A new view on boundary conditions in the Grioli–Koiter–Mindlin–Toupin indeterminate couple stress model

• Generalized continua, indeterminate couple stress model.
• New boundary conditions.
• No “a priori” equivalence can be established between Mindlin's and our approach.

In this paper we consider the Grioli–Koiter–Mindlin–Toupin linear isotropic indeterminate couple stress model. Our main aim is to show that, up to now, the boundary conditions have not been completely understood for this model. As it turns out, and to our own surprise, restricting the well known boundary conditions stemming from the strain gradient or second gradient models to the particular case of the indeterminate couple stress model, does not always reduce to the Grioli–Koiter–Mindlin–Toupin set of accepted boundary conditions. We present, therefore, a proof of the fact that when specific “mixed” kinematical and traction boundary conditions are assigned on the boundary, no “a priori” equivalence can be established between Mindlin's and our approach.