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

Method of image charges for describing linear deformation of bounded 2D solid structures with circular holes and inclusions