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Mechanical Comparison of Arrangement Strategies for Topological Interlocking Assemblies

Tom Goertzen, Domen Macek, Lukas Schnelle, Meike Weiß, Stefanie Reese, Hagen Holthusen, Alice C. Niemeyer

TL;DR

This work examines how the arrangement of planar topological interlocking assemblies, built from the Versatile Block, governs load transfer, deflection, and stress distribution. It combines finite element analysis with a novel combinatorial model, Interlocking Flows, to predict frame loading and compare three wallpaper-symmetric configurations. The study demonstrates substantial arrangement-dependent differences in mechanical response and validates the discrete model against FEM results, enabling rapid pre-evaluation of thousands of potential assemblies. The approach offers a path toward designing resource-efficient, reusable block-based structures by exploiting combinatorial structure to tailor load paths and performance.

Abstract

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.

Mechanical Comparison of Arrangement Strategies for Topological Interlocking Assemblies

TL;DR

This work examines how the arrangement of planar topological interlocking assemblies, built from the Versatile Block, governs load transfer, deflection, and stress distribution. It combines finite element analysis with a novel combinatorial model, Interlocking Flows, to predict frame loading and compare three wallpaper-symmetric configurations. The study demonstrates substantial arrangement-dependent differences in mechanical response and validates the discrete model against FEM results, enabling rapid pre-evaluation of thousands of potential assemblies. The approach offers a path toward designing resource-efficient, reusable block-based structures by exploiting combinatorial structure to tailor load paths and performance.

Abstract

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.
Paper Structure (25 sections, 18 equations, 15 figures, 1 table)

This paper contains 25 sections, 18 equations, 15 figures, 1 table.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Design Principles and Applications
  4. Mechanical and Experimental Investigations
  5. Symmetric topological interlocking assemblies
  6. Topological Interlocking
  7. The Versatile Block
  8. Wallpaper groups
  9. Planar Assemblies of the Versatile Block
  10. Mechanical investigation of interlocking assemblies
  11. Problem formulation
  12. Simulation setup
  13. Numerical results
  14. Deformed state and maximum deflection
  15. Distribution of stresses
  16. ...and 10 more sections

Figures (15)

  • Figure 1: Three views of the Versatile Block
  • Figure 2: Planar interlocking assemblies of size $9 \times 9$ with a gap of $0.1$ between blocks, generated by a their respective wallpaper group
  • Figure 3: View of the bottom-plane with arrows towards vertex $3$ to indicate the orientation
  • Figure 4: View of the top-plane with arrows towards vertex $3$ to indicate the orientation
  • Figure 5: Displacement fields in $z$-direction of the TIA.
  • ...and 10 more figures

Theorems & Definitions (2)

  • Definition 3.1
  • Definition 5.1