  We present a method for predicting the linear response deformation of finite
and semi-infinite 2D solid structures with circular holes and inclusions by
employing the analogies with image charges and induction in electrostatics.
Charges in electrostatics induce image charges near conductive boundaries and
an external electric field induces polarization (dipoles, quadrupoles, and
other multipoles) of conductive and dielectric objects. Similarly, charges in
elasticity induce image charges near boundaries and external stress induces
polarization (quadrupoles and other multipoles) inside holes and inclusions.
Stresses generated by these induced elastic multipoles as well as stresses
generated by their images near boundaries then lead to interactions between
holes and inclusions and with their images, which induce additional
polarization and thus additional deformation of holes and inclusions. We
present a method that expands induced polarization in a series of elastic
multipoles, which systematically takes into account the interactions of
inclusions and holes with the external field, between them, and with their
images. The results of our method for linear deformation of circular holes and
inclusions near straight and curved boundaries show good agreement with both
linear finite element simulations and experiments.
