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.

Cited by in corpus (6)

• A new view on boundary conditions in the Grioli-Koiter-Mindlin-Toupin indeterminate couple stress model
• Analytical solutions of the cylindrical bending problem for the relaxed micromorphic continuum and other generalized continua (including full derivations)
• Foundations of consistent couple stress theory
• Couple stress theories: Theoretical underpinnings and practical aspects from a new energy perspective
• A variant of the linear isotropic indeterminate couple stress model with symmetric local force-stress, symmetric nonlocal force-stress, symmetric couple-stresses and complete traction boundary conditions
• An assessment of higher gradient theories from a continuum mechanics perspective