Motivated by recent experiments on the bending of porous strips towed through a fluid bath, a combined theoretical and experimental study is made of the bending response of perforated plates. The focus is on the practically relevant class of thin plates (with thickness $h$) made of a homogeneous isotropic material that is perforated with periodic distributions (with unit-cell size $\epsilon$) of monodisperse holes spanning a large range of porosities, from the dilute limit to nearly the percolation threshold. From the theoretical point of view, with the objective of quantifying the roles that the various constitutive and geometric inputs play on the their bending response, the perforated plates are modeled by means of three different approaches: $\left(i\right)$ as 3D structures made of a perforated nonlinear elastic material and as 2D structures made of homogeneous linear elastic materials whose effective properties result from $\left(ii\right)$ first taking the limit of dimension reduction ($h\searrow 0$) and then that of homogenization ($\epsilon \searrow 0$) and, vice versa, $\left(iii\right)$ first taking the limit of homogenization ($\epsilon \searrow 0$) and then that of dimension reduction ($h\searrow 0$). From the experimental point of view, laser-engraved molds are utilized to fabricate perforated elastomeric plates with hexagonal distributions of elliptical holes. The resulting perforated plates are then subject to cantilever-bending due to their self weight and their pointwise deformation measured by means of X-ray tomography. Remarkably, counter to the general expectation from available mathematical results for heterogeneous plates at large, the results indicate that the bending response of perforated plates is fairly insensitive to whether the holes are smaller or larger than the plate thickness. Instead, it is dominated by their porosity, while the spatial distribution and shape of the underlying holes only have relatively marginal effects.

受最近关于通过流体浴拖曳的多孔条带弯曲实验的启发，对多孔板的弯曲响应进行了理论和实验相结合的研究。重点是实际相关的薄板类别（厚度$H$) 由均匀的各向同性材料制成，具有周期性分布（具有晶胞大小） $\epsilon$) 的单分散孔跨越大范围的孔隙率，从稀释极限到接近渗透阈值。从理论的角度来看，为了量化各种本构和几何输入对其弯曲响应所起的作用，穿孔板通过三种不同的方法进行建模：$\left(\mathrm{一世}\right)$ 作为由穿孔非线性弹性材料制成的 3D 结构和由均质线性弹性材料制成的 2D 结构，其有效特性来自 $\left(\mathrm{一世}\mathrm{一世}\right)$ 首先取降维的极限（$H\searrow 0$) 然后是均质化 ($\epsilon \searrow 0$)，反之亦然， $\left(\mathrm{一世}\mathrm{一世}\mathrm{一世}\right)$ 首先取同质化的极限（$\epsilon \searrow 0$) 然后是降维 ($H\searrow 0$）。从实验的角度来看，激光雕刻模具用于制造具有六边形椭圆孔分布的穿孔弹性板。由于自重和通过 X 射线断层扫描测量的点状变形，所得到的穿孔板然后经受悬臂弯曲。值得注意的是，与对整体异质板的可用数学结果的普遍预期相反，结果表明穿孔板的弯曲响应对孔是小于还是大于板厚度相当不敏感。相反，它受孔隙度的支配，而底层孔洞的空间分布和形状仅具有相对边缘的影响。