Topological Interlocking assemblies are arrangements of blocks kinematically constrained by a fixed frame, such that all rigid body motions of each block are constrained only by its permanent contact with other blocks and the frame. In the literature several blocks are introduced that can be arranged into different interlocking assemblies. In this study we investigate the influence of arrangement on the overall structural behaviour of the resulting interlocking assemblies. This is performed using the Versatile Block, as it can be arranged in three different doubly periodic ways given by wallpaper symmetries. Our focus lies on the load transfer mechanisms from the assembly onto the frame. For fast a priori evaluation of the assemblies we introduce a combinatorial model called Interlocking Flows. To investigate our assemblies from a mechanical point of view we conduct several finite element studies. These reveal a strong influence of arrangement on the structural behaviour, for instance, an impact on both the point and amount of maximum deflection. The results of the finite element analysis are in very good agreement with the predictions of the Interlocking Flow model. Our source code, data and examples are available under https://doi.org/10.5281/zenodo.10246034.

翻译：拓扑互锁组装体是由固定框架运动学约束的块体排列，其中每个块体的所有刚体运动仅通过其与其他块体及框架的永久接触受到约束。文献中已提出多种可排列成不同互锁组装体的块体形式。本研究探讨排列方式对所得互锁组装体整体结构行为的影响。我们选用多功能块体作为研究对象，因其可依据壁纸对称性以三种不同的双周期方式排列。研究重点聚焦于组装体向框架传递荷载的机制。为快速实现组装体的先验评估，我们提出一种名为"互锁流"的组合模型。通过开展多项有限元研究从力学角度分析组装体，结果表明排列方式对结构行为具有显著影响，例如最大挠度的位置与数值均受其影响。有限元分析结果与互锁流模型的预测具有高度一致性。我们的源代码、数据集及算例可通过 https://doi.org/10.5281/zenodo.10246034 获取。