A couple-stress formulation for the boundary element method

A boundary element methodology is developed for the analysis of two-dimensional linear elastic bodies within the context of couple-stress theory. This theory is the simplest generalised continuum theory that can effectively model size effects in elastic solids. The couple-stress theory, whose origins go back to the beginning of the last century, has attracted a renewed and growing interest during recent years. The couple-stress fundamental solutions are explicitly derived and used to construct the boundary integral equations of the problem with the aid of the reciprocal theorem. A new boundary integral equation is also required to model the rotations and moments. We validate the formulation using an analytical solution from the literature