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Thread: QAS model and mTHOR algorithm vs. AUTODYN & LS-DYNA FEA simulations

  1. #1

    QAS model and mTHOR algorithm vs. AUTODYN & LS-DYNA FEA simulations

    These two technical papers describe the use of ANSYS AUTODYN and LS-DYNA software to analyze the transit time and residual velocities (incremental and terminal) of 9x19mm projectiles passing through 10% ordnance gelatin during high-velocity impact events.

    Investigation of bullet penetration in ballistic gelatin via finite element simulation and experiment, Yoon, et. al., Jrn. Mech, Sci & Tech, 29; 9 (2015)

    https://link.springer.com/article/10...206-015-0821-7

    The experimental and numerical investigation of pistol bullet penetrating soft tissue simulant, Wang, et. al., Forensic Science Intl; 249 (2015)

    https://www.sciencedirect.com/scienc...79073815000766

    The FEA simulation predictions contained in the two cited technical papers can be used to evaluate the validity of projectile transit time (ΔT) and residual velocity (Vr) predictions made by the Q-model and mTHOR algorithm closed-form bullet penetration equations.

    Note: The cost of licensing FEA software like ANSYS AUTODYN or LS-DYNA is approximately $30,000 to $60,000 depending upon the functionality desired.

    For the uninitiated reader, it is important to explain what FEA software does.

    FEA software numerically simulates the mechanical response of materials (in this case, a block of shear-validated 10% ordnance gelatin) undergoing high strain-rate events like projectile/fragment impacts or and energetic events such as explosions. FEA simulation requires the division of an object into discrete three-dimensional, non-overlapping components called 'elements' (which can be easily visualized as very small Lego building blocks). The entire object is modeled as a mesh framework composed of several hundreds of thousands—or even millions—of elements. During this process, PDEs (partial differential equations) which govern rate-dependent material properties such as density, yield strength, bulk, shear, and compressive moduli, visco-elastic properties, linear and non-linear shock equations of state, etc. are assigned to the elements composing the model's mesh framework. This numerical modeling process is performed for all other objects (in this case, a 9x19mm FMJRN bullet) striking a primary target model (a 10% ordnance gelatin block). Once the correct PDEs have been entered into the FEA software, experimental simulations are conducted under variable conditions where velocity, material properties, and mesh size is varied to investigate desired physical phenomena. Finite element analysis solutions are generated numerically and graphically.

    ANSYS AUTODYN:

    1.) In Investigation of bullet penetration in ballistic gelatin via finite element simulation and experiment, Yoon, et. al., Jrn Mech, Sci & Tech, 29; 9 (2015), a 9x19mm 124-grain FMJRN bullet was fired into a 15cm x 15cm x 30cm block of shear-validated 10% ordnance gelatin at a velocity of 313 meters per second. The following excerpt and images detail the test protocol and data obtained from both the FE simulation and the 10% ordnance gelatin test. Imaging of the 10% ordnance gelatin test was conducted using a Phantom V7.3 high-frame rate camera.

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    The 10% ordnance gelatin test arrangement was replicated using the AUTODYN FEA software and the test results of the two events were compared to one another. With an impact velocity of 313 meters per second, it took the 9x19mm 124-grain FMJRN bullet 1.200 milliseconds to traverse and exit a 10% ordnance gelatin block having a length of 30cm. The AUTODYN software predicts that it would take 1.700 milliseconds for the 9x19mm 124-grain FMJRN bullet (at 313 meters per second) to traverse and exit an ordnance gelatin block of the same length (30cm).

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    A 9x19mm 124-grain FMJRN bullet striking a 15cm x 15cm x 30cm block of shear-validated 10% ordnance gelatin at a velocity at 313 meters per second was modeled using the Q-model and the mTHOR algorithm equations. When compared to the ANSYS AUTODYN FEA simulation illustrated above, the Q-model predicts that the 9x19mm 124-grain FMJRN bullet at 313 meters per second would fully traverse and exit the gelatin block in 1.311 milliseconds closely matching the 10% ordnance gelatin test data in which the 9x19mm 124-grain FMJRN exited the 10% ordnance gelatin block in 1.200 milliseconds. Predicted residual velocity of the 9x19mm 124-grain bullet is 474.4464 feet per second.

    The Q-model predictive yield:
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    The mTHOR algorithm also predicts that the 9x19mm 124-grain FMJRN bullet at 313 meters per second would fully traverse and exit the 10% ordnance gelatin block in 1.331 milliseconds in strong agreement with the 10% ordnance gelatin test data. The mTHOR algorithm’s prediction closely duplicates the predicted terminal transit time of the prior Q-model analysis. Predicted residual velocity of the test bullet is 451.889 feet per second.

    The mTHOR algorithm predictive yield:
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    Conclusion: The Q-model and the mTHOR algorithm bullet penetration equations produce more accurate projectile transit time predictions through 10% ordnance gelatin than the AUTODYN software.



    LS-DYNA:

    2.) In The experimental and numerical investigation of pistol bullet penetrating soft tissue simulant, Wang, et. al., Forensic Science Intl; 249 (2015), a 9x19mm 115-grain FMJRN bullet was fired into a 200mm x 240mm x 340mm block of shear-validated 10% ordnance gelatin at a velocity of 337.35 meters per second. Incremental and terminal transit time and residual velocity predictions were obtained by conducting several LS-DYNA FEA simulations. The LS-DYNA FEA data was compared to data obtained from a test conducted using 10% ordnance gelatin. Imaging of the 10% ordnance gelatin test was conducted using a Phantom V710 high-frame rate camera.

    In the following illustration, incremental and terminal transit times predicted by the LS-DYNA FE software are compared to those obtained in the 10% ordnance gelatin test. Frame #6 clearly shows that the 9x19mm 115-grain FMJRN (with an impact velocity of 337.35 meters per second) fully traverses and exits the end of the 340mm-long gelatin block at 1,700 μs (micro-seconds). The LS-DYNA simulation prediction of 1,700 μs agrees strongly with the terminal transit time (also 1,700 μs) observed in the 10% ordnance gelatin test data.

    LS-DYNA simulation v. 10% ordnance gelatin test:
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    Name:  2.) 340mm 10% ordnance gelatin block detail at 1.700 milliseconds.jpg
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    LS-DYNA simulation: strain rates and incremental transit times:
    Name:  3.) LS-DYNA strain v. time; 9x19mm 115 FMJ in 340mm 10% ordnance gelatin block.jpg
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    The Q-model and mTHOR algorithm equations were used to model the actual terminal transit time of the 9x19mm 115-grain FMJRN as it passed through the 340mm-long 10% ordnance gelatin block. The Q-model predicts a terminal transit time of 1,666.68 μs. The mTHOR algorithm predicts a terminal transit time of 1,625.24 μs. The Q-model and mTHOR algorithm strongly agree with the LS-DYNA FEA software predictions and the 10% ordnance gelatin test’s terminal transit time of 1,700.00 μs with respect to instantaneous projectile position (Z).

    The Q-model predictive yield:
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    The mTHOR algorithm predictive yield:
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    The Q-model and mTHOR algorithm produce predictions that strongly agree with the LS-DYNA FEA software predictions of incremental and terminal transit times with respect to instantaneous projectile position (Z) in the 340-mm-long 10% ordnance gelatin block.

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    Finally, LS-DYNA simulation predictions were numerically modeled for the terminal residual velocity of the 9x19mm 115-grain FMJRN across a range of varying impact velocities (200 – 400 meters per second) in a 300mm-long 10% ordnance gelatin block.

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    As shown in the following table, the Q-model and mTHOR algorithm equations produce incremental residual velocity predictions that closely match those produced by the LS-DYNA FEA software.

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    Conclusion: Predictions made by simple closed-form bullet penetration equations (Q-model and mTHOR) were directly compared against data obtained from 10% ordnance gelatin tests and FE simulations. The Q-model and mTHOR algorithm bullet penetration equations offer qualitatively and quantitatively valid predictive yields for the projectile transit time (ΔT) and incremental and terminal residual velocity (Vr) of 115-grain and 124-grain 9x19mm FMJRN projectiles passing through shear-validated 10% ordnance gelatin blocks. The predictive yields of the closed-form Q-model and mTHOR algorithm bullet penetration equations were compared via statistical ANOVA (analyses of variance) to those of FEA software and actual tests conducted in blocks of 10% ordnance gelatin. The Q-model's and mTHOR algorithm's predictive yields were found to correlate very strongly with the predictive yields produced by the ANYSYS AUTODYN and the LS-DYNA finite element analysis software cited in the two technical papers.
    Last edited by the Schwartz; 07-22-2022 at 06:57 PM.
    ''Politics is for the present, but an equation is for eternity.'' ―Albert Einstein

    Full disclosure per the Pistol-Forum CoC: I am the author of Quantitative Ammunition Selection. www.quantitativeammunitionselection.com

  2. #2
    riding the slimline train Leroy Suggs's Avatar
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    You deserve a like for the time and effort that went into that post.

  3. #3
    Swimming past it all fatdog's Avatar
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    I have always wondered why nobody ever bothered to do some serious mechanical energy FE analysis in this arena and create or validate a mathematical model for bullet behavior. Thanks for sharing. These guys at least scratched the surface.

    I got to know Ansys/Anvil back in the mid 80's when it was young software and drove the sales of those Unix "engineering workstations" from Apollo, Sun, and HP. I am sure it has matured into quite a beast now and justifies that price point for the serious users.

  4. #4
    Quote Originally Posted by Leroy Suggs View Post
    You deserve a like for the time and effort that went into that post.
    Thank you very much.

    While it was certainly a lot of work, it was also a lot of fun—at least for a science nerd (and mathlete) like me.

    Confirming that a couple of my own creations (the Q-model and mTHOR algorithm) compare so favorably to the highly respected AUTODYN and LS-DYNA numerical processes...well, sir...that's just ''icing on the cake''.
    ''Politics is for the present, but an equation is for eternity.'' ―Albert Einstein

    Full disclosure per the Pistol-Forum CoC: I am the author of Quantitative Ammunition Selection. www.quantitativeammunitionselection.com

  5. #5
    Quote Originally Posted by fatdog View Post
    I have always wondered why nobody ever bothered to do some serious mechanical energy FE analysis in this arena and create or validate a mathematical model for bullet behavior. Thanks for sharing. These guys at least scratched the surface.

    I got to know Ansys/Anvil back in the mid 80's when it was young software and drove the sales of those Unix "engineering workstations" from Apollo, Sun, and HP. I am sure it has matured into quite a beast now and justifies that price point for the serious users.
    It's out there, I'm sure. I suspect that there is probably a lot more terminal ballistic FE analysis to be had. I've simply not had the time lately to research it to the extent that I'd like. Analytical KE-partitioning methodology is very common in the field of armor penetration analysis usually in combination with the modified Bernoulli equation as modified by V.P. Alekseevskii in 1966 and A. Tate in 1967. So far, the only application of numerical KE-partitioning to soft tissue simulants that I have been able to locate is in the two white papers that I listed earlier.

    Unfortunately, the expense—in addition to the complex technical nature—of FEA software puts it far beyond the grasp of the vast majority of everyone with the notable exception of engineers employed by well-funded organizations. Fortunately, this is where closed-form bullet penetration equations like the Q-model and mTHOR come into their own as options that provide the same answers as FE analysis without breaking the bank. As I am sure you know, while FEA software models the physical phenomena being investigated, closed form-equations are the 'laws' that FE analyses must obey in order to perform those investigations. I've often thought about offering software that would reduce the technical burden (probably in an Excel format) for sale to users interested in getting the answers that they are looking for. Obviously, such an offering would occur at a much, much lower price point than what current FEA software is offered.
    ''Politics is for the present, but an equation is for eternity.'' ―Albert Einstein

    Full disclosure per the Pistol-Forum CoC: I am the author of Quantitative Ammunition Selection. www.quantitativeammunitionselection.com

  6. #6
    Swimming past it all fatdog's Avatar
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    The Excel thing for running validated equations might be something useful, but I guess also requires the users to understand the context of the result of those equations. The further you get away from engineers who understand the underlying physics, the harder that will get I think.

    On the FE software front, I cannot help but believe some part of academia at some point makes a capable open source tool available.

    The human body is commonly FE modeled for radiated energy (e.g. planning radiation treatments with linear accelerators) but I have never heard of somebody doing it for the purpose of making dynamic mechanical/force and stress analysis beyond the stuff the artificial joint guys do. Someday maybe somebody could come closer to expressing the variations a bullet encounters with a good detailed FE model of the various tissues. Makes me wonder if some defense outfit has secretly done some of that, until then I guess all we will have is the benchmark media of ballistic gel.

    again thanks for those links, I am going to dive in at some point and read all of that to try to understand those equations and the import of the things they are predicting

  7. #7
    Quote Originally Posted by fatdog View Post
    The Excel thing for running validated equations might be something useful, but I guess also requires the users to understand the context of the result of those equations. The further you get away from engineers who understand the underlying physics, the harder that will get I think.

    On the FE software front, I cannot help but believe some part of academia at some point makes a capable open source tool available.

    The human body is commonly FE modeled for radiated energy (e.g. planning radiation treatments with linear accelerators) but I have never heard of somebody doing it for the purpose of making dynamic mechanical/force and stress analysis beyond the stuff the artificial joint guys do. Someday maybe somebody could come closer to expressing the variations a bullet encounters with a good detailed FE model of the various tissues. Makes me wonder if some defense outfit has secretly done some of that, until then I guess all we will have is the benchmark media of ballistic gel.

    again thanks for those links, I am going to dive in at some point and read all of that to try to understand those equations and the import of the things they are predicting
    I'd enjoy seeing an open-source version of either FE software—or both.

    Still debating the Excel option at the request of several folks in the field who would like to duplicate the validity and accuracy of FEA without the expense and technical challenges of the FE software. Obviously, there's going to have to be a compromise somewhere.

    As for the 'secret' stuff, I'd be willing to bet a month's income that that's already been done by our military.
    ''Politics is for the present, but an equation is for eternity.'' ―Albert Einstein

    Full disclosure per the Pistol-Forum CoC: I am the author of Quantitative Ammunition Selection. www.quantitativeammunitionselection.com

  8. #8

    Further validation of the Q-model and mTHOR algorithm bullet penetration equations

    As fate would have it, I discovered another technical paper authored in 2016.

    In this particular paper—

    Development of a numerical model for the ballistic penetration of Fackler gelatine by small calibre projectiles, L. Gilson, et. al., Eur. Phys. J. Special Topics 225 (2016)

    https://link.springer.com/article/10.../e2016-02640-9

    —the terminal ballistic transit times (ΔT) of 9x19mm FMJRN and .44 Magnum FMJFN bullets fired into 290mm-long 10% ordnance gelatin soft tissue simulant was investigated. Terminal ballistic transit times of 9x19mm FMJRN and .44 Magnum FMJFN bullets fired into 10% ordnance gelatin were compared to FEA simulations conducted with LS-DYNA software.

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    The 9x19mm 124-grain FMJRN and .44 Magnum 240-grain FMJFN bullets and the 290mm-long 10% ordnance gelatin block were modeled for the FE simulations.

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    The LS-DYNA FE simulation agrees with the terminal ballistic transit time (ΔT) 1,000 µseconds observed for the 9x19mm 124-grain FMJRN in the 10% ordnance gelatin block. Impact velocity for the 10% ordnance gelatin experiment and the FE analysis was 388 meters per second.

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    The Q-model predictions for the 9x19mm 124-grain FMJRN tests using ρ = 1.030 g/cc and ρ = 1.040 g/cc compared to the FE simulation and 10% ordnance gelatin test:

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    The mTHOR prediction for the 9x19mm 124-grain FMJRN tests using ρ = 1.040 g/cc:

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    The LS-DYNA FE simulation agrees with the terminal ballistic transit time (ΔT) 875 µseconds observed for the .44 Magnum 240-grain FMJFN in the 10% ordnance gelatin block. Impact velocity for the 10% ordnance gelatin experiment and the FE analysis was 424 meters per second.

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    The Q-model predictions for the .44 Magnum 240-grain FMJFN tests using ρ = 1.030 g/cc and ρ = 1.040 g/cc compared to the FE simulation and 10% ordnance gelatin test:

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    The mTHOR prediction for the .44 Magnum 240-grain FMJFN tests using ρ = 1.040 g/cc:

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    Comparison of experimental data, LS-DYNA FE simulation yields, and Q-model and mTHOR algorithm predictions:

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    Conclusion: Experiments were conducted by firing 9x19mm FMJRN and .44 Magnum FMJFN bullets into 290mm-long 10% ordnance gelatin blocks. Terminal ballistic transit times (ΔT) of 1,000 µs for the 9x19mm FMJRN bullets and 875 µs for the .44 Magnum FMJFN bullets were measured during the experiments and duplicated by the LS-DYNA FE simulations modeling the 10% ordnance gelatin test series. The closed-form Q-model and mTHOR algorithm bullet penetration equations produced terminal ballistic transit time predictions that correlate very strongly with the 10% ordnance gelatin experimental data and with the predictions made during the LS-DYNA simulations. Comparison of FE analysis yields with predictions made by the Q-model and mTHOR algorithm suggests that both simple closed-form bullet penetration equations found in Quantitative Ammunition Selection produce results that are qualitatively and quantitatively equivalent to those obtained through 10% ordnance gelatin experiments and FE analysis.
    Last edited by the Schwartz; 07-24-2022 at 08:34 PM.
    ''Politics is for the present, but an equation is for eternity.'' ―Albert Einstein

    Full disclosure per the Pistol-Forum CoC: I am the author of Quantitative Ammunition Selection. www.quantitativeammunitionselection.com

  9. #9
    Site Supporter orionz06's Avatar
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    I'm just here to say that it's nice to see ANSYS popping up here. That's about 50% of my work these days.
    Think for yourself. Question authority.

  10. #10
    That is amazing work.

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