论文标题
放松的微态连续体和其他广义连续性的圆柱弯曲问题的分析溶液（包括全推导）
Analytical solutions of the cylindrical bending problem for the relaxed micromorphic continuum and other generalized continua (including full derivations)
论文作者
论文摘要
我们考虑了无限板的圆柱弯曲问题，该板是由一系列广义连续模型（包括微态方法）建模的。这些模型可以描述长度尺寸的效果，从而使标本相对更硬。我们为每种情况提供分析解决方案，并展示预测的弯曲刚度。松弛的微态连续体显示了任意薄样本的界面弯曲刚度，而经典的微态连续性或梯度弹性以及哥斯拉来模型[35]表现出非小型的无界弯曲弯曲刚度的任意薄样本。这一发现突出了使用松弛的微态模型的优点，该模型具有针对小样本的明确极限刚度，并有助于识别相关的材料参数。
We consider the cylindrical bending problem for an infinite plate as modelled 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 exhibit 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 [35] 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.
