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 Cracking Composite Design: Trace-Driven Scaling for Cluster-Based 
 Universal Design
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 Author:
     Francesco Danzi

 Reference:
     F. Danzi, "Cracking Composite Design: Trace-Driven Scaling for 
     Cluster-Based Universal Design," Composite Structures, 2025.
     DOI: [insert DOI once published]

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 Overview
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This repository contains MATLAB scripts accompanying the paper
"Cracking Composite Design: Trace-Driven Scaling for Cluster-Based
Universal Design."

The codes implement the π-space clustering, sensitivity analysis,
and validation procedures described in the manuscript. Together,
they reproduce Tables 1–3, Figure 1, and results reported in Appendix 1.

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 Workflow
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To reproduce the results or apply the framework to a new dataset,
run the scripts in the following order:

 1. Composite_Materials_Clusters.m
    - Clusters the material systems using the K-means algorithm.
    - Computes the cluster centroids and plots the clusters with their
      respective centroids.
    - Includes all materials listed in Table 1 and reproduces the results
      shown in Table 3, Figure 1, and Appendix 1.
    - The number of clusters can be modified in the input section
      (see the line indicated in the script).

 2. davies_bouldin.m
    - Computes the Davies–Bouldin Index (DBI) to evaluate the 
      cohesiveness and separation of clusters.

 3. my_silhouette.m
    - Computes the Silhouette Index to assess intra-cluster compactness
      and inter-cluster separation.

 4. Sensitivity Analysis (run independently)
    - Sensitivity_Trace_EigenvalueNorm.m
         Computes sensitivity with respect to the Eigenvalue Norm
         (Section 3.2 of the manuscript).
    - Sensitivity_Trace_FrobeniusNorm.m
         Computes sensitivity with respect to the Frobenius Norm.
    - Sensitivity_Trace_SpectralNorm.m
         Computes sensitivity with respect to the Spectral Norm.

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 Output
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The scripts generate:
    - Cluster plots and centroids (corresponding to Figure 1)
    - Davies–Bouldin and Silhouette indices (Table 2 metrics)
    - Sensitivity results (Section 3.2 of the manuscript)

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 License
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All scripts are released under the MIT License for research and 
educational use.

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 Citation
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If you use this code, please cite:

    F. Danzi, "Cracking Composite Design: Trace-Driven Scaling for 
    Cluster-Based Universal Design," Composite Structures, 2025.
    DOI: [insert DOI once published]

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 Repository Link
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GitHub Repository:
    https://github.com/FDanzi/Clustering-Composite-Materials
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