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 (V_{r}) predictions made by the Q-model andmTHOR 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.) InInvestigation 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.

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).

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 themTHOR 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 in1.311 millisecondsclosely matching the 10% ordnance gelatin test data in which the 9x19mm 124-grain FMJRN exited the 10% ordnance gelatin block in1.200 milliseconds. Predicted residual velocity of the 9x19mm 124-grain bullet is 474.4464 feet per second.

The Q-model predictive yield:

ThemTHOR 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. ThemTHOR 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.

ThemTHOR algorithm predictive yield:

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

LS-DYNA:

2.) InThe 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:

LS-DYNA simulation: strain rates and incremental transit times:

The Q-model andmTHOR 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. ThemTHOR algorithm predicts a terminal transit time of 1,625.24 μs. The Q-model andmTHOR 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:

ThemTHOR algorithm predictive yield:

The Q-model andmTHOR 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.

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.

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

Conclusion:Predictions made by simple closed-form bullet penetration equations (Q-model andmTHOR) were directly compared against data obtained from 10% ordnance gelatin tests and FE simulations. The Q-model andmTHOR algorithm bullet penetration equations offer qualitatively and quantitatively valid predictive yields for the projectile transit time (ΔT) and incremental and terminal residual velocity (V_{r}) 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 andmTHOR 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 andmTHOR 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.