Due to their good ratio of stiffness and strength to weight, foam materials find use in lightweight engineering. Though, in many applications like structural bending or tension, the scale separation between macroscopic structure and the foam’s mesostructure like cells size, is relatively weak and the mechanical properties of the foam appear to be size dependent. Positive as well as negative size effects have been observed for certain basic tests of foams, i.e., the material appears either to be more compliant or stiffer than would be expected from larger specimens. Performing tests with sufficiently small specimens is challenging as any disturbances from damage of cell walls during sample preparation or from loading devices must be avoided. Correspondingly, the number of respective data in literature is relatively low and the results are partly contradictory.

In order to avoid the problems from sample preparation or bearings, the present study employs virtual tests with CT data of real medium-density ceramic foams. A number of samples of different size is “cut” from the resulting voxel data. Subsequently, the apparent elastic properties of each virtual sample are “measured” directly by a free vibrational analysis using finite cell method, thereby avoiding any disturbances from load application or bearings. The results exhibit a large scatter of the apparent moduli per sample size, but with a clear negative size effect in all investigated basic modes of deformation (bending, torsion, uniaxial). Finally, the results are compared qualitatively and quantitatively to available experimental data from literature, yielding common trends as well as open questions.

由于泡沫材料具有良好的刚度和强度与重量比，因此可用于轻质工程。然而，在结构弯曲或拉伸等许多应用中，宏观结构和泡沫的细观结构（如泡孔尺寸）之间的尺度分离相对较弱，并且泡沫的机械性能似乎依赖于尺寸。对于泡沫的某些基本测试，已经观察到正的和负的尺寸效应，即，材料看起来比较大样本所预期的更柔顺或更硬。使用足够小的样本进行测试具有挑战性，因为必须避免样品制备过程中细胞壁损坏或加载装置造成的任何干扰。相应地，

为了避免样品制备或轴承问题，本研究采用真实中密度泡沫陶瓷的CT数据进行虚拟测试。从生成的体素数据中“切割”出许多不同大小的样本。随后，使用有限单元方法通过自由振动分析直接“测量”每个虚拟样品的表观弹性特性，从而避免来自负载应用或轴承的任何干扰。结果显示，每个样本尺寸的表观模量存在很大的分散性，但在所有研究的基本变形模式（弯曲、扭转、单轴）中都存在明显的负尺寸效应。最后，将结果与文献中可用的实验数据进行定性和定量比较，得出共同趋势以及悬而未决的问题。