Mesoscale Modelling of Confined Split-Hopkinson Pressure Bar Tests on Concrete: Effects of Internal Damage and Strain Rates

Qingchen Liu; Yixiang Gan

arxiv: 2601.11176 · v1 · submitted 2026-01-16 · ❄️ cond-mat.mtrl-sci

Mesoscale Modelling of Confined Split-Hopkinson Pressure Bar Tests on Concrete: Effects of Internal Damage and Strain Rates

Qingchen Liu , Yixiang Gan This is my paper

Pith reviewed 2026-05-16 13:47 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci

keywords concretemesoscale modelingSHPB testsdynamic increase factorstrain rateconfining pressureinternal damagefinite element

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The pith

Mesoscale simulations show loading ramp rate, unlike friction or confining pressure, amplifies the strain-rate sensitivity of concrete's dynamic strength through greater internal damage.

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

This paper deploys finite element mesoscale models of three-phase concrete, with realistic aggregate shapes, to replicate confined Split-Hopkinson Pressure Bar tests. It tracks how loading ramp rate, internal friction, and confining pressure each alter the dynamic increase factor (DIF) while recording the resulting internal strain-rate and damage fields in mortar and aggregate. The results indicate that all three variables raise overall DIF, yet only faster ramp rates intensify the dependence of DIF on strain rate; friction and confinement instead blunt that dependence by producing smaller damage increases in the mortar phase. The work matters for infrastructure design because it supplies a microscopic basis for predicting concrete strength under impact and blast loads that involve varying confinement and loading speeds.

Core claim

Increasing loading ramp rates, internal friction, and confining pressure generally produce higher DIF values, but only a higher loading ramp rate significantly amplifies the strain-rate effect on DIF, shown by larger rises in internal strain rate and damage within both mortar and aggregate phases; higher friction and confining pressure instead weaken the strain-rate effect on DIF because the mortar phase exhibits a less pronounced damage increase with rising strain rate.

What carries the argument

Three-phase mesoscale finite-element representation of concrete (mortar matrix, realistic aggregates, and interfaces) that computes internal strain-rate and local damage distributions to explain DIF changes under varying ramp rates, friction, and confinement.

If this is right

Faster loading ramp rates produce larger DIF gains because they drive higher internal strain rates and more extensive damage in mortar and aggregates.
Higher internal friction or confining pressure raises DIF but reduces its sensitivity to strain rate by limiting the growth of mortar damage.
The mortar phase dominates the weakening of rate sensitivity under increased friction or confinement.
These trends hold across the range of confined SHPB conditions simulated with realistic aggregate shapes.

Where Pith is reading between the lines

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

The same modeling approach could be used to explore even higher strain rates encountered in explosive loading of concrete structures.
Concrete mixes engineered for lower internal friction might exhibit stronger rate sensitivity and therefore better performance under sudden impacts.
Direct comparison of simulated damage fields against X-ray tomography data from confined tests would test the model's internal predictions.

Load-bearing premise

The chosen three-phase mesoscale geometry and material models correctly reproduce the internal strain-rate and damage patterns that control how DIF responds to ramp rate, friction, and confinement.

What would settle it

High-speed imaging or digital-volume-correlation measurements from real SHPB experiments that show mortar damage increasing at the same rate across different ramp rates would falsify the claim that ramp rate amplifies DIF sensitivity via accelerated internal damage.

read the original abstract

The dynamic strength of concrete under complex loading conditions is a key consideration in the design and maintenance of infrastructures. To assess this mechanical property, Split Hopkinson Pressure Bar (SHPB) tests are typically adopted across a wide range of loading and confining conditions. In this study, mesoscale modelling based on the finite element method (FEM) is employed to simulate SHPB tests on three-phase concrete with realistic aggregate shape, in order to investigate the effects of loading ramp rate, internal friction, and confining pressure on the dynamic increase factor (DIF). Microscopic evidence to explain these effects is explored through analysing the distributions of the internal strain rate and local damage. As key results, increasing loading ramp rates, internal friction, and confining pressure can generally leads to higher DIF values. Only a higher loading ramp rate significantly amplifies the strain-rate effect on the DIF, as evidenced by pronounced increases in both internal strain rate and damage in the mortar and aggregate phases. In contrast, higher internal friction and confining pressure weaken the strain-rate effect on the DIF. Both can be attributed to the mortar phase, which shows a less pronounced increase in damage with increasing strain rate. This study enriches the understanding of the dynamic fracture of concrete toward complex loading scenarios.

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.

Desk Editor's Note private letter to a colleague

The simulations show ramp rates boost DIF and its strain-rate sensitivity via higher internal rates and damage, while friction and confinement raise DIF but weaken that sensitivity through muted mortar damage growth.

read the letter

The main takeaway is that these mesoscale FEM runs of confined SHPB tests find higher loading ramp rates increase the dynamic increase factor by producing faster internal strain rates and more damage across mortar and aggregate phases. Higher internal friction and confining pressure also lift overall DIF values, but they reduce the strength of the strain-rate effect on DIF because mortar damage grows less with rate under those conditions. The paper links the trends directly to the phase-specific distributions rather than just reporting bulk curves. That breakdown is the clearest new element. The three-phase model with realistic aggregate shapes is a standard but workable extension of prior mesoscale SHPB work, and the systematic parameter sweeps make the separate influences of ramp rate, friction, and pressure easy to compare. The central limitation is the absence of any reported experimental checks. No match to measured SHPB wave signals, post-test crack patterns, or published DIF values appears in the available summary, and mesh convergence or material parameter sourcing is not discussed. The differential trends could therefore trace back to choices in the rate-dependent damage laws instead of physical mechanisms. This work is for people already running mesoscale simulations of concrete under impact or blast loads. A reader who uses similar FEM setups would get usable parametric insights to test against their own models, though they would need to treat the numbers as provisional until validation data is added. I would send it for peer review. The simulation framework is reproducible and the claims are specific enough that referees can ask for the missing experimental comparisons without starting from scratch.

Referee Report

1 major / 1 minor

Summary. The manuscript employs mesoscale finite-element modeling of confined Split-Hopkinson Pressure Bar tests on three-phase concrete with realistic aggregate shapes. It examines the separate and combined influences of loading ramp rate, internal friction coefficient, and confining pressure on the dynamic increase factor (DIF), using internal strain-rate and damage fields in the mortar and aggregate phases to explain the observed trends. The principal results are that all three parameters raise DIF values, yet only an increase in ramp rate markedly strengthens the strain-rate sensitivity of the DIF, while higher friction and confinement weaken that sensitivity, an effect attributed primarily to the mortar phase.

Significance. If the simulated internal fields are accurate, the study supplies mechanistic explanations for how ramp rate, friction, and confinement modulate strain-rate sensitivity in concrete, which could improve interpretation of SHPB data and constitutive modeling for dynamic infrastructure loading.

major comments (1)

[Abstract] Abstract and results sections: the central claim that only ramp-rate changes significantly amplify the strain-rate effect on DIF (while friction and confinement weaken it) rests on the mesoscale model correctly reproducing internal strain-rate and damage distributions; however, no experimental validation against measured SHPB wave signals, post-test crack patterns, or literature DIF values is reported, leaving open the possibility that the differential trends arise from constitutive choices rather than physical mechanisms.

minor comments (1)

[Abstract] Abstract: grammatical error ('can generally leads to' should read 'can generally lead to').

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive comments and the positive assessment of the study's significance. We address the single major comment below and outline the revisions we will make.

read point-by-point responses

Referee: [Abstract] Abstract and results sections: the central claim that only ramp-rate changes significantly amplify the strain-rate effect on DIF (while friction and confinement weaken it) rests on the mesoscale model correctly reproducing internal strain-rate and damage distributions; however, no experimental validation against measured SHPB wave signals, post-test crack patterns, or literature DIF values is reported, leaving open the possibility that the differential trends arise from constitutive choices rather than physical mechanisms.

Authors: We acknowledge that the manuscript does not present new direct comparisons of simulated SHPB incident/reflected/transmitted waves or post-test crack patterns against experiments performed in this study. The three-phase mesoscale model and its constitutive parameters for mortar (including strain-rate-dependent damage) and aggregates (elastic-brittle) were taken from our prior validated implementations, which reproduced experimental stress-strain responses and damage evolution under both quasi-static and dynamic uniaxial compression. The simulated DIF trends with ramp rate are consistent with the well-documented increase in strain-rate sensitivity of concrete at higher loading rates, while the weakening effect of friction and confinement matches experimental reports on confined SHPB tests where lateral restraint suppresses crack growth. To address the concern explicitly, we will add a dedicated subsection (new Section 3.4) that (i) summarizes the prior experimental validation of the constitutive laws against literature DIF data and crack patterns, (ii) shows that the internal strain-rate and damage fields produce DIF values lying within the scatter of published confined SHPB results, and (iii) includes a brief sensitivity study confirming that the reported differential trends are robust to modest variations in the damage parameters. These additions will make clear that the mechanistic explanations arise from the resolved internal fields rather than from untested constitutive assumptions. revision: partial

Circularity Check

0 steps flagged

No circularity: DIF trends are direct outputs of FEM simulation

full rationale

The paper performs mesoscale finite-element simulations of confined SHPB tests on three-phase concrete with realistic aggregate geometry. The reported effects of ramp rate, friction, and confinement on DIF are obtained by post-processing the computed fields of internal strain rate and damage in mortar and aggregate phases. No target DIF values are used to fit model parameters, no equations reduce the observed trends to inputs by construction, and the abstract and available text contain no self-citations that bear the central claim. The derivation chain is the standard numerical solution of continuum balance laws plus rate-dependent constitutive models; the results are therefore independent of the quantities they are said to explain.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The modeling rests on standard continuum damage mechanics for each concrete phase and on the assumption that mesoscale geometry controls macroscopic DIF trends; no new entities are introduced.

free parameters (2)

internal friction coefficient
Varied parametrically in the simulations; specific values chosen to represent realistic interface behavior but not derived from first principles.
confining pressure levels
Selected discrete values used to explore the parameter space; calibrated or chosen to match typical experimental ranges.

axioms (1)

domain assumption The three-phase (mortar-aggregate-interface) discretization with realistic aggregate shapes sufficiently captures the dominant damage and strain-rate heterogeneity governing DIF.
Invoked throughout the mesoscale modeling description in the abstract.

pith-pipeline@v0.9.0 · 5529 in / 1324 out tokens · 80593 ms · 2026-05-16T13:47:06.873259+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

The CDP model defines compression and tension as the two primary failure mechanisms... strain-rate dependent based on the formulas in FIB-MC2010

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