Many closed-cell foams exhibit an elongated cell shape in the foam rise direction, resulting in anisotropic compressive properties. Nevertheless, the underlying deformation mechanisms and how cell shape anisotropy induces this mechanical anisotropy are not yet fully understood, in particular for the foams with a high cell face fraction and low relative density. Moreover, the impacts of mesostructural stochastics are often overlooked. This contribution conducts a systematic numerical study on the anisotropic compressive behaviour of low-density closed-cell foams, which accounts for cell shape anisotropy, cell structure and different mesostructural stochastics. Representative volume elements (RVE) of foam mesostructures are modeled, with cell walls described as Reissner-Mindlin shells in a finite rotation setting. A mixed stress-strain driven homogenization scheme is introduced, which allows for enforcing an overall uniaxial stress state. Quantitative analysis of the cell wall deformation behavior confirms the dominant role of membrane deformation in the initial elastic region, while the bending contribution gets important only after foam yielding. Following the identified deformation mechanisms, analytical models are developed that relates mechanical anisotropy to cell shape anisotropy. It is found that cell shape anisotropy translates into the anisotropy of compressive properties through three pathways, cell load-bearing area fraction, cell wall buckling stress and cell wall inclination angle. Besides, the resulting mechanical anisotropy is strongly affected by the cell shape anisotropy stochastics while almost insensitive to the cell size and cell wall thickness stochastics. The present findings provide deeper insights into the relationships between the anisotropic compressive properties and mesostructural features of close-cell foams.

翻译：许多闭孔泡沫在发泡上升方向上呈现拉长的泡孔形状，导致其压缩性能呈现各向异性。然而，其内在的变形机制以及泡孔形状各向异性如何诱发这种力学各向异性尚未被完全理解，特别是对于具有高泡孔面占比和低相对密度的泡沫体系。此外，介观结构随机性的影响常被忽视。本研究对低密度闭孔泡沫的各向异性压缩行为进行了系统的数值研究，综合考虑了泡孔形状各向异性、泡孔结构及不同的介观结构随机性。通过建立泡沫介观结构的代表性体积单元（RVE）模型，采用有限转动框架下的Reissner-Mindlin壳单元描述泡孔壁行为。研究引入了混合应力-应变驱动的均匀化方案，该方案能够实现整体单轴应力状态的施加。对泡孔壁变形行为的定量分析证实了膜变形在初始弹性区域的主导作用，而弯曲贡献仅在泡沫屈服后变得重要。基于所识别的变形机制，建立了将力学各向异性与泡孔形状各向异性相关联的解析模型。研究发现，泡孔形状各向异性通过三条路径转化为压缩性能的各向异性：泡孔承载面积占比、泡孔壁屈曲应力和泡孔壁倾角。此外，最终呈现的力学各向异性受泡孔形状各向异性随机性的强烈影响，而对泡孔尺寸和泡孔壁厚度随机性几乎不敏感。本研究为深入理解闭孔泡沫各向异性压缩性能与其介观结构特征之间的关系提供了新的见解。