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Influence of a generative parameter on the mechanical performance of topological interlocking assemblies of a hexagonal block

Lukas Schnelle, Meike Weiß, Reymond Akpanya, Kai-Uwe Schröder, Alice C. Niemeyer

TL;DR

This work investigates how a geometric design parameter $d$ in hexagon-based topological interlocking assemblies (TIAs) influences mechanical performance under transverse loading. The starfish block is generated by deformations of a fundamental domain of wallpaper group $p6$, producing a planar assembly with $24$ inner blocks and a $30$-block frame, analyzed with FEM (Abaqus/Explicit) under a uniform load of $0.15$ MPa. The results show an optimum around $d \approx 10$ mm, with performance improving up to that point and declining thereafter due to stress concentrations in thin regions. The study demonstrates that TIAs' mechanical response can be tailored via block geometry and motivates multi-parameter optimization, larger-scale assemblies, and exploration of other wallpaper groups.

Abstract

A topological interlocking assembly is an arrangement of blocks, where all blocks are kinematically constrained by their neighboring blocks and a fixed frame. This concept has been known for a long time, attracting recent interest due to its advantageous mechanical properties, such as reusability, redundancy and limited crack propagation. New mathematical methods enable the generation of vast numbers of new topologically interlocking blocks. A natural next question is the quantification of the mechanical performance of these new blocks. We conduct a numerical study of topological interlocking assemblies whose blocks are constructed based on the hexagonal grid. By varying a design parameter used in the generation of these blocks, we study its influence on the structural performance of the entire assembly. The results improve our understanding of the link between the block parameters and the mechanical performance. This enhances the ability to custom design blocks for certain mechanical requirements of the topological interlocking assemblies.

Influence of a generative parameter on the mechanical performance of topological interlocking assemblies of a hexagonal block

TL;DR

This work investigates how a geometric design parameter in hexagon-based topological interlocking assemblies (TIAs) influences mechanical performance under transverse loading. The starfish block is generated by deformations of a fundamental domain of wallpaper group , producing a planar assembly with inner blocks and a -block frame, analyzed with FEM (Abaqus/Explicit) under a uniform load of MPa. The results show an optimum around mm, with performance improving up to that point and declining thereafter due to stress concentrations in thin regions. The study demonstrates that TIAs' mechanical response can be tailored via block geometry and motivates multi-parameter optimization, larger-scale assemblies, and exploration of other wallpaper groups.

Abstract

A topological interlocking assembly is an arrangement of blocks, where all blocks are kinematically constrained by their neighboring blocks and a fixed frame. This concept has been known for a long time, attracting recent interest due to its advantageous mechanical properties, such as reusability, redundancy and limited crack propagation. New mathematical methods enable the generation of vast numbers of new topologically interlocking blocks. A natural next question is the quantification of the mechanical performance of these new blocks. We conduct a numerical study of topological interlocking assemblies whose blocks are constructed based on the hexagonal grid. By varying a design parameter used in the generation of these blocks, we study its influence on the structural performance of the entire assembly. The results improve our understanding of the link between the block parameters and the mechanical performance. This enhances the ability to custom design blocks for certain mechanical requirements of the topological interlocking assemblies.

Paper Structure

This paper contains 11 sections, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Advantages and applications
  3. Literature review
  4. Construction of the Blocks
  5. Simulation setup
  6. Assembly generation
  7. Simulation setup
  8. Results and discussion
  9. Results
  10. Discussion
  11. Conclusion and outlook

Figures (4)

  • Figure 1: Deformation of the fundamental domain and a part of an assembly
  • Figure 2: Blocks (a,c,e) and assemblies (b,d,f), the frame colored red.
  • Figure 3: Parameter $d$ w.r.t. to mechanical performance indicators of the TIA.
  • Figure 4: Stresses ($\mathrm{Pa}$) and deformations ($\mathrm{mm}$) on selected assemblies