We consider the cylindrical bending problem for an infinite plate as modeled with a family of generalized continuum models, including the micromorphic approach. The models allow to describe length scale effects in the sense that thinner specimens are comparatively stiffer. We provide the analytical solution for each case and exhibits the predicted bending stiffness. The relaxed micromorphic continuum shows bounded bending stiffness for arbitrary thin specimens, while classical micromorphic continuum or gradient elasticity as well as Cosserat models (Neff et al. in Acta Mechanica 211(3–4):237–249, 2010) exhibit unphysical unbounded bending stiffness for arbitrary thin specimens. This finding highlights the advantage of using the relaxed micromorphic model, which has a definite limit stiffness for small samples and which aids in identifying the relevant material parameters.

我们考虑了用一系列广义连续体模型（包括微形方法）建模的无限板的圆柱弯曲问题。从较薄的样品相对较硬的意义上讲，这些模型可以描述长度尺度效应。我们提供每种情况的分析解决方案，并显示出预测的弯曲刚度。松弛的微晶连续体显示出任意薄试样的有限弯曲刚度，而经典的微晶连续体或梯度弹性以及Cosserat模型（Neff等人在Acta Mechanica 211（3–4）：237–249，2010）显示出无物理的无边界弯曲任意薄样品的刚度。这一发现凸显了使用松弛微形态模型的优势，