A new view on boundary conditions in the Grioli-Koiter-Mindlin-Toupin indeterminate couple stress model
arXiv:1505.00995 · doi:10.1016/j.euromechsol.2016.02.009
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.
References in corpus (5)
- On some fundamental misunderstandings in the indeterminate couple stress model. A comment on recent papers of A.R. Hadjesfandiari and G.F. Dargush
- Evolution of generalized couple-stress continuum theories: a critical analysis
- Correct traction boundary conditions in the indeterminate couple stress model
- Existence results in dislocation based rate-independent isotropic gradient plasticity with kinematical hardening and plastic spin: The case with symmetric local backstress
- Polar continuum mechanics
Cited by in corpus (7)
- Real wave propagation in the isotropic relaxed micromorphic model
- Analytical solutions of the cylindrical bending problem for the relaxed micromorphic continuum and other generalized continua (including full derivations)
- Computational homogenization of higher-order continua
- Couple stress theories: Theoretical underpinnings and practical aspects from a new energy perspective
- Green's functions for the isotropic planar relaxed micromorphic model -- concentrated force and concentrated couple
- An assessment of higher gradient theories from a continuum mechanics perspective
- Analytical solutions of the simple shear problem for certain types of micromorphic continuum models -- including full derivations