Data from: Electrical transport in tunably-disordered metamaterials
Abstract
Naturally occurring materials are often disordered, with their bulk properties being challenging to predict from the structure, due to the lack of underlying crystalline axes. In this paper, we develop a digital pipeline from algorithmically-created configurations with tunable disorder to 3D printed materials, as a tool to aid in the study of such materials, using electrical resistance as a test case. The designed material begins with a random point cloud that is iteratively evolved using Lloyd's algorithm to approach uniformity, with the points being connected via a Delaunay triangulation to form a disordered network metamaterial. Utilizing laser powder bed fusion additive manufacturing with stainless steel 17-4 PH and titanium alloy Ti-6Al-4V, we are able to experimentally measure the bulk electrical resistivity of the disordered network. We found that the graph Laplacian accurately predicts the effective resistance of the structure, but is highly sensitive to anisotropy and global network topology, preventing a single network statistic or disorder characterization from predicting global resistivity.
https://doi.org/10.5061/dryad.d2547d8bd
Description of the data and file structure
Three types of data are provided within the data.tgz folder.
STL (design) files for printing the experimental samples used in the paper
STL file were generated in house, using computer-aided design (CAD) software and generative modeling. All connecting beams were designed with rectangular cross sections 1 mm wide and 3 mm tall and are printed within a bounding box that has dimensions 75 mm × 75 mm (±2 mm).
Experimental resistance measurements taken on these samples
We conducted 4-point probe electrical resistance measurements using a Keithley 2450 SourceMeter in two measurement orientations (A and B) on a total of 4 sets of 4 steel samples and 1 set of 5 titanium samples. The instrument applied a force current I = 100 mA on two leads, and measured voltage V on two independently-connected leads for a duration of 500 ms.
Numerical computations performed on the mathematical descriptions of the samples
Utilizing the weighted graph Laplacian of the network based on the point cloud point Locations, (x,y), the voltage at each node, current along each edge, and effective resistance is computed. Additional statistics on distributions are computed.
Files and variables
STL files
The five STL files used to print the samples come from configuration "PC10021", for L=1, 3, 10, 30, 100 (number of iterations of Lloyd's algorithm), with N = 200 nodes.
- 2024_2D_N200L001.stl
- 2024_2D_N200L003.stl
- 2024_2D_N200L010.stl
- 2024_2D_N200L030.stl
- 2024_2D_N200L100.stl
Plotted data
Fig 3: distributions
Files for 4 different numbers of nodes N:
- distribution_data_N100.mat
- distribution_data_N200.mat
- distribution_data_N300.mat
- distribution_data_N500.mat
Variables within each file:
- Iter: vector containing the number of Lloyds iterations performed
- deg_bins: vector containing the bin centers for historgram of degree distribution
- deg_counts: matrix containing corresponding frequency counts for each Lloyds iteration number
- edge_bins: vector containing the bin centers for historgram of edge-length distribution. Units: mm
- edge_counts: matrix containing corresponding frequency counts for each Lloyds iteration number
- conduc_entropy: vector containing the entropy of 1/length (Units mm^{-1}) of edges.
- resist_entropy: vector containing the entropy of length (Units mm) of edges.
Fig 4: entropy
- degree_entropy_N200_mean.txt: list of mean entropy values of degree distribution for Lloyds iteration numbers 0 to 100 averaged over 20 realizations
- degree_entropy_N200_std.txt: list of standard deviation of entropy values of degree distribution for Lloyds iteration numbers 0 to 100 averaged over 20 realizations
- edge_entropy_N200_mean.txt: list of mean entropy values of 1/length distribution for Lloyds iteration numbers 0 to 100 averaged over 20 realizations
- edge_entropy_N200_std.txt: list of standard deviation entropy values of 1/length distribution for Lloyds iteration numbers 0 to 100 averaged over 20 realizations
Fig 5: Reff + experiment
Numerical Simulations:
Steel, with resistivity rho = 80 \mu \Ohm \cdot cm:
- N200_resistance_voltage_current_all_configA_240515.mat
- N200_resistance_voltage_current_all_configB_240515.mat
Titanium, with resistivity rho = 178 \mu \Ohm \cdot cm:
- N200_resistance_Ti64_test_configA_240917.mat
- N200_resistance_Ti64_test_configB_240917.mat
Important variables in the above 4 files:
- n_node: number of points in point cloud (network nodes)
- crs: list of (x,y) coordinates of the corners of the bounding box
- x_loc: cell structure for 20 realizations (rows) and Lloyds iterations 0-100 (columns) each containing the x-location of the 200 point cloud points
- y_loc: cell structure for 20 realizations (rows) and Lloyds iterations 0-100 (columns) each containing the y-location of the 200 point cloud points
- R_total: matrix containing the effective resistance for 20 realizations (rows) and Lloyds iterations 0-100 (columns). Units: mOhm
- I_vars: cell structure for 20 realizations (rows) and Lloyds iterations 0-100 (columns) each containing the current flowing in an edge in the default order of the edge list. 10 Amp applied across network, units: Amp
- V_vars: cell structure for 20 realizations (rows) and Lloyds iterations 0-100 (columns) each containing the voltage at all N=200 nodes. 10 Amp applied across network, units: mVolt
Experimental Measurements:
- 174PHSteel_A_lloyds_resis_err.csv
- 174PHSteel_B_lloyds_resis_err.csv
- Ti64_A_lloyds_resis_err.csv
- Ti64_B_lloyds_resis_err.csv
Columns in the above 4 files:
- 1: Lloyds iteration number
- 2: average resistance in mOhm of one sample, multiple trials
- 3: error of average resistance in mOhm of one sample
Fig 6: current L=10
- Fig_Current_Data_A.mat
- Fig_Current_Data_B.mat
Variables:
- G: MatLab graph structure of the network
- I: vector of the current flowing in an edge in the default order of the edge list. 10 Amp applied across network, units: Amp
- V: voltage at all N=200 nodes. 10 Amp applied across network, units: mVolt
- x: x-location of each node (point cloud point)
- y: y-location of each node (point cloud point)
Fig 7: N=200 and N=500
- N200_resistance_voltage_current_all_configA_240515.mat
- N200_resistance_voltage_current_all_configB_240515.mat
- N500_resistance_voltage_current_all_configA_240830.mat
- N500_resistance_voltage_current_all_configB_240830.mat
Important variables in the above 4 files:
- n_node: number of points in point cloud (network nodes)
- crs: list of (x,y) coordinates of the corners of the bounding box
- x_loc: cell structure for 20 realizations (rows) and Lloyds iterations 0-100 (columns) each containing the x-location of the 200 point cloud points
- y_loc: cell structure for 20 realizations (rows) and Lloyds iterations 0-100 (columns) each containing the y-location of the 200 point cloud points
- R_total: matrix containing the effective resistance for 20 realizations (rows) and Lloyds iterations 0-100 (columns). Units: mOhm
- I_vars: cell structure for 20 realizations (rows) and Lloyds iterations 0-100 (columns) each containing the current flowing in an edge in the default order of the edge list. 10 Amp applied across network, units: Amp
- V_vars: cell structure for 20 realizations (rows) and Lloyds iterations 0-100 (columns) each containing the voltage at all N=200 nodes. 10 Amp applied across network, units: mVolt
Fig 8: D^2_min
- d2min_PC10021.txt
Columns:
- 1: Lloyds iteration number
- 2: D2min: a measure of the non-affine deformations from subsequent lloyds iteration. Units: mm^2
Code/software
All code is available at https://github.com/DMREF-networks
Access information
N/A
These files contain the data used to design and print the disordered lattice metamaterials used in the study, and well as data collected in laboratory experiments and numerical analyses of the configurations.