Generation of representative powder particle packing in 2D/3D: which tool for which application?

Technical Summary: Generation of Representative Powder Particle Packing in 2D/3D

Problem Statement
In powder metallurgy, additive manufacturing (specifically Laser Powder Bed Fusion and Binder Jetting), and granular physics, the generation of a realistic, dense packing of spherical particles is a prerequisite for numerical simulations. This initial configuration serves as the Representative Volume Element (RVE) from which downstream processes—such as sintering, densification, or melt pool evolution—are initialized. Despite the critical nature of this initial state, the selection of a packing generator lacks a systematic benchmark. A representative packing must satisfy five simultaneous criteria: (i) physical admissibility (no particle overlap), (ii) gravitational equilibrium (force and moment balance), (iii) fidelity to the target Particle Size Distribution (PSD), (iv) a relative density ($\phi$) matching experimental references, and (v) computational affordability. Existing literature often neglects conditions (i) and (ii) in purely geometric algorithms or fails to provide a unified framework for comparing tools across these constraints.

Methodology
The authors benchmarked four open-source or academic implementations representing two families of algorithms that satisfy conditions (i) and (ii) by construction:

1. Sequential Geometric Methods:
   • D&R (Dropping-and-Rolling): Particles are placed sequentially, rolling over settled neighbors to reach a local minimum in gravitational potential energy.
   • D&R-ME (Moving-Enlarging): A post-processing variant of D&R that displaces particles toward the barycentre of their Delaunay neighbors and inflates radii to increase density, though it may slightly alter the target PSD.
2. Dynamic Methods (Discrete Element Method - DEM):
   • LAMMPS: Simulates particle settling under gravity until kinetic energy thresholds are met.
   • dp3D: Simulates isostatic compression of a periodic domain until a volumetric strain rate threshold is reached.

The tools were evaluated across four configurations: 2D lognormal packing, 3D binary bimodal packing, 3D lognormal packing (using an industrial MIM-grade IN718 powder), and a 3D domain-size parametric study.

Key Metrics and Evaluation

• PSD Fidelity: Measured using the bin-width-independent Hellinger distance ($H$) on both number-weighted and surface/volume-weighted distributions.
• Relative Density ($\phi$): Calculated on a central 90% sub-box ($B_{90}$) to mitigate boundary effects, using a clipped-volume estimator to account for particles protruding from the sub-domain. This was compared against an experimental solid loading reference ($\phi_{exp} = 0.62$) derived from Archimedes' method.
• Computational Cost: Measured as wall-clock time on a single workstation.

Key Results

• Density vs. Speed Trade-off: In 3D, DEM codes (dp3D and LAMMPS) achieved the densest packings but were computationally expensive. For approximately 20,000 particles, D&R ran 1,800 times faster than dp3D but resulted in a 9% lower relative density ($\phi \approx 0.64$ vs. $\phi \approx 0.72$ for dp3D in the no-adhesion/no-friction case).
• PSD Fidelity:
  • dp3D and D&R/D&R-ME faithfully reproduced both number- and volume-weighted PSDs.
  • LAMMPS exhibited a systematic truncation of the large-particle tail (failing to generate particles $>11$ $\mu$m despite a target max of $50$ $\mu$m), attributed to its pre-processing discretization stage rather than the DEM physics itself. This limitation disqualified it for highly polydisperse distributions in this study.
• Bimodal Robustness: In 3D binary bimodal studies, DEM methods became impractical at high size ratios ($\rho \ge 20$) due to memory limits (dp3D) or insufficient discretization resolution (LAMMPS). D&R remained usable up to $\rho=20$, though it showed anomalous density drops at $\rho=40$ due to its fixed stopping criterion ($N_{max}=200$ failed attempts) preventing small particles from fully surrounding large ones.
• Control Mechanisms: dp3D allows direct prescription of a target relative density via compression increments. LAMMPS offers only indirect control via adhesion and friction parameters. D&R and D&R-ME lack direct levers to tune density once the PSD is fixed, though D&R-ME yields marginally higher densities than standard D&R.

Significance and Claims
The paper claims to provide the first unified benchmark for powder packing generators that strictly enforces physical admissibility and gravitational equilibrium. The authors conclude that tool selection should be application-driven:

• D&R is recommended for fast prototyping and large RVEs where moderate density is sufficient, offering a massive speed advantage.
• dp3D/LAMMPS are necessary when a prescribed, high-density state and strict PSD fidelity are required, despite the computational cost.
• D&R-ME serves as a low-cost intermediate for slightly higher density if minor PSD shifts are acceptable.
• A hybrid approach is proposed: using D&R to generate an initial state, followed by dp3D isostatic compression to reach a target density, which is substantially faster than running dp3D from scratch.

The authors note that while these packings serve as idealized initial states, they do not capture process-specific deposition mechanics (e.g., recoater effects in LPBF). Future work is suggested to validate these packings against experimental tomography data using neighborhood descriptors (coordination number, radial distribution function) and to extend the framework to non-spherical morphologies.