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arxiv: 2412.04647 · v1 · pith:MDTX3ZQFnew · submitted 2024-12-05 · ⚛️ physics.flu-dyn · physics.comp-ph

Fluid-structure coupled simulation framework for lightweight explosion containment structures under large deformations

Aditya Narkhede , Shafquat Islam , Xingsheng Sun , Kevin Wang This is my paper

Pith reviewed 2026-05-23 08:07 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn physics.comp-ph
keywords fluid-structure interactionexplosion containmentpartitioned couplingRiemann problemsplastic deformationshock wave propagationfinite volume methodfinite element method
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The pith

Coupled fluid-structure simulation shows decoupled blast models overestimate plastic strain by 44 percent.

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

The paper introduces a three-stage framework that couples a finite-volume compressible fluid solver to a finite-element structural solver through a partitioned procedure. It tests the claim that lightweight flexible containment structures experience significant dynamic interaction with explosion gases, an effect ignored by simpler decoupled or pressure-load approximations. In a case study of a thin steel chamber with 250 g TNT, the coupled model produces a 30 percent volume increase from plastic deformation while strains stay below fracture, and it shows that reflected shocks add substantial loading after the first pulse. The comparisons demonstrate that decoupling overestimates plastic strain by 43.75 percent and a first-pulse pressure fit underestimates it by 31.25 percent. This matters for designing affordable single-use containment vessels whose safety depends on accurate deformation predictions.

Core claim

The paper establishes a partitioned coupling procedure that tracks fluid-fluid and fluid-structure interfaces with level-set and embedded-boundary methods and computes interfacial fluxes by locally solving one-dimensional bi-material Riemann problems. Applied to an internal explosion in a thin-walled steel chamber, the procedure captures a 30 percent volume expansion from plastic deformation, shows that later reflected pulses contribute meaningfully to strain, and reveals large errors when fluid-structure interaction is omitted or approximated by a transient pressure load fitted only to the initial shock.

What carries the argument

The partitioned coupling procedure that solves locally constructed one-dimensional bi-material Riemann problems at the fluid-structure interface to transmit mass, momentum, and energy fluxes during large deformations.

If this is right

  • Accurate strain predictions for lightweight explosion chambers require full fluid-structure coupling rather than decoupling or single-pulse pressure approximations.
  • Reflected shock pulses after the initial blast contribute substantially to total plastic deformation.
  • The high compressibility and energy of explosion products produce spatially and temporally varying shock speeds that affect structural response.
  • Containment structures can be sized to remain below fracture while allowing up to 30 percent volume increase under internal blast loading.

Where Pith is reading between the lines

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

  • The same coupling approach could be tested on other high-speed fluid-structure problems such as underwater explosions or rapid gas inflation of flexible membranes.
  • Direct comparison of simulated interface motion against high-speed video of a physical test would check whether the Riemann-problem flux transmission holds during extreme deformation.
  • If the method scales to even lighter materials, designers might need to include coupling from the outset to avoid both overbuilt and underbuilt containment vessels.

Load-bearing premise

The partitioned coupling procedure with locally solved one-dimensional bi-material Riemann problems accurately transmits mass, momentum, and energy fluxes without introducing significant numerical artifacts during large structural deformations.

What would settle it

A physical experiment measuring the final plastic strain in an identical thin-walled steel chamber after a 250 g TNT internal explosion would falsify the central claim if the measured strain does not lie between the decoupled-model overestimate and the pressure-load underestimate reported in the simulations.

Figures

Figures reproduced from arXiv: 2412.04647 by Aditya Narkhede, Kevin Wang, Shafquat Islam, Xingsheng Sun.

Figure 1
Figure 1. Figure 1: A three-stage simulation procedure: The global models (left) and local models applied at material interfaces (right). radially at speed 𝑈CJ. Leveraging spherical symmetry, the governing Euler equations and boundary conditions are given by 𝜕 𝜕𝑡 ⎡ ⎢ ⎢ ⎣ 𝜌 𝜌𝑢r 𝐸 ⎤ ⎥ ⎥ ⎦ + 𝜕 𝜕𝑟 ⎡ ⎢ ⎢ ⎣ 𝜌𝑢r 𝜌𝑢2 r + 𝑝 (𝐸 + 𝑝) 𝑢r ⎤ ⎥ ⎥ ⎦ = − 2 𝑟 ⎡ ⎢ ⎢ ⎣ 𝜌𝑢r 𝜌𝑢2 r (𝐸 + 𝑝) 𝑢r ⎤ ⎥ ⎥ ⎦ , 0 < 𝑟 < 𝑈CJ𝑡, 0 < 𝑡 < 𝑟0 𝑈CJ , (6) 𝑢𝑟 (0, 𝑡) =… view at source ↗
Figure 2
Figure 2. Figure 2: illustrates the simulation setup for this stage. We assume the containment structure has cylindrical symmetry, but not spherical symmetry. Specifically, its cross-section is circular, while the planform has a general closed shape, as depicted in [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The detonation process: Velocity distribution behind the spherical detonation wave, scaled using the detonation wave speed (𝑈CJ) and the front’s radial distance (𝑟 ∗ ). 3.2. Spherical gas expansion To verify the spherical fluid simulation in Stage 2, we conduct four tests with the mass of explosive charge, 𝑚0 = 226.8 g, 453.6 g, 680.4 g, and 907.2 g, respectively. In all the tests, the explosive is assumed… view at source ↗
Figure 4
Figure 4. Figure 4: Spherical expansion of burnt gas: simulation results (𝑚0 = 226.8 g) at (a) 𝑡 = 0 𝑠, (b) 𝑡 = 1.5 × 10−6 𝑠, and (c) 𝑡 = 6.0 × 10−6 𝑠. the equation in [24] for over-pressures from explosions, 𝑝 ( 𝑍 ) = 808 × ( 1 + ( Z 4.5 )2) √( 1 + ( Z 0.048 )2) × ( 1 + ( Z 0.32 )2) × ( 1 + ( Z 1.35 )2) × 105 Pa, (28) where 𝑍 represents a scaled distance ( dimension: [length]∕[mass]1∕3) [PITH_FULL_IMAGE:figures/full_fig_p0… view at source ↗
Figure 5
Figure 5. Figure 5: shows that for all four test cases, the numerical results are in close agreement with values obtained using the empirical model [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Blast loaded plate. (a) Solid mesh with boundary conditions. (b) Pressure pulse obtained from Equation (29). [5]. Specifically, we replicate their Test D77-15, in which a deformable Docol 600 DL plate is exposed to a shock load generated by a 15 bar firing pressure. The plate is discretized using the shell finite elements [8]. The exposed area is of size 300 mm × 300 mm with a plate thickness of 0.8 mm. Th… view at source ↗
Figure 7
Figure 7. Figure 7: Blast loaded plate: mesh sensitivity analysis. which was presented by Friedlander in [21]. We set 𝑝𝑎 = 99.3 kPa, 𝑝𝑟,𝑚𝑎𝑥 = 606.6 kPa, 𝑡𝑎 = 0.64 × 10−3 𝑠, 𝑡𝑑+ = 44.1 s, and 𝑏 = 2.025, according to [5]. The numerical setup along with the pressure time history are shown in [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Blast loaded plate: time-history of mid-point displacement magnitude. In external explosion events, such as the one illustrated here, the initial impact is of utmost significance. Depending on the incident shock pulse, the plate may respond elastically or elasto-plastically. In this case, the shock is strong enough to drive the plate material into the plastic regime, as shown in [PITH_FULL_IMAGE:figures/f… view at source ↗
Figure 9
Figure 9. Figure 9: Blast loaded plate: Predicted effective plastic strain (𝜀P ) at 𝑡 = 40 ms. (a) LS-Dyna. (b) Aero-S. 4. Case study: Lightweight explosion-containment chamber Previous studies on structural responses to internal explosions have often relied on predefined pressure loads, neglecting the dynamic interaction between structural deformation and the internal fluid flow. We hypothesize that this approach may be inad… view at source ↗
Figure 10
Figure 10. Figure 10: depicts the explosion containment structure used in all three simulations. It is made of steel with the following material properties: density 𝜌S = 7.9 × 10−3 g∕mm3 , Young’s modulus 𝐸 = 210 GPa, Poisson’s ratio 𝜈 = 0.3, and yield strength 𝜎Y = 355 MPa. The material is assumed to be perfectly plastic beyond its elastic limit. We employ the well-known 𝐽2 radial return algorithm to model the material’s elas… view at source ↗
Figure 11
Figure 11. Figure 11: Comparison between the two-phase flow model in Stage 2 and the simplified single phase model used for Stage 3. The ambient air outside the containment structure is still modeled using the perfect gas EOS, with 𝛾 = 1.4. Therefore, the fluid domain features two material subdomains separated by a moving fluid-structure interface. 4.2.1. Mesh sensitivity analysis The fluid-structure coupled simulation is cond… view at source ↗
Figure 12
Figure 12. Figure 12: Comparison of results obtained with six pairs of meshes. (a) Maximum structural velocity and fluid pressure impulse at sensor 1. (b) Time-history of structural velocity magnitude at sensor 1. 4.2.2. Results and discussion [PITH_FULL_IMAGE:figures/full_fig_p015_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Snapshots of fluid velocity and pressure fields obtained from the FSI simulation. The velocity vectors are also shown as black arrows [PITH_FULL_IMAGE:figures/full_fig_p016_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Temporal evolution of (a) fluid pressure and (b) structural displacement, recorded at respective sensor locations shown in [PITH_FULL_IMAGE:figures/full_fig_p016_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Total (i.e., internal and kinetic) energy per unit volume within the fluid domain, overlaid with its gradient (magnitude) to track wave propagation. and 3.12 × 103 Pa ⋅ s for the second. This indicates that the second shock pulse has a clear effect on the structure. Figures 16(b) demonstrate that this pulse is strong enough to induce yielding in the structural material, increasing mid￾plane deformations f… view at source ↗
Figure 16
Figure 16. Figure 16: Structural response to the internal explosion. In each subfigure, the displacement field is visualized on the left, while the effective plastic strain is shown on the right. end of the simulation, the maximum effective plastic strain is found to be 16.1% ( [PITH_FULL_IMAGE:figures/full_fig_p018_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Comparison of fluid pressure in FSI, FSD (a), and the curve fit used in SD (b). Figures 18 and 19 compare the structural results obtained from the three simulations. At sensor 1, FSD overpredicts the maximum structural displacement by 30.18%, as the structure is subjected to an overestimated pressure load. For the same reason, it overpredicts the effective plastic strain by 43.75%. The SD simulation under… view at source ↗
Figure 18
Figure 18. Figure 18: Comparison of structural displacement at sensor locations. (a) Sensor 1. (b) Sensor 2 [PITH_FULL_IMAGE:figures/full_fig_p019_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Comparison of effective plastic strain at the end of each simulation (𝑡 = 2 ms). The findings presented in this section align with those of Aune et al., who conducted experimental and numerical studies on the effects of fluid-structure coupling on thin deformable steel plates subjected to shock-generated pressure A. Narkhede et al.: Preprint submitted to Elsevier Page 19 of 23 [PITH_FULL_IMAGE:figures/fu… view at source ↗
read the original abstract

Lightweight, single-use explosion containment structures provide an effective solution for neutralizing rogue explosives, combining affordability with ease of transport. This paper introduces a three-stage simulation framework that captures the distinct physical processes and time scales involved in detonation, shock propagation, and large, plastic structural deformations. The hypothesis is that as the structure becomes lighter and more flexible, its dynamic interaction with the gaseous explosion products becomes increasingly significant. Unlike previous studies that rely on empirical models to approximate pressure loads, this framework employs a partitioned procedure to couple a finite volume compressible fluid dynamics solver with a finite element structural dynamics solver. The level set and embedded boundary methods are utilized to track the fluid-fluid and fluid-structure interfaces. The interfacial mass, momentum, and energy fluxes are computed by locally constructing and solving one-dimensional bi-material Riemann problems. A case study is presented involving a thin-walled steel chamber subjected to an internal explosion of $250~\text{g}$ TNT. The result shows a $30\%$ increase in the chamber volume due to plastic deformation, with its strains remaining below the fracture limit. Although the incident shock pulse carries the highest pressure, the subsequent pulses from wave reflections also contribute significantly to structural deformation. The high energy and compressibility of the explosion products lead to highly nonlinear fluid dynamics, with shock speeds varying across both space and time. Comparisons with simpler simulation methods reveal that decoupling the fluid and structural dynamics overestimates the plastic strain by $43.75\%$, while modeling the fluid dynamics as a transient pressure load fitted to the first shock pulse underestimates the plastic strain by $31.25\%$.

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 / 0 minor

Summary. The manuscript presents a three-stage partitioned fluid-structure interaction framework coupling a finite-volume compressible fluid solver to a finite-element structural solver via level-set/embedded-boundary tracking and local one-dimensional bi-material Riemann problems for interface fluxes. Applied to a thin-walled steel chamber under internal 250 g TNT detonation, it reports 30% volume increase from plastic deformation and claims that decoupling overestimates plastic strain by 43.75% while a first-shock pressure-load approximation underestimates it by 31.25%.

Significance. If the interface treatment is shown to be accurate, the result establishes that full fluid-structure coupling is quantitatively important for lightweight flexible containment structures, where explosion-product compressibility and multiple shock reflections drive nonlinear loading; this would inform design of portable neutralization devices beyond empirical pressure approximations.

major comments (2)
  1. [Abstract] Abstract (paragraph on partitioned procedure and interfacial flux computation): the reported 43.75% and 31.25% plastic-strain differences are load-bearing for the central claim that coupling matters, yet no benchmark verification, manufactured-solution test, or standard FSI benchmark (e.g., shock-tube flexible plate) is provided to confirm that the 1D bi-material Riemann solves transmit correct mass/momentum/energy fluxes without O(1) artifacts once wall velocity becomes comparable to post-shock gas velocity during 30% volume change.
  2. [Abstract] Abstract (case-study results): quantitative strain differences are presented without mesh-convergence data, material-model parameters (plasticity law, yield surface), or error bars, leaving the 30% volume-increase and percentage-difference claims without demonstrated numerical reliability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which highlight important aspects of verification and numerical reliability. We address each major comment below and will revise the manuscript accordingly to strengthen the presentation of the partitioned FSI framework and case-study results.

read point-by-point responses

  1. Referee: [Abstract] Abstract (paragraph on partitioned procedure and interfacial flux computation): the reported 43.75% and 31.25% plastic-strain differences are load-bearing for the central claim that coupling matters, yet no benchmark verification, manufactured-solution test, or standard FSI benchmark (e.g., shock-tube flexible plate) is provided to confirm that the 1D bi-material Riemann solves transmit correct mass/momentum/energy fluxes without O(1) artifacts once wall velocity becomes comparable to post-shock gas velocity during 30% volume change.

    Authors: We acknowledge that the current manuscript does not include dedicated benchmark verification for the interfacial flux computation specifically under conditions where structural wall velocities become comparable to post-shock gas velocities during large (30%) volume changes. The 1D bi-material Riemann solver follows established embedded-boundary techniques, but explicit tests confirming absence of O(1) artifacts in this regime are absent. To directly address this, we will add a verification subsection in the revised manuscript that applies the method to a standard FSI benchmark (shock-tube flexible plate) and reports flux accuracy metrics. revision: yes

  2. Referee: [Abstract] Abstract (case-study results): quantitative strain differences are presented without mesh-convergence data, material-model parameters (plasticity law, yield surface), or error bars, leaving the 30% volume-increase and percentage-difference claims without demonstrated numerical reliability.

    Authors: The referee is correct that the quantitative claims in the case study lack supporting mesh-convergence data, explicit material-model parameters, and error bars. While the full text describes the overall setup, these elements are not presented for the reported 30% volume increase or the 43.75%/31.25% strain differences. In the revision we will incorporate mesh-convergence studies for both solvers, detail the plasticity law and yield-surface parameters employed for the steel, and add error estimates or sensitivity results to substantiate the numerical reliability of the findings. revision: yes

Circularity Check

0 steps flagged

No significant circularity; comparisons rest on independent simulations

full rationale

The paper presents a partitioned FSI framework (level-set/embedded-boundary tracking plus local 1D bi-material Riemann solves) and reports plastic-strain differences versus two separately described simpler methods (fully decoupled dynamics and a transient pressure load fitted only to the first shock pulse). No equation or procedure in the provided text reduces the reported 43.75% or 31.25% differences to quantities that are fitted or defined inside the coupled simulation itself. No self-citation chain, uniqueness theorem, or ansatz smuggling is invoked to justify the central numerical results. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The framework rests on standard conservation laws and numerical interface treatments without introducing new free parameters, axioms beyond classical mechanics, or invented physical entities.

axioms (2)
  • standard math Conservation of mass, momentum, and energy govern both the compressible fluid and the elastoplastic solid.
    Invoked implicitly as the basis for the finite-volume and finite-element solvers.
  • domain assumption The level-set and embedded-boundary methods correctly represent moving fluid-fluid and fluid-structure interfaces.
    Stated as the tracking technique used in the partitioned procedure.

pith-pipeline@v0.9.0 · 5828 in / 1455 out tokens · 34911 ms · 2026-05-23T08:07:02.444356+00:00 · methodology

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