structure boundaries by considering interactions between induced elastic multipoles. However, when holes are near the structure boundaries, their deformation is affected by the boundary conditions. In electrostatics, the boundary effects can be dealt with the method of image charges. Here we employ the concept of image charges in 2D elasticity to discuss how deformation of holes is affected near flat edges and near wedges.