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

T0 review · 3 major / 6 minor · reviewed 2026-07-30 · grok-4.5

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Pith's one-line read In 3D powder packings, dropping-and-rolling runs about 1800× faster than DEM at a 9% density shortfall, so the right open-source generator depends on the job.

desk verdict Useful head-to-head on packing generators with a real speed/density trade-off, slightly oversold as a single-score ranking because gravity settle and isostatic jam are different ensembles. read the letter →

arxiv 2607.26992 v1 pith:CKSC72EZ submitted 2026-07-29 cond-mat.mtrl-sci

Antoine Tainturier , Louis Lemarquis , Victor Szczepan , Marc Bernacki This is my paper · ORCID
classification cond-mat.mtrl-sci
keywords spherepackingrepresentativevolumeelementdiscretemethoddroppingandrollingadditivemanufacturingparticlesizedistributionrelativedensity
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Dense sphere packings are the usual starting geometry for simulations in powder metallurgy, additive manufacturing, and granular physics, yet the choice of generator is seldom backed by a common benchmark. This paper compares four open-source tools that already enforce non-overlapping particles in gravitational equilibrium: sequential dropping-and-rolling (D&R), its densified moving-enlarging variant, and two discrete-element codes (LAMMPS under gravity and dp3D under isostatic compression). Across 2D and 3D lognormal packs based on an industrial MIM-grade powder, a controlled 3D bimodal study, and a domain-size sweep, they score size-distribution fidelity with the bin-width-independent Hellinger distance and packing fraction against the feedstock solid loading of 0.62. DEM reaches the densest assemblies but costs more than three orders of magnitude in runtime; for roughly 20,000 particles in 3D, D&R is about 9% less dense than the densest DEM result while finishing about 1800 times faster. The outcome is application-driven selection guidance rather than a single preferred tool.

What carries the argument

Five simultaneous criteria for a representative packing—no overlaps, gravitational equilibrium, PSD fidelity via Hellinger distance on number and surface/volume weights, relative density on a clipped central 90% sub-box, and compute cost—applied uniformly to D&R, D&R-ME, LAMMPS, and dp3D.

What would settle it

Measure the dry packing fraction of the same MIM-grade powder, or extract density and contact statistics from high-resolution tomography of the actual bed, and check whether the tool ranking versus that measured density still matches the ranking versus 0.62.

Watch

Extended reading notes

Core claim

Among open-source generators that satisfy hard-sphere and gravitational-equilibrium constraints by construction, DEM methods produce the densest packings while preserving the target size distribution, but sequential dropping-and-rolling recovers that distribution at a fraction of the cost—with a roughly 9% relative-density shortfall versus the densest DEM case at about 20,000 particles in 3D and an 1800× speedup—yielding concrete rules for choosing a tool by whether speed, a prescribed dense packing fraction, or strict size-distribution fidelity dominates the application.

Load-bearing premise

That the MIM feedstock solid loading of 0.62 is a fair powder-specific density target for dry hard-sphere gravitational packings, treating the binder as merely filling voids.

Editorial extensions

If this is right

  • Choose D&R for fast prototyping and large representative volumes when moderate density is enough.
  • Choose dp3D or LAMMPS when both a prescribed dense packing fraction and a faithful size distribution are required.
  • Choose D&R-ME when a small density gain over plain D&R is worth a slight size-distribution shift.
  • Seed dp3D compression from a finished D&R packing to reach high density cheaper than running DEM from scratch.
  • Score generators with Hellinger distance and clipped-sub-box density when boundary treatments differ.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Contact-network metrics from tomography (coordination, radial distribution) would likely reorder the tools even when bulk density matches, because sequential gravitational placement and isostatic jamming build different neighbourhoods.
  • The large-particle truncation seen in LAMMPS is a preprocessing discretisation limit, so any polydisperse DEM workflow that bins the size law upstream needs an independent tail check before trusting volume-weighted statistics.
  • For powder-bed fusion layers, process-specific spreading may dominate these idealised gravitational packs, so D&R’s speed is most useful as a cheap initialisation rather than a final bed surrogate.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The manuscript benchmarks four open-source sphere-packing generators (D&R, D&R-ME, LAMMPS in gravity mode, and dp3D in isostatic compression) against a five-criterion checklist for representative powder RVEs: hard-sphere non-overlap, gravitational equilibrium, PSD fidelity (Hellinger distance on number- and surface/volume-weighted histograms), relative density φ (via a clipped central 90% sub-box estimator), and wall-clock cost. Across 2D/3D lognormal (industrial MIM-grade IN718 PSD), 3D binary bimodal, and a 3D domain-size sweep, the authors report that DEM codes can reach the highest densities but are orders of magnitude slower; the headline quantitative claim is that for ~20 000 particles in 3D, D&R is ~9% short in φ relative to dp3D while running ~1800× faster. Application-driven selection guidelines follow from these idealised model packings, with φ also compared to an Archimedes feedstock solid loading φ_exp = 0.62.

Significance. A systematic, multi-configuration comparison of widely used open-source packing tools under matched domains and external metrics (prescribed industrial PSD, Hellinger fidelity, fixed-hardware timings, and a powder-specific density anchor) is genuinely useful for powder metallurgy, AM, and granular-physics communities that currently choose generators ad hoc. Strengths include: transparent reporting of both Lee2018 and NANF DEM contact settings; a bin-width-independent Hellinger metric on probability masses; the B90 clipped-volume estimator that enables fair sequential-vs-periodic comparison; empirical scaling exponents; and explicit speed/density trade-offs (Tables 2–4, Fig. 4). The work does not claim new packing physics, but the practical guidelines and the reproducible open-tool framing are a solid contribution if the ensemble and criterion-(ii) issues below are cleaned up.

major comments (3)
  1. [§1 criteria (i)–(ii); §2 dp3D jamming mode; Abstract] Criterion (ii) is defined (§1) as gravitational equilibrium (vertical CoM projection inside the contact convex hull). Section 2 and the abstract state that all four tools meet (i)–(ii) “by construction,” yet dp3D is run in gravity-free isostatic jamming under periodic BCs (domain contracts until ė_v < ė_v,stop). That ensemble is mechanically equilibrated but not gravitationally settled. The unified (i)–(v) rubric and the headline φ ranking therefore mix distinct physical protocols. Please either (a) restate (ii) as mechanical/force balance and treat gravity-settle vs isostatic jam as separate application classes, or (b) restrict the “meets (ii) by construction” claim to D&R/D&R-ME/LAMMPS-gravity and flag dp3D as a densification/jamming reference. The 9% gap cannot be read as a pure generator-efficiency delta without this caveat.
  2. [Abstract; Table 4; §4 3D lognormal; §5] The abstract and conclusion state that “the DEM codes reach the densest packings” and that D&R shows a “9% φ shortfall relative to dp3D” at ~1800× speedup. Table 4 shows this holds only for dp3D_NANF (φ = 0.723 vs D&R 0.636); dp3D_Lee2018 is the loosest packing in the table (φ = 0.584), below both D&R variants. Contact-parameter variation alone moves dp3D by Δφ ≈ 0.14, comparable to the reported D&R–dp3D gap. The main quantitative claim and the tool-selection guidelines must be stated conditionally on the DEM contact setting (and on gravity vs jamming), not as an unconditional DEM-vs-D&R density ordering.
  3. [§3 Simulation parameters; Table 1; §4 3D lognormal discussion of φ_exp] φ_exp = 0.62 is the MIM feedstock solid loading (powder + binder) by Archimedes (§3, Table 1). The text treats the binder as merely filling inter-particle voids and uses φ_exp as a powder-specific target for dry hard-sphere packings. Feedstock rheology and wet packing are not the same physics as the dry, cohesion/friction-modulated assemblies being scored; method ranking versus φ_exp can shift if a dry-bed or tomography density were used. This idealisation is partly disclosed but under-discussed relative to its role as the external density anchor. A short limitations paragraph (and, if available, any dry-poured or tomographic reference density) would keep the comparison honest without new campaigns.
minor comments (6)
  1. [§4 2D lognormal; §4 3D lognormal; Fig. 1(f), 3(f)] LAMMPS large-particle truncation (r ≲ 11 µm vs r_max = 50 µm) is correctly identified as a pre-processing/discretisation limit, not a DEM contact failure. State earlier (methods or 2D results) that LAMMPS φ and H_V are only loosely comparable for this highly polydisperse PSD, so readers do not over-interpret Table 2/4 LAMMPS rows.
  2. [§4 3D bimodal; Table 3] D&R at ρ = 40 (Table 3, parenthesised φ = 0.644) is attributed to the fixed N_max = 200 stopping rule. A one-sentence sensitivity check (or a note that N_max was not re-tuned) would strengthen the bimodal trend discussion.
  3. [§4; Fig. 4(d); Eq. (11)] Eq. (11) scaling exponents are useful; report the fitted range of N and R² (or equivalent) in the caption of Fig. 4(d) so the β values can be assessed.
  4. [§4 2D lognormal] Clarify that the 2D DEM runs are pseudo-2D (single-particle-layer thickness) when comparing native-2D D&R to LAMMPS/dp3D, so dimensionality artefacts are explicit.
  5. [Abstract; passim] Minor typography: abstract “approximatively”; consistent D&R vs DR hyphenation between abstract and body; ensure φ vs Phi is uniform in the abstract HTML/text.
  6. [§5] The conclusion’s suggestion to validate against coordination number / g(r) from tomography is well taken; if any such descriptor is already computable from the generated packings, even a brief internal comparison among the four methods would add value without new experiments.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: external PSD, Archimedes φ_exp, Hellinger, and wall-clock benchmarks; same-group tools do not win by construction.

full rationale

This is an empirical tool benchmark, not a first-principles derivation of a predicted quantity from fitted inputs. Conditions (i)–(ii) are admission filters satisfied by construction for all retained codes; the scored claims are (iii)–(v): Hellinger distance to a prescribed industrial lognormal/bimodal PSD, clipped-sub-box relative density φ versus an external Archimedes feedstock solid loading φ_exp = 0.62, and single-workstation wall-clock. Contact parameters are taken from Lee et al. 2018 or set to the disclosed NANF bound (W, μ) = (0, 0), not fitted to make any method win. D&R/D&R-ME are same-group implementations, but they are evaluated with the same estimators as LAMMPS/dp3D and lose on density; the headline 9% φ / 1800× speed trade-off is a measured comparison, not a quantity forced by definition or by a self-citation uniqueness chain. Ensemble mismatch (gravity settle vs isostatic jam) is a methodology/commensurability concern, not circularity. No self-definitional loop, no fitted-input-called-prediction, no load-bearing uniqueness import.

Assumptions & free parameters 5 free parameters · 6 assumptions · 2 invented entities

Load-bearing content is mostly standard hard-sphere/DEM practice plus protocol choices. The claim rests on accepting hard-sphere non-overlap, a geometric gravitational-stability rule, a specific industrial PSD and feedstock density as reference, literature contact parameters, and the authors’ B90/Hellinger/Nmax protocol—not on new physical entities.

free parameters (5)
  • Nmax (D&R stop after consecutive failed insertions) = 200
    Fixed at 200; controls when sequential packing terminates and is implicated in the anomalous low φ at ρ=40.
  • DEM contact pair (μ, W, α_damp) from Lee2018 = μ=0.577, W=4, α_damp=0.8
    Friction, adhesion work, and restitution taken from cited LPBF packing study; directly shifts achievable φ between Lee2018 and NANF bounds.
  • B90 inset fraction = 0.05 per face (central 90%)
    5% face inset defining the central sub-box for clipped φ; chosen for boundary mitigation, not derived.
  • Reference domain sizes = 600 µm; 133 µm cube
    600 µm (2D) and 133 µm (3D) chosen a priori to host ~2e4 particles affordably; affects reported N and timing.
  • NL ≥ 100 large-particle representativity floor (bimodal) = 100
    Hand-set minimum large-particle count that drives N up to ~2e6 at extreme ρ and changes cost/feasibility rankings.
assumptions (6)
  • domain assumption Hard-sphere / hard-disk non-overlap is required of any admissible initial packing (condition i).
    Stated in §1 as criterion (i); standard for the target downstream simulations.
  • domain assumption Gravitational equilibrium holds when the vertical projection of a particle’s center lies in the convex hull of its contacts (frictional, cohesionless).
    Criterion (ii) in §1; used to admit only D&R-family and DEM and to exclude dense constructive methods.
  • ad hoc to paper Hellinger distance on binned probability masses is a bin-width-independent PSD fidelity metric for number and r^2/r^3 weights.
    §3 Eqs. 3; standard statistical distance but chosen here over L2 on densities as the reporting metric.
  • domain assumption Feedstock solid loading φ_exp=0.62 by Archimedes is a powder-specific reference for achievable packing fraction of the dry model.
    Table 1 and §3; binder assumed only to fill voids.
  • domain assumption Newton–Euler DEM with Hertz–Mindlin (±JKR/DMT adhesion) produces physically admissible equilibrated packs.
    §2 Eqs. 1 and contact-law discussion; standard DEM premise.
  • ad hoc to paper Dense constructive packers that violate (i) or (ii) are out of scope for initial states of mechanical/sintering simulations.
    §1–2 exclusion of inflation/advancing-front/RSA family from the benchmark.
invented entities (2)
  • B90 clipped-volume (area) relative-density estimator
    purpose: Enable fair φ comparison between sequential bounding-box packs and periodic DEM packs by measuring only the central 90% with exact cap/segment subtraction.
    Defined in §3 Eqs. 5–10; not a physical object but a new protocol object the rankings depend on.
  • Five-criterion representativity checklist (i)–(v) for powder RVEs
    purpose: Unified frame for deciding whether a generated packing is fit as a simulation initial state.
    Introduced in §1; organizes the benchmark but is a normative checklist rather than a measured entity.

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Cite this review

Pith. "Pith review of Generation of representative powder particle packing in 2D/3D: which tool for which application?." pith.science (2026). https://pith.science/paper/CKSC72EZ

@misc{pith2026260726992,
  author       = {Pith},
  title        = {Pith review of: Generation of representative powder particle packing in 2D/3D: which tool for which application?},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CKSC72EZ}},
  note         = {Machine review of arXiv:2607.26992}
}
read the original abstract

Although dense sphere packings serve as the initial state for simulations in powder metallurgy, additive manufacturing and granular physics, the choice of a packing generator is rarely guided by a systematic benchmark. A representative packing must be (i)-(ii) physically admissible (non-overlapping particles in gravitational equilibrium); (iii) faithful to the target particle size distribution (PSD); (iv) representative in relative density Phi; and (v) computationally affordable. Four open-source tools have been benchmarked, meeting (i)-(ii) by construction: the sequential DR (dropping-and-rolling) and its densified variant DR-ME, and the discrete element method (DEM) codes LAMMPS (gravity) and dp3D (isostatic compression). Across four configurations (2D/3D lognormal, 3D bimodal, and a 3D domain-size study), they are compared against an industrial MIM-grade powder, with PSD fidelity measured by the bin-width-independent Hellinger distance and Phi against the feedstock solid loading (phi_exp = 0.62, by Archimedes' method). In 3D, the DEM codes reach the densest packings but run more than three orders of magnitude slower: for approximatively 20 000 particles, DR shows a 9% phi shortfall relative to dp3D while running 1800x faster. These idealised model packings yield application-driven tool-selection guidelines.

Figures

Figures reproduced from arXiv: 2607.26992 by the authors.

Figure 1
Figure 1. 2D particle packings: spatial distributions (a)–(d) and particle size histograms, number-weighted (e), surface-weighted (f). [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. 3D binary bimodal packings at the Furnas composition [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. 3D particle packings: spatial distributions (a)–(d) and particle size histograms, number-weighted (e), volume-weighted (f). [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Evolution of the Hellinger distance H, number-weighted (a) and volume-weighted (b), of the relative density φ (c) and of the computational time (d) as functions of domain size and particle number in 3D granular packings. system size. D&R exhibits the most favourable sc…

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Pith tools

Reviewed July 30, 2026 · model on record in the stance chip above.