A meshfree method for elasticity problems with interfaces

In this work, we develop a meshfree method based on fundamental solutions basis functions for a transmission problem in linear elasticity. The addressed problem consists in, given the displacement field on the boundary, compute the corresponding displacement field of an elastic object (which has piecewise constant Lamé coefficients). The Lamé coefficients are assumed to be constant in non overlapping subdomains and, on the corresponding interface (interior boundaries), non homogeneous jump conditions on the displacement and on the traction vectors are considered. The main properties of the method are analyzed and illustrated with several numerical simulations in 2D domains.