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.

中文翻译：

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松弛微晶连续体和其他广义连续体（包括完全推导）的圆柱扭转问题的解析解

我们解决了无限圆柱杆的 St. Venant 扭转问题，该杆的行为由一系列各向同性广义连续体描述，包括松弛微晶模型和经典微晶模型。结果可用于确定这些模型的材料参数。特别注意对于消失的杆直径可能存在的非物理刚度奇点，因为细长的试样通常被描述为更硬。