Supplementary codes and datasets for "Wang tiles enable combinatorial design and robot-assisted manufacturing of modular mechanical metamaterials"

This repository provides data and codes for manuscript “Wang tiles enable combinatorial design and robot-assisted manufacturing of modular mechanical metamaterials”  by M. Doškář, M. Somr, R. Hlůžek, J. Havelka, J. Novák, and J. Zeman, published first as a preprint arXiv:2305.09280 at arXiv.org; see the actual description of the Zenodo entry for the latest reference.

This repository contains:

1. MATLAB and C++ source codes for combinatorial design and numerical analyses (folder ./numerics/),
2. experimental data (folder ./experiments/),
3. 3D models of parts used in robotic-assembly (folder ./models/),
4. a control script for robotic assembly (folder ./robotics/).

Numerics

All simulations were performed with an in-house MATLAB code, which extends the finite element toolbox for finite strain calculations accompanying the work of van Bree, S. E. H. M., Rokoš, O., Peerlings, R. H. J., Doškář, M., & Geers, M. G. D. (2020). A Newton solver for micromorphic computational homogenization enabling multiscale buckling analysis of pattern-transforming metamaterials. Computer Methods in Applied Mechanics and Engineering, 372, 113333. In particular, this snapshot corresponds to a cleaned-up version (excluding files unrelated to the publications) of commit 21cfc2e9.

The MATLAB codebase contains MEX files written in C++ to accelerate selected procedures. In order to run any code, these MEX files must be compiled first. We use CMake build automation, with the main CMakeLists.txt located in ./numerics/mex.

Combinatorial search was performed by the RUN_modular_exploration.m script; see definition of problems with the script. The results of the enumerations, stored in ./dat/exploration, were analysed with POST_modular_S_v3.m, identifying layouts leading to the extreme (min/max) tilt angles.

Comparison against experimental measurements was facilitated by a series of scripts POST_DIC_{...}.m. First, run POST_DIC_step1_extract_points_in_mesh.m to identify locations.mat. Next, post-process extensometer data with POST_DIC_step2_merge_extensometer_data.m, and use POST_DIC_step3_impose_extracted_BC.m to parse DIC results in a format suitable for imposing BC later in this script. Finally, comparison between experimental and computed displacements is provided by POST_DIC_step4_modular_comparison_experiments.m. (Note that the particular files need to be manually provided in the “Compute deformation process” part of POST_DIC_step4_modular_comparison_experiments.m.)

Experimental data

This folder contains data from (i) an unixaial tension test of a dogbone specimen (both from a MTS loading machine and DIC data) and (ii) two measurement sessions extracting the L-shape domain responses using DIC (20_11_30 - Hluzek_Elka_newassemblyplan and 21_04_12 - Hluzek_ Elka_quarters with lower loading threshold). For post-processing, see the above-mentioned POST_DIC_{...}.m scripts. *.mat files present directly in ./experiments/ folder were obtained and are need by those scripts.

3D models

The folder contains geometrical models for individual parts needed for robot-assisted assembly of module molds for casting. This includes:

1. a silo extension to store more tiles (file silo_extension.stl),
2. formwork modules around the main structure for the purpose of casting silicone (file tile_formwork.stl),
3. all types of tiles for the inside structure (file tile_inside_types.stl),
4. a spacer shaped for YuMi base to ensure correct distance of the silo and build plate (file yumi_base_1.stl),
5. a spacer shaped for YuMi base to ensure correct distance of the silo and build plate (file yumi_base_2.stl),
6. a spacer shaped for YuMi base to ensure correct distance of the silo and build plate (file yumi_base_3.stl),
7. connection for spacers (file yumi_base_4.stl),
8. spacer holding a silo and the build plate (file yumi_base_5.stl),
9. YuMi grippers with extensions to hold the tiles (file grippers_extend.st).

Robotics

The folder contains a single file with a script created in RobotStudio (RobotWare Version: 6.08.01.00, SmartGripper Version: 3.55.0000.00) to assemble the plan with YuMi IRB 14000-0.5/0.5 left hand.

Acknowledgement

The related research, experiments, and code development were supported by the Czech Science Foundation, project No. 19-26143X.