Correct traction boundary conditions in the indeterminate couple stress model

Abstract

In this paper we consider the Grioli-Koiter-Mindlin-Toupin indeterminatecouple stress model. The main aim is to show that the traction boundary conditions were not yet completely deduced. As it turns out, and to our own surprise, restricting the boundary condition framework from the strain gradient models to the couple stress model does not reduce to Mindlin's set of accepted boundary conditions. We present therefore, for the first time the complete, consistent set of traction boundary conditions.