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

TL;DR

This paper provides an analytical solution to the torsion problem for cylindrical rods modeled by generalized continua, including relaxed micromorphic models, aiding in parameter identification and addressing stiffness singularities.

Contribution

It offers the first full derivation of the torsion problem for relaxed micromorphic and other generalized continua, including analysis of stiffness singularities.

Findings

Analytical solutions for torsion in generalized continua.

Method to determine material parameters from torsion data.

Insight into nonphysical stiffness singularities for slender rods.

Abstract

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.