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

TL;DR

This paper clarifies the boundary conditions in the Grioli-Koiter-Mindlin-Toupin indeterminate couple stress model, revealing that existing assumptions about their equivalence are incomplete and highlighting the need for a more nuanced understanding.

Contribution

The paper demonstrates that traditional boundary conditions do not fully capture the model's behavior and introduces a refined perspective on boundary condition formulation for this model.

Findings

Boundary conditions are not always equivalent to classical models.

Mixed boundary conditions require careful treatment.

Existing assumptions about boundary condition equivalence are incomplete.

Abstract

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.