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arxiv: 1907.05613 · v1 · pith:4B5TPQBKnew · submitted 2019-07-12 · ❄️ cond-mat.soft

Inertial drag in granular media

Shivakumar Athani , Pierre Rognon This is my paper

Pith reviewed 2026-05-24 22:35 UTC · model grok-4.3

classification ❄️ cond-mat.soft
keywords granular materialsdrag forceinertial regimeelasto-inertial modelgrain mobilizationunsteady loadingrate-independent regime
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The pith

Objects accelerating through granular media experience strongly enhanced drag forces in an inertial regime.

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

The paper examines how an object's acceleration alters the drag force it experiences while moving through a granular packing, using simulations of a plate being uplifted at controlled acceleration patterns. Results distinguish a rate-independent regime, where drag follows the usual velocity dependence, from an inertial regime in which higher acceleration markedly increases the drag. The authors construct an elasto-inertial model that reproduces the measured forces in both regimes by incorporating the gradual mobilization of grains sitting above the plate. The analysis underscores that mobility under steady motion differs from mobility under unsteady acceleration in granular materials.

Core claim

Simulations of vertically uplifting a plate through a granular packing with prescribed acceleration patterns reveal that the drag force depends on the object's acceleration. Depending on plate size, depth, and acceleration, there is a rate-independent regime and an inertial regime where acceleration strongly enhances the drag. An elasto-inertial drag force model, based on gradual elasto-inertial mobilisation of grains located above the plate, captures the measured forces in these regimes.

What carries the argument

An elasto-inertial drag force model that incorporates gradual mobilization of grains above the accelerating plate.

If this is right

  • In the rate-independent regime the drag force follows the usual dependence on depth and plate size without additional acceleration terms.
  • In the inertial regime the drag force rises in proportion to the object's acceleration.
  • The same elasto-inertial model reproduces measured forces across varied plate sizes, depths, and acceleration histories.
  • Mobility under steady loading differs fundamentally from mobility under unsteady acceleration in granular packings.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Dynamic loads on buried objects, such as rapid uplift or impact, would require an inertial correction to standard drag estimates.
  • The distinction between regimes may extend to other unsteady processes in granular systems, such as seismic shaking or rapid penetration.

Load-bearing premise

Grain mobilization processes observed in the simulations generalize to physical granular materials.

What would settle it

Measuring the drag force on an accelerated plate in a laboratory granular packing and testing whether the inertial-regime data match the elasto-inertial model's quantitative predictions.

Figures

Figures reproduced from arXiv: 1907.05613 by Pierre Rognon, Shivakumar Athani.

Figure 1
Figure 1. Figure 1: FIG. 1. Dynamic uplift tests. (a) Example of a system com [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Effect of the ultimate uplift velocity [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Effect of the ultimate uplift velocity [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: shows the effect of the acceleration time τ on the maximum drag for a plate of size B = 30d and em￾bedment H = B. The linear increase (6) is recovered for all acceleration times. However, the value of the accel￾eration time τ strongly influences the parameter α. For large values of τ (τ & 0.1tg), α appears to be inversely proportional to the acceleration time: α ∝ τ −1 for τ & 0.1tg (7) In contrast, the pa… view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Effect of the inter granular coefficient of restitution [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Scaling of the coefficient [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Illustration of the elasto-inertial process controlling [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Snapshots illustrating the grain mobilisation and contact compression when the maximum drag force is reached [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Examples of drag force evolutions during uplift tests ( [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: shows the values of the post peak drag force Fpost obtained for two plates, as a function of the ulti￾mate velocity and acceleration time. For long acceleration times (τ = 4tg), post peak drag force linearly increases with the ultimate velocity v∞. This linear increase is similar to the maximum drag be￾haviour. This suggests that the plate is still accelerating after the maximum drag is reached, and that … view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Snapshot of contact network evolution during uplift. Right and left columns shows two tests performed with two [PITH_FULL_IMAGE:figures/full_fig_p011_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Time [PITH_FULL_IMAGE:figures/full_fig_p012_12.png] view at source ↗
read the original abstract

Like in liquids, objects moving in granular materials experience a drag force. We investigate here whether and how the object acceleration affect this drag force. The study is based on simulations of a canonical drag test, which involves vertically uplifting a plate through a granular packing with a prescribed acceleration pattern. Depending on the plate size, plate depth and acceleration pattern, results evidence a rate-independent regime and an inertial regime where the object acceleration strongly enhances the drag force. We introduce an elasto-inertial drag force model that captures the measured drag forces in these two regimes. The model is based on observed physical processes including a gradual, elasto-inertial mobilisation of grains located above the plate. These results and analysis point out fundamental differences between mobility in granular materials upon steady and unsteady loadings.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript uses discrete-element simulations of a canonical plate-uplift test in which a plate is driven vertically through a granular packing according to prescribed acceleration histories. Depending on plate size, burial depth and acceleration pattern, the simulations exhibit a rate-independent drag regime and an inertial regime in which plate acceleration markedly increases the measured drag force. From direct observation of grain kinematics the authors construct an elasto-inertial drag model that is stated to reproduce the simulated forces in both regimes; the model is built on a gradual, elasto-inertial mobilisation of grains above the plate. The work concludes that steady and unsteady loadings produce qualitatively different mobility in granular media.

Significance. If the reported regimes and the associated model are robust, the paper supplies a mechanistic, simulation-derived framework for inertial drag under unsteady loading that is absent from most steady-state granular-drag literature. The explicit link between observed grain-mobilisation processes and the functional form of the drag law is a methodological strength. The results are relevant to any application involving rapid acceleration of objects in granular beds (penetration, locomotion, seismic loading) and could motivate targeted experiments.

major comments (2)
  1. [§4] §4 (elasto-inertial model): the manuscript states that the model 'captures the measured drag forces' but provides no explicit account of how the model coefficients are obtained, whether they are held fixed across all acceleration patterns, or whether they are determined by fitting the same data used to identify the two regimes. This information is load-bearing for the central claim that the model reproduces both regimes.
  2. [Results] Results section (regime identification): the distinction between rate-independent and inertial regimes is presented without quantitative thresholds, error bars on the drag-force data, or statistics across independent realisations. Without these, it is difficult to judge the robustness of the reported transition and therefore the scope of the model.
minor comments (2)
  1. [Abstract] Abstract: no numerical values (e.g., range of accelerations, magnitude of drag enhancement, plate dimensions) are supplied, reducing the reader's ability to gauge the practical significance of the regimes.
  2. [Figures] Figure captions and text: several figures that illustrate grain mobilisation would benefit from additional annotations (arrows, colour scales) that directly link the visualised kinematics to the terms appearing in the elasto-inertial model.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and the positive overall assessment. We address the two major comments point by point below. Both points identify genuine gaps in the current manuscript that we will correct in revision.

read point-by-point responses

  1. Referee: [§4] §4 (elasto-inertial model): the manuscript states that the model 'captures the measured drag forces' but provides no explicit account of how the model coefficients are obtained, whether they are held fixed across all acceleration patterns, or whether they are determined by fitting the same data used to identify the two regimes. This information is load-bearing for the central claim that the model reproduces both regimes.

    Authors: We agree that the procedure for determining the model coefficients must be stated explicitly. In the revised manuscript we will add a dedicated paragraph in §4 that (i) describes the fitting protocol, (ii) states that a single set of coefficients is used for all acceleration histories, and (iii) clarifies whether the coefficients were obtained from an independent subset of the data or from auxiliary simulations. These additions will remove any ambiguity about the scope of the model. revision: yes

  2. Referee: [Results] Results section (regime identification): the distinction between rate-independent and inertial regimes is presented without quantitative thresholds, error bars on the drag-force data, or statistics across independent realisations. Without these, it is difficult to judge the robustness of the reported transition and therefore the scope of the model.

    Authors: The referee correctly identifies the absence of quantitative support for the regime boundaries. In revision we will (i) define explicit numerical thresholds (e.g., a critical acceleration or force-ratio value) used to separate the regimes, (ii) add error bars derived from multiple independent realizations, and (iii) report the number of realizations and the observed variability. These changes will allow readers to assess the robustness of the transition directly from the figures and text. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper reports DEM simulation outcomes for a plate-uplift test under prescribed accelerations, identifies rate-independent and inertial drag regimes from those runs, and constructs a phenomenological elasto-inertial model directly from the observed grain-mobilization processes in the same simulations. No load-bearing step reduces by construction to its own inputs: the model is presented as capturing the measured forces via observed processes rather than as an independent prediction, there are no self-citations invoked as uniqueness theorems, and no parameters are fitted on a subset then renamed as predictions of closely related quantities. The derivation chain remains self-contained against the simulation data and does not exhibit any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Review based on abstract only; no explicit free parameters, axioms, or invented entities are quantified in the provided text. The model is described as introduced to capture simulation results from observed processes.

pith-pipeline@v0.9.0 · 5647 in / 1187 out tokens · 55122 ms · 2026-05-24T22:35:53.949058+00:00 · methodology

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Reference graph

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