Algorithm 1 Workflow summary for regularization-enabled fracture simulation

1: Generate a conforming polyhedral tessellation (Voronoi or Laguerre) representing the

composite microstructure.

2: Apply centroidal relaxation (e.g., CVT/CLT updates) to remove large-scale geometric

irregularities.

3: Prescribe a minimum admissible feature length ${\mathcal{l}}_{min}^{\left(0\right)}$ consistent with the target FE mesh

resolution.

4: Identify polyhedral edges with $\mathcal{l}\left(e\right)<{\mathcal{l}}_{min}^{\left(0\right)}$ as candidates for geometric regularization.

5: Perform local topology-preserving edge collapse operations subject to admissibility

checks (non-inversion, valid connectivity, boundary constraints).

6: Update local connectivity and remove any degenerate geometric entities introduced by

accepted collapses.

7: Generate a volumetric tetrahedral mesh of the regularized geometry and insert cohesive

elements along grain boundaries.

8: Perform finite element simulation with cohesive-zone modeling under the prescribed

loading conditions.