Analytical solution of the cylindrical torsion problem for the relaxed micromorphic continuum and other generalized continua (including full derivations)

@article{Rizzi2020AnalyticalSO,
  title={Analytical solution of the cylindrical torsion problem for the relaxed micromorphic continuum and other generalized continua (including full derivations)},
  author={Gianluca Rizzi and Geralf H{\"u}tter and Hassam Khan and Ionel‐Dumitrel Ghiba and Angela Madeo and Patrizio Neff},
  journal={Mathematics and Mechanics of Solids},
  year={2020},
  volume={27},
  pages={507 - 553}
}
We solve the St. Venant torsion problem for an infinite cylindrical rod whose behaviour is described by a family of isotropic generalized continua, including the relaxed micromorphic and classical micromorphic model. The results can be used to determine the material parameters of these models. Special attention is given to the possible nonphysical stiffness singularity for a vanishing rod diameter, because slender specimens are, in general, described as stiffer. 

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