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

Gianluca Rizzi (1) , Geralf Hütter (2) , Hassam Khan (3) , Ionel Dumitrel Ghiba (4, 5) , Angela Madeo (1) , Patrizio Neff (3)

1 GEOMAS - Géomécanique, Matériaux et Structures
2 IMFD - Institute of Mechanics and Fluid Dynamics - Institut für Mechanik und Fluiddynamik [Freiberg]
3 Universität Duisburg-Essen, Fakultät für Mathematik
4 UAIC - Alexandru Ioan Cuza University of Iași = Universitatea Alexandru Ioan Cuza din Iași
5 Octav Mayer Institute of Mathematics of the Romanian Academy

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, since slender specimens are in general described as stiffer.

Mots clés: micropolar; relaxed micromorphic model; micro-stretch model; micro-strain model; micro-void model; bounded stiffness; generalized continua; torsion; torsional stiffness; characteristic length; size-effect; micromorphic continuum; Cosserat continuum; couple stress model; gradient elasticity

Domaines: Mécanique des solides [physics.class-ph]

Gianluca Rizzi, Geralf Hütter, Hassam Khan, Ionel Dumitrel Ghiba, Angela Madeo, et al.. Analytical solution of the cylindrical torsion problem for the relaxed micromorphic continuum and other generalized continua (including full derivations). 2021. ⟨hal-03200030⟩