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REVIEW 5 major objections 5 minor 57 references

Multiscale modelling of thermally stressed superelastic polyimide

T0 review · 5 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read A molecular-dynamics-fed continuum model predicts polyimide insulation holds thermal stress below 5000 Pa, versus 480 MPa uninsulated.

desk verdict A salvageable multiscale workflow with sound thermal validation, but the headline 480 MPa insulation claim comes from an elastic calculation that contradicts the paper's own stated perfect-plasticity assumption. read the letter →

arxiv 2504.20123 v1 pith:ILJK777J submitted 2025-04-28 cond-mat.mtrl-sci cs.CE

Jerome Samuel S , Puneet Kumar Patra , Md Rushdie Ibne Islam This is my paper · ORCID
classification cond-mat.mtrl-scics.CE
keywords multiscalemodellingmoleculardynamicssmoothedparticlehydrodynamicsthermo-mechanicalcouplingsuperelasticpolyimidethermalstressinsulationKapton
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

Thermal stress originates when atoms shift their equilibrium positions as temperature changes, so this paper tries to capture it by feeding atomistic molecular dynamics (MD) results into a continuum smoothed particle hydrodynamics (SPH) simulation. The MD cell, a cross-linked Kapton-like superelastic polyimide, is equilibrated and mechanically and thermally probed to yield elastic modulus, bulk modulus, equation of state, thermal conductivity, and thermal expansion coefficient. These numbers are used unchanged in a thermo-mechanically coupled SPH solver, which is checked against analytical heat-transfer and thermal-stress benchmarks. Applied to a 0.5 m aluminium plate with one side at 500 K and the other at 50 K, the model reports that a 0.05 m superelastic polyimide layer keeps the left-end thermal stress below 5000 Pa at 50 s, while the uninsulated plate reaches about 480 MPa. The point of the paper is that this property-to-prediction chain works without macroscopic fitting, making it useful for materials whose macroscale thermal data do not yet exist.

What carries the argument

The load-bearing object is the sequential MD-to-SPH bridge. The MD stage builds a 202,752-atom supercell of cross-linked polyimide, equilibrates it to a converged density, and extracts properties from production runs: uniaxial stretching with the averaged virial stress fit to a quadratic curve, giving a strain-dependent modulus and a zero-strain value of 6.39 GPa; hydrostatic compression for the bulk modulus and the linear equation of state; reverse non-equilibrium MD for thermal conductivity; and NPT thermal-expansion runs for the coefficient of thermal expansion. The SPH stage then solves the continuity, momentum, internal-energy, and coupled heat equations using these MD numbers, with artificial viscosity and a tensile-instability correction for stability. The coupling term that carries thermal stress is $3K\alpha(T-T_0)$ inside the Cauchy stress, so the temperature field directly produces stress, while the equation of state closes the mechanical response.

What would settle it

Measure the thermal conductivity and elastic modulus of the superelastic polyimide of ref. [25] at room temperature using laser-flash and micro-tensile tests; if they differ significantly from 0.32 W/mK and 6.39 GPa, rerun the SPH insulation test with the measured values and check whether the left-end thermal stress stays below 5000 Pa.

Watch

Extended reading notes

Core claim

The central claim, as the authors present it, is that a sequential multiscale chain can carry coupled thermo-mechanical behaviour from atoms to a structural part. Constitutive inputs — $E=6.39$ GPa, $K=3.8$ GPa, $\kappa=0.32$ W/mK, $\alpha=4.723\times10^{-5}$ /K, density $1.36$ g/cm$^3$, and a linear equation of state $p=K(\rho/\rho_0-1)$ — are obtained from MD simulations of cross-linked polyimide, then used directly in the SPH stress update $\sigma^{\alpha\beta}=S^{\alpha\beta}-[p_r+3K\alpha(T-T_0)]\delta^{\alpha\beta}$ and in the coupled heat equation. The model matches analytical solutions for transient heat conduction in one and two dimensions and for thermally induced deformation. In the application case, it predicts that a 0.05 m superelastic polyimide coating reduces the left-end thermal stress of an aluminium plate from roughly 480 MPa to below 5000 Pa at 50 s while strongly slowing the temperature field. The authors read these distributions as demonstrating the material's superior insulating capability for spacecraft-type thermal protection.

Load-bearing premise

The quantitative result depends on the assumption that the elastic and thermal constants measured on the dense, fast-strained atomic cell represent the actual low-density, slowly loaded superelastic polyimide aerogel, because the SPH insulation prediction uses those numbers directly.

Editorial extensions

If this is right

  • If the central claim is right, thermo-mechanical input sets for SPH can be generated purely from MD, removing the need for macroscale property tables for new polyimide variants.
  • The validated coupled SPH solver reproduces the analytical one- and two-dimensional heat-transfer and thermal-stress solutions, so the same code can be applied to other geometries and boundary conditions without revalidation.
  • In the GEO-like thermal-shock scenario, the model predicts the uninsulated aluminium plate's left-end thermal stress reaches about 480 MPa at 50 s, while the insulated plate stays below 5000 Pa, a reduction of roughly five orders of magnitude.
  • Because the coupled temperature equation carries the $3K\alpha(T-T_0)$ term, the model quantifies thermal stress directly from the temperature field, making it a design tool for thermal-protection layers.
  • The framework opens a route to modelling thermal-stress relief in spacecraft components before experimental property tables exist for a new polyimide variant.

Reading between the lines

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

  • An implication the authors leave implicit: the MD cell equilibrates to 1.36 g/cm$^3$, close to dense Kapton, while the cited superelastic polyimide is a low-density aerogel; rerunning the SPH case with aerogel-appropriate density and conductivity would show how much of the stress reduction is material-specific rather than an artefact of the dense model.
  • A testable extension: extract the elastic modulus at lower, quasi-static strain rates or from stress relaxation, feed that value into the SPH run, and compare the resulting 5000 Pa figure; this would bracket how sensitive the insulation prediction is to the extreme strain rate used in MD extraction.
  • The paper's mass-scaling of aluminium by a factor of 100 changes the mechanical time scale; a useful check is to repeat the 50 s simulation with smaller scaling factors and confirm that the left-end thermal stress remains below 5000 Pa.
  • The same MD-to-SPH pipeline could be applied to cyclic thermal loading, where the paper's single 50 s snapshot would miss ratcheting or fatigue effects.
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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

5 major / 5 minor

Summary. The paper develops a sequential multiscale model in which molecular dynamics (MD) simulations of a cross-linked Kapton-like polyimide supply elastic, bulk, thermal-conductivity, and thermal-expansion properties to a smoothed particle hydrodynamics (SPH) thermo-mechanical code. The SPH model is validated against analytic solutions for one- and two-dimensional transient heat conduction and for a two-dimensional thermoelastic deformation problem. The authors then simulate the 50 s thermal response of an aluminium plate with and without a superelastic polyimide insulation layer, reporting a dramatic reduction in thermal stress, strain, and temperature when the polyimide is present. The quantified claim is that the uninsulated plate develops about 480 MPa of left-end thermal stress, while the insulated plate remains below 5000 Pa.

Significance. If the method and its application are sound, the paper offers a useful template for passing MD-derived constitutive and transport properties into a mesh-free continuum solver for a practically relevant space-insulation material. The benchmark heat-conduction tests genuinely match analytic solutions, and the MD-to-SPH property transfer is forward rather than fitted, which are strengths. The qualitative conclusion that a low-conductivity polyimide layer reduces thermal stress is plausible and likely robust. However, the quantitative conclusions are weakened by an unimplemented plasticity assumption and by unverified transferability of dense-polymer MD properties to the low-density superelastic polyimide aerogel cited as the target material.

major comments (5)
  1. [Sec. 4.4 vs. Sec. 3] The paper states that the aluminium plate response is assumed to be perfectly plastic and lists a yield stress of sigma_Y = 30 MPa, but the constitutive update in Sec. 3 is purely elastic: Eq. (15) defines the Cauchy stress from a linear equation of state plus a thermal term, and Eq. (16) updates the deviatoric stress with a Jaumann rate. No yield function, flow rule, plastic multiplier, or return mapping appears anywhere, and sigma_Y is not used in any equation. The reported left-end thermal stress of about 480 MPa in the uninsulated plate therefore comes from an elastic calculation that exceeds the declared yield stress by more than an order of magnitude. The authors must either implement an actual elastic-perfectly-plastic update and rerun the simulation, or explicitly present the 480 MPa value as an elastic upper-bound calculation and remove the perfectly plastic assumption from Sec. 4.4 and the conclusions.
  2. [Sec. 2.1, 2.2, 4.4] The MD cell is a dense cross-linked Kapton-like structure with converged density 1.36 g/cm3, and the paper uses its properties directly in the insulation simulation of Sec. 4.4. The cited superelastic polyimide of ref. [25] is a low-density aerogel, not a dense Kapton film. No comparison is made to the density, morphology, or stiffness of the actual aerogel, and no discussion is given of how a dense MD cell can represent a high-porosity material. This transferability question is load-bearing because the quantitative stress-reduction claim depends on the values E = 6.39 GPa, kappa = 0.32 W/mK, alpha = 4.723e-5 /K, and density = 1360 kg/m3. The authors should justify this mapping or repeat the property extraction on a representative low-density structure.
  3. [Sec. 2.2 vs. Sec. 3] The text states that the strain-dependent modulus obtained from the quadratic fit in Eq. (5) is used to model nonlinear behaviour in SPH, but the SPH formulation in Sec. 3 uses a constant Young's modulus E = 6.39 GPa and a constant shear modulus in Eq. (16), with no strain-dependent stiffness appearing anywhere in the continuum equations. This is a mismatch between the claimed nonlinear transfer and the implemented constitutive model. The authors should either incorporate the nonlinear stress-strain relation into the SPH update or clarify that the SPH model is linear elastic with properties extracted only from the zero-strain limit of the MD data.
  4. [Sec. 2.2] The elastic properties are extracted from production runs of 100,000 steps at 0.1 fs, i.e., 10 ps, at an engineering strain rate of 0.000005/fs (5 x 10^9 /s), up to 50% strain. This is an extremely high rate compared with the quasi-static superelastic response relevant to the insulation scenario. No rate-convergence study, temperature-control check, or comparison with experimental or literature values for superelastic polyimide is provided, so the reported E = 6.39 GPa may reflect viscoelastic or rate-dependent contributions rather than the effective quasi-static stiffness. The authors should demonstrate rate insensitivity or otherwise bound the effect of strain rate on the values passed to the SPH model.
  5. [Sec. 4.4] The calculation of thermal stress in Sec. 4.4 uses the relation pr = 3K alpha (T - T0), while the SPH stress in Eq. (15) is sigma = S - [pr + 3K alpha (T - T0)] delta. The relationship between the plotted 'thermal stress' and the full Cauchy stress used in the momentum equation should be stated explicitly; as written, it is unclear whether the reported 480 MPa value is the full stress, the thermal part only, or the hydrostatic part.
minor comments (5)
  1. [Sec. 4.1] The sentence introducing the 1D transient heat transfer case contains an empty citation, '[]', which should be filled or removed.
  2. [Throughout] There are numerous typographical errors, including 'Direc-delta' (twice in Sec. 3), 'special derivatives', 'occuring', 'unwated deformations', 'e ffect', and 'Aluminium-superelastic polyimide film' in the conclusions. A thorough language edit is needed.
  3. [Sec. 2.3] The description of the thermal expansion calculation is ambiguous: the text says the box is equilibrated to final temperatures 'ranging from 10K to 100K', which likely means temperature increments relative to T0 = 300 K, not absolute temperatures of 10-100 K. Please clarify the actual temperature range and how L(T) in Eq. (10) is used.
  4. [Sec. 2.3 / Table 1] The Poisson ratio (0.218) is listed in Table 1 but its derivation from MD is never described. Please state how it was obtained.
  5. [Sec. 3, Eq. (30)] The thermal stability criterion is written with both h and Delta x; the relationship between the smoothing length and the initial particle spacing should be defined clearly, since the numerical value 1.44 assumes a particular relation between h and Delta x.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: MD-derived constants are inputs to a forward SPH simulation, benchmarks are independent, and no fitted output is renamed as a prediction.

full rationale

The derivation chain is forward and self-contained. Molecular dynamics runs generate stress-strain data, bulk modulus, thermal conductivity, and thermal expansion coefficient through standard methods (virial stress, Muller-Plathe rNEMD, NPT length variation); the quadratic and linear fits in Eqs. (5), (6), and (10) are calibrations of MD data, not fits to any SPH result. These MD-derived constants are then supplied as inputs to the SPH constitutive model in Eqs. (15) and (16), and the insulation problem in Section 4.4 is an initial/boundary-value simulation whose output (thermal stress, strain, temperature) is computed, not fitted. The SPH solver is validated against independent analytical benchmarks for 1D and 2D transient heat transfer and for 2D thermal deformation, so the pipeline has external checks. The self-citations to the authors' prior MD-SPH framework and equivalence studies are methodological references and are not load-bearing as a uniqueness argument or a smuggled ansatz. The reviewer-identified issue that the declared perfectly plastic aluminum response is not implemented in the purely elastic constitutive update is a modeling-correctness concern, not circularity, because the reported 480 MPa stress is still a forward output of the stated equations rather than a quantity forced by a fitted parameter. Overall, no prediction in the paper reduces by construction to its own input.

Assumptions & free parameters 11 free parameters · 7 assumptions · 0 invented entities

The central claim rests on a chain of MD-extracted material constants and on numerical choices (mass scaling, artificial viscosity). The most consequential assumptions are the representativeness of the dense MD cell for a low-density aerogel material and the unmodeled plasticity of aluminum. No new physical entities are introduced.

free parameters (11)
  • Elastic modulus E = 6.39 GPa
    Derived as the zero-strain slope of the quadratic fit to virial stress vs strain from 8 MD production runs at 5e-6/fs strain rate; used as a constant in SPH (Table 1).
  • Quadratic stress-strain coefficients = A=-66.7 GPa, B=6.39 GPa, C=-0.0128 GPa
    Best-fit coefficients to averaged MD virial stress (Eq. 5); the nonlinearity is noted but only E enters SPH.
  • Bulk modulus K = 3.8 GPa
    Linear fit of hydrostatic pressure vs volumetric strain (Eq. 6) from 8 MD runs; used in SPH equation of state and thermal stress term.
  • Poisson ratio = 0.218
    Reported in Table 1 without a described MD procedure; needed to compute Lame/shear parameters for SPH.
  • Thermal conductivity = 0.32 W/mK
    From Muller-Plathe rNEMD with imposed 100 K hot/cold difference; convergence study referenced but not shown.
  • Coefficient of thermal expansion = 4.723e-5 /K
    Secant coefficient from quadratic L(T) fit (Eqs. 10-11); the reported value is not tied to a specified temperature T.
  • L(T) quadratic coefficients = c2=5.491e-6 A/K^2, c1=2.5e-3 A/K, c0=131.8 A
    Empirical fit to MD box length vs temperature; used only via the CTE value.
  • Density = 1.36 g/cm3
    Converged MD density after NPT equilibration; input to SPH. Differs markedly from the aerogel density of ref [25].
  • Specific heat capacity of polyimide = 1090 J/kgK
    Listed in Sec. 4.4 for SPH, but no MD or experimental source is given.
  • Mass scaling factor = 100
    Aluminum density and thermal conductivity are multiplied by 100 to enlarge the timestep while keeping thermal diffusivity constant; no unsacled verification is shown.
  • Artificial viscosity and tensile parameters = beta1=beta2=0.5; gamma not specified
    Numerical stabilization coefficients chosen by hand; they affect stress oscillations in the 2D thermo-mechanical benchmark.
assumptions (7)
  • domain assumption Cauchy-Born rule maps affine deformation to atom positions during MD stretching.
    Invoked in Sec. 2.2 ('coordinates of all atoms are remapped accordingly') to relate continuum strain to MD geometry.
  • domain assumption Virial stress computed from MD equals the continuum Cauchy stress.
    Eq. (4) uses virial stress as the stress measure for modulus extraction; standard but an assumption for the constitutive fit.
  • domain assumption ReaxFF force field parameters describe the cross-linked polyimide accurately.
    No force field parameters or validation against experiments are given; all mechanical/thermal properties inherit this.
  • domain assumption The dense MD cell represents the superelastic polyimide material.
    Sec. 2.1 builds a dense cross-linked Kapton network, while the cited superelastic polyimide (ref [25]) is a low-density aerogel.
  • domain assumption Mass scaling preserves the thermal-mechanical response of the aluminum plate.
    Sec. 4.4 scales density and conductivity by 100; no baseline comparison is provided.
  • standard math Linear thermoelasticity with Fourier heat conduction governs the SPH continuum.
    Sec. 3 uses Eqs. (14)-(27), a standard coupled linear thermoelastic SPH formulation.
  • standard math The analytical heat-conduction solutions used for validation are correct for the stated boundary conditions.
    Sec. 4.1-4.2 use Eqs. (32) and (35), standard series solutions.

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Cite this review

Pith. "Pith review of Multiscale modelling of thermally stressed superelastic polyimide." pith.science (2026). https://pith.science/paper/ILJK777J

@misc{pith2026250420123,
  author       = {Pith},
  title        = {Pith review of: Multiscale modelling of thermally stressed superelastic polyimide},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ILJK777J}},
  note         = {Machine review of arXiv:2504.20123}
}
read the original abstract

Many thermo-mechanical processes, such as thermal expansion and stress relaxation, originate at the atomistic scale. We develop a sequential multiscale approach to study thermally stressed superelastic polyimide to explore these effects. The continuum-scale smoothed particle hydrodynamics (SPH) model is coupled with atomistic molecular dynamics (MD) through constitutive modelling, where thermo-mechanical properties and equations of state are derived from MD simulations. The results are verified through benchmark problems of heat transfer. Finally, we analyse the insulating capabilities of superelastic polyimide by simulating the thermal response of an aluminium plate. The result shows a considerable reduction in the thermal stress, strain and temperature field development in the aluminium plate when superelastic polyimide is used as an insulator. The present work demonstrates the effectiveness of the multi-scale method in capturing thermo-mechanical interactions in superelastic polyimide.

Figures

Figures reproduced from arXiv: 2504.20123 by the authors.

Figure 1
Figure 1. (a) Ball and stick figure of the molecular structure of Pristine Kapton, (b) the central crosslinker necessary [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Equilibration of superelastic polyimide chain. (a) Density convergence plot. (b) Converged structure [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Instantaneous variation of normal stress, [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (13 more)
Figure 4
Figure 4. Figure 4: (Left) Hydrostatic pressure fluctuations during bulk modulus calculations, obtained from eight repeated [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: Plot illustrating the variation of the simulation box length (L) with temperature (T), along with linear and [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: Initial and boundary conditions for 1D transient heat transfer example [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]
Figure 7
Figure 7. Figure 7: Temperature plot comparing SPH and analytical results at time 10s, 100s, 300s and 500s for 1D transient [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]
Figure 8
Figure 8. Figure 8: Initial and boundary conditions for the 2D transient heat transfer example [PITH_FULL_IMAGE:figures/full_fig_p014_8.png]
Figure 9
Figure 9. Figure 9: Temperature and thermal stress plots comparing SPH and analytical results at times 10s, 100s, 300s and [PITH_FULL_IMAGE:figures/full_fig_p014_9.png]
Figure 10
Figure 10. Figure 10: Temperature and thermal stress plots comparing analytical results with SPH results. The SPH results [PITH_FULL_IMAGE:figures/full_fig_p015_10.png]
Figure 11
Figure 11. Figure 11: The nearly identical displacement (in meters) of SPH particles at 0.9s (Top left), 3.9s (Top right), and 5.6s [PITH_FULL_IMAGE:figures/full_fig_p016_11.png]
Figure 12
Figure 12. Figure 12: Displacement profiles of SPH particles along the central horizontal axis at various time steps, compared [PITH_FULL_IMAGE:figures/full_fig_p017_12.png]
Figure 14
Figure 14. Figure 14: Temperature distribution results for an uninsulated aluminium plate (Left) and an aluminium plate [PITH_FULL_IMAGE:figures/full_fig_p019_14.png]
Figure 15
Figure 15. Figure 15: Thermal strain distribution for an uninsulated aluminium plate (Left) and an aluminium plate insulated [PITH_FULL_IMAGE:figures/full_fig_p020_15.png]
Figure 16
Figure 16. Figure 16: Thermal stress distribution (in Pa) for an uninsulated aluminium plate (Left) and an aluminium plate [PITH_FULL_IMAGE:figures/full_fig_p021_16.png]
Figure 17
Figure 17. Figure 17: Temperature plot comparing the results of thermomechanical SPH (TMC-SPH) and the finite di [PITH_FULL_IMAGE:figures/full_fig_p021_17.png]

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Reference graph

Works this paper leans on

57 extracted references · 54 canonical work pages

  1. [25]

    Cheng, X

    Y . Cheng, X. Zhang, Y . Qin, P. Dong, W. Yao, J. Matz, P. M. Ajayan, J. Shen, M. Ye, Super-elasticity at 4 k of covalently crosslinked polyimide aerogels with negative poisson’s ratio, Nature communications 12 (1) (2021) 4092

    work page 2021

  2. [1]

    Y . Gong, Y . Kou, Q. Yue, X. Zhuang, F. Qin, Q. Wang, T. Rabczuk, The application of thermomechanically coupled phase-field models in electronic packaging interconnect structures, International Communications in Heat and Mass Transfer 159 (2024) 108033

    work page 2024

  3. [2]

    Patel, K

    T. Patel, K. Co, R. Hebert, S. Alpay, Ferroelectric films on metal substrates: The role of thermal expansion mismatch on dielectric, piezoelectric, and pyroelectric properties, Journal of Applied Physics 126 (13) (2019)

    work page 2019

  4. [3]

    Pantousa, K

    D. Pantousa, K. Tzaros, M.-A. Kefaki, Thermal buckling behaviour of unstiffened and stiffened fixed-roof tanks under non-uniform heating, Journal of Constructional Steel Research 143 (2018) 162–179

    work page 2018

  5. [4]

    J.-A. J. Wang, R. C. Singleterry Jr, R. J. Ellis, H. T. Hunter, Radiation e ffects on spacecraft structural materials, in: Proceedings of International Conference on Advanced Nuclear Power Plants, American Nuclear Society La Grange Park, IL, 2002. 22

    work page 2002

  6. [5]

    Dever, B

    J. Dever, B. Banks, K. de Groh, S. Miller, Degradation of spacecraft materials, in: Handbook of environmental degradation of materials, Elsevier, 2005, pp. 465–501

    work page 2005

  7. [6]

    A. M. Abd El-Hameed, Radiation e ffects on composite materials used in space systems: A review, NRIAG Journal of Astronomy and Geophysics 11 (1) (2022) 313–324

    work page 2022

  8. [7]

    Boley, J

    B. Boley, J. Weiner, Theory of thermal stresses. mineola (1997)

    work page 1997

Show all 57 references
  1. [8]

    Nowacki, Thermoelasticity, Elsevier, 2013

    W. Nowacki, Thermoelasticity, Elsevier, 2013

    2013

  2. [9]

    R. B. Hetnarski, M. R. Eslami, G. Gladwell, Thermal stresses: advanced theory and applications, V ol. 41, Springer, 2009

    2009

  3. [10]

    Y . Lee, X. Zhao, J. Reddy, Postbuckling analysis of functionally graded plates subject to compressive and thermal loads, Computer Methods in Applied Mechanics and Engineering 199 (25-28) (2010) 1645–1653

    2010

  4. [11]

    G. Lu, E. Kaxiras, An overview of multiscale simulations of materials, arXiv preprint cond-mat/0401073 (2004)

    2004 arXiv

  5. [12]

    Y . Lee, C. Basaran, A multiscale modeling technique for bridging molecular dynamics with finite element method, Journal of Computational Physics 253 (2013) 64–85

    2013

  6. [13]

    Yamakov, E

    V . Yamakov, E. Saether, E. H. Glaessgen, A new concurrent multiscale methodology for coupling molecular dynamics and finite element analyses, Tech. rep. (2008)

    2008

  7. [14]

    Y . Gu, L. Zhang, A concurrent multiscale method based on the meshfree method and molecular dynamics analysis, Multiscale Modeling & Simulation 5 (4) (2006) 1128–1155

    2006

  8. [15]

    Q. Wang, T. Ng, H. Li, K. Lam, Multiscale simulation of coupled length-scales via meshless method and molec- ular dynamics, Mechanics of Advanced Materials and Structures 16 (1) (2009) 1–11

    2009

  9. [16]

    S. Li, N. Sheng, On multiscale non-equilibrium molecular dynamics simulations, International Journal for Nu- merical Methods in Engineering 83 (8-9) (2010) 998–1038

    2010

  10. [17]

    Bhattacharyya, M

    S. Bhattacharyya, M. R. I. Islam, P. K. Patra, Multiscale modelling of fracture in graphene sheets, Theoretical and Applied Fracture Mechanics 122 (2022) 103617

    2022

  11. [18]

    J. J. Monaghan, R. A. Gingold, Shock simulation by the particle method sph, Journal of computational physics 52 (2) (1983) 374–389

    1983

  12. [19]

    J. J. Monaghan, Sph without a tensile instability, Journal of computational physics 159 (2) (2000) 290–311

    2000

  13. [20]

    J. Chen, J. Beraun, T. Carney, A corrective smoothed particle method for boundary value problems in heat conduction, International Journal for Numerical Methods in Engineering 46 (2) (1999) 231–252

    1999

  14. [21]

    W. G. Hoover, Smooth particle applied mechanics: the state of the art (2006)

    2006

  15. [22]

    M. R. I. Islam, K. V . Ganesh, P. K. Patra, On the equivalence of eulerian smoothed particle hydrodynamics, total lagrangian smoothed particle hydrodynamics and molecular dynamics simulations for solids, Computer Methods in Applied Mechanics and Engineering 391 (2022) 114591

    2022

  16. [23]

    K. V . Ganesh, P. K. Patra, K. P. Travis, Multiscale modeling of impact through molecular dynamics and smooth particle hydrodynamics, Physica A: Statistical Mechanics and its Applications 593 (2022) 126903

    2022

  17. [24]

    K. V . Ganesh, M. R. I. Islam, P. K. Patra, K. P. Travis, A pseudo-spring based sph framework for studying fatigue crack propagation, International Journal of Fatigue 162 (2022) 106986

    2022

  18. [26]

    Rahnamoun, A

    A. Rahnamoun, A. Van Duin, Reactive molecular dynamics simulation on the disintegration of kapton, poss polyimide, amorphous silica, and teflon during atomic oxygen impact using the reax ff reactive force-field method, The Journal of Physical Chemistry A 118 (15) (2014) 2780–2787

    2014

  19. [27]

    K. Min, A. R. Rammohan, H. S. Lee, J. Shin, S. H. Lee, S. Goyal, H. Park, J. C. Mauro, R. Stewart, V . Botu, et al., Computational approaches for investigating interfacial adhesion phenomena of polyimide on silica glass, Scientific reports 7 (1) (2017) 10475

    2017

  20. [28]

    Rahnamoun, D

    A. Rahnamoun, D. P. Engelhart, S. Humagain, H. Koerner, E. Plis, W. J. Kennedy, R. Cooper, S. G. Greenbaum, R. Hoffmann, A. C. van Duin, Chemical dynamics characteristics of kapton polyimide damaged by electron beam irradiation, Polymer 176 (2019) 135–145

    2019

  21. [29]

    Marque, S

    G. Marque, S. Neyertz, J. Verdu, V . Prunier, D. Brown, Molecular dynamics simulation study of water in amor- phous kapton, Macromolecules 41 (9) (2008) 3349–3362

    2008

  22. [30]

    X. Lu, X. Wang, Q. Li, X. Huang, S. Han, G. Wang, A reax ff-based molecular dynamics study of the pyrolysis 23 mechanism of polyimide, Polymer Degradation and Stability 114 (2015) 72–80

    2015

  23. [31]

    A. P. Thompson, H. M. Aktulga, R. Berger, D. S. Bolintineanu, W. M. Brown, P. S. Crozier, P. J. in ’t Veld, A. Kohlmeyer, S. G. Moore, T. D. Nguyen, R. Shan, M. J. Stevens, J. Tranchida, C. Trott, S. J. Plimpton, LAMMPS - a flexible simulation tool for particle-based materials...

    2022

  24. [32]

    Nos ´e, A unified formulation of the constant temperature molecular dynamics methods, The Journal of chem- ical physics 81 (1) (1984) 511–519

    S. Nos ´e, A unified formulation of the constant temperature molecular dynamics methods, The Journal of chem- ical physics 81 (1) (1984) 511–519

    1984

  25. [33]

    W. G. Hoover, Canonical dynamics: Equilibrium phase-space distributions, Physical review A 31 (3) (1985) 1695

    1985

  26. [34]

    G. J. Martyna, D. J. Tobias, M. L. Klein, Constant pressure molecular dynamics algorithms, J. chem. Phys 101 (4177) (1994) 10–1063

    1994

  27. [35]

    A. C. Van Duin, S. Dasgupta, F. Lorant, W. A. Goddard, Reax ff: a reactive force field for hydrocarbons, The Journal of Physical Chemistry A 105 (41) (2001) 9396–9409

    2001

  28. [36]

    Heinz, T.-J

    H. Heinz, T.-J. Lin, R. Kishore Mishra, F. S. Emami, Thermodynamically consistent force fields for the assembly of inorganic, organic, and biological nanostructures: the interface force field, Langmuir 29 (6) (2013) 1754– 1765

    2013

  29. [37]

    T. P. Senftle, S. Hong, M. M. Islam, S. B. Kylasa, Y . Zheng, Y . K. Shin, C. Junkermeier, R. Engel-Herbert, M. J. Janik, H. M. Aktulga, et al., The reaxff reactive force-field: development, applications and future directions, npj Computational Materials 2 (1) (2016) 1–14

    2016

  30. [38]

    W. Zhao, Q. Wei, C. Huang, Y . Zhu, N. Hu, Dependence of incidence angle and flux density in the damage effect of atomic oxygen on kapton film, Polymers 14 (24) (2022) 5444

    2022

  31. [39]

    M ¨uller-Plathe, A simple nonequilibrium molecular dynamics method for calculating the thermal conductivity, The Journal of chemical physics 106 (14) (1997) 6082–6085

    F. M ¨uller-Plathe, A simple nonequilibrium molecular dynamics method for calculating the thermal conductivity, The Journal of chemical physics 106 (14) (1997) 6082–6085

    1997

  32. [40]

    H. N. Pishkenari, E. Mohagheghian, A. Rasouli, Molecular dynamics study of the thermal expansion coe fficient of silicon, Physics Letters A 380 (48) (2016) 4039–4043

    2016

  33. [41]

    H. Hu, P. Eberhard, Thermomechanically coupled conduction mode laser welding simulations using smoothed particle hydrodynamics, Computational Particle Mechanics 4 (2017) 473–486

    2017

  34. [42]

    R. A. Gingold, J. J. Monaghan, Smoothed particle hydrodynamics: theory and application to non-spherical stars, Monthly notices of the royal astronomical society 181 (3) (1977) 375–389

    1977

  35. [43]

    J. J. Monaghan, Simulating free surface flows with sph, Journal of computational physics 110 (2) (1994) 399– 406

    1994

  36. [44]

    L. D. Libersky, A. G. Petschek, T. C. Carney, J. R. Hipp, F. A. Allahdadi, High strain lagrangian hydrodynamics: a three-dimensional sph code for dynamic material response, Journal of computational physics 109 (1) (1993) 67–75

    1993

  37. [45]

    M. Liu, G. Liu, Smoothed particle hydrodynamics (sph): an overview and recent developments, Archives of computational methods in engineering 17 (2010) 25–76

    2010

  38. [46]

    G.-R. Liu, M. B. Liu, Smoothed particle hydrodynamics: a meshfree particle method, World scientific, 2003

    2003

  39. [47]

    Eringen, Mechanics of continua

    A. Eringen, Mechanics of continua. jhon wiley and sons, New York (1967)

    1967

  40. [48]

    P. W. Cleary, J. J. Monaghan, Conduction modelling using smoothed particle hydrodynamics, Journal of Com- putational Physics 148 (1) (1999) 227–264

    1999

  41. [49]

    J. J. Monaghan, H. E. Huppert, M. G. Worster, Solidification using smoothed particle hydrodynamics, Journal of computational Physics 206 (2) (2005) 684–705

    2005

  42. [50]

    J. J. Monaghan, Smoothed particle hydrodynamics, Reports on progress in physics 68 (8) (2005) 1703

    2005

  43. [51]

    A. Shaw, S. R. Reid, Heuristic acceleration correction algorithm for use in sph computations in impact mechan- ics, Computer methods in applied mechanics and engineering 198 (49-52) (2009) 3962–3974

    2009

  44. [52]

    Z. Zhou, J. Bi, Y . Zhao, C. Wang, Y . Zhang, Thermal-mechanical coupling smooth particle hydrodynamics- phase field method modelling of cracking in rocks, Computers and Geotechnics 173 (2024) 106476

    2024

  45. [53]

    D. Mu, Z. Li, A. Tang, Q. Liu, D. Huang, A coupled thermo-mechanical bond-based smoothed particle dynamics model for simulating thermal cracking in rocks, Engineering Fracture Mechanics 265 (2022) 108364

    2022

  46. [54]

    C. Yan, H. Zheng, A coupled thermo-mechanical model based on the combined finite-discrete element method for simulating thermal cracking of rock, International Journal of Rock Mechanics and Mining Sciences 91 (2017) 24 170–178

    2017

  47. [55]

    D’Antuono, M

    P. D’Antuono, M. Morandini, Thermal shock response via weakly coupled peridynamic thermo-mechanics, International Journal of Solids and Structures 129 (2017) 74–89

    2017

  48. [56]

    W. Sun, W. Lu, F. Bao, P. Ni, A pd-fem coupling approach for modeling thermal fractures in brittle solids, Theoretical and Applied Fracture Mechanics 116 (2021) 103129

    2021

  49. [57]

    Heinze, G

    T. Heinze, G. Jansen, B. Galvan, S. A. Miller, Systematic study of the effects of mass and time scaling techniques applied in numerical rock mechanics simulations, Tectonophysics 684 (2016) 4–11. 25

    2016

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.