35
6.5 Conclusions
A modified Poncelet analysis was presented in this study for describing penetration resistance into loose and dense dry
Ottawa sand at transition impact velocities. Two sets of C and R values were proposed, separated by a transition velocity. The
transition velocity range was identified using an error analysis. An exponential function was used to describe the transition
regime. It was found that an improved fit could be found to the data using the Poncelet equation and the proposed approach,
with a reduced error of up to two orders of magnitude. However, the available data do not allow high confidence evaluation
of the R term, and precise predictions for terminal penetration depth requires additional data with velocity measurements
from impact to the terminal penetration depth.
Acknowledgement The authors gratefully acknowledge the support of the Strategic Environmental Research and Development Program
(SERDP) of the United States of America, Grant No.: MR19-1277.
References
1. Allen, W.A., Mayfield, E.B., Morrison, H.L.: Dynamics of a projectile penetration sand. J. Appl. Phys. 28(3), 370–376 (1957)
2. Omidvar, M., Chen, Z., Bless, S., Iskander, M.: Scale bridging interactions during penetration of granular materials. Dyn. Behav. Mater. 1,
335–340 (2014)
3. Clark, A.H., Behringer, R.P.: Granular impact model as an energy- depth relation. Europhys. Lett. 101(6), 64001 (2013)
4. Borg, J.P., Morrissey, M., Perich, C., Vogler, T., Chhabildas, L.: In situ velocity and stress characterization of a projectile penetrating a sand
target: experimental measurements and continuum simulations. Int. J. Impact Eng. 51, 23–35 (2013)
5. Glössner, C., Moser, S., Külls, K., Hess, S., Nau, S., Penamadu, D., Petrinic, N.: Instrumented projectile penetration testing of granular materials. Exp. Mech. 57, 271–272 (2017)
6. Peden, R., Omidvar, M., Bless, S., Iskander, M.: Photonic Doppler velocimetry for study of rapid penetration into sand. Geotechn. Test. J. 37,
139–150 (2014)
7. Omidvar, M., Iskander, M., Bless, S.: Response of granular media to rapid penetration. Int. J. Impact Eng. 66, 60–82 (2013)
8. Omidvar, M., Malioche, J.D., Bless, S., Iskander, M.: Phenomenology of rapid projectile penetration into granular soils. Int. J. Impact Eng. 85,
60–82 (2015)
9. Iskander, M., Bless, S., Omidvar, M.: Rapid Penetration into Granular Media: Visualizing the Fundamental Physics of Rapid Earth Penetration.
Elsevier, San Diego, CA (2015)
10. Omidvar, M., Bless, S., Iskander, M.: Recent insights into penetration of sand and similar granular materials. In: Shock Phenomena in Granular
and Porous Materials, pp. 137–163. Springer, Cham (2019)
11. Bless, S., Omidvar, M., Iskander, M.: Poncelet coefficients for dry sand. AIP Conf. Proc. 1979. 1, 110001 (2018)
12. Penumadu, D., Kim, F.: Multimodel radiation-based tomography and diffraction of granular materials using neutrons and photons and instrumented penetration mechanics. In: Iskander, M., Bless, S., Omidvar, M. (eds.) Rapid Penetration into Granular Media. Elsevier, San Diego,
CA (2015)
13. Parab, N.D., Claus, B., Hudspeth, M.C., Black, J.T., Mondal, A.J., Sun, J., Fezzas, K., Xiao, X., Luo, S.N., Chen, W.: Experimental assessment
of fracture in individual sand particles at different loading rates. Int. J. Impact Eng. 68, 8–14 (2014)
6 Observations of Velocity-Dependent Drag and Bearing Stress in Sand Penetration
6.5 Conclusions
A modified Poncelet analysis was presented in this study for describing penetration resistance into loose and dense dry
Ottawa sand at transition impact velocities. Two sets of C and R values were proposed, separated by a transition velocity. The
transition velocity range was identified using an error analysis. An exponential function was used to describe the transition
regime. It was found that an improved fit could be found to the data using the Poncelet equation and the proposed approach,
with a reduced error of up to two orders of magnitude. However, the available data do not allow high confidence evaluation
of the R term, and precise predictions for terminal penetration depth requires additional data with velocity measurements
from impact to the terminal penetration depth.
Acknowledgement The authors gratefully acknowledge the support of the Strategic Environmental Research and Development Program
(SERDP) of the United States of America, Grant No.: MR19-1277.
References
1. Allen, W.A., Mayfield, E.B., Morrison, H.L.: Dynamics of a projectile penetration sand. J. Appl. Phys. 28(3), 370–376 (1957)
2. Omidvar, M., Chen, Z., Bless, S., Iskander, M.: Scale bridging interactions during penetration of granular materials. Dyn. Behav. Mater. 1,
335–340 (2014)
3. Clark, A.H., Behringer, R.P.: Granular impact model as an energy- depth relation. Europhys. Lett. 101(6), 64001 (2013)
4. Borg, J.P., Morrissey, M., Perich, C., Vogler, T., Chhabildas, L.: In situ velocity and stress characterization of a projectile penetrating a sand
target: experimental measurements and continuum simulations. Int. J. Impact Eng. 51, 23–35 (2013)
5. Glössner, C., Moser, S., Külls, K., Hess, S., Nau, S., Penamadu, D., Petrinic, N.: Instrumented projectile penetration testing of granular materials. Exp. Mech. 57, 271–272 (2017)
6. Peden, R., Omidvar, M., Bless, S., Iskander, M.: Photonic Doppler velocimetry for study of rapid penetration into sand. Geotechn. Test. J. 37,
139–150 (2014)
7. Omidvar, M., Iskander, M., Bless, S.: Response of granular media to rapid penetration. Int. J. Impact Eng. 66, 60–82 (2013)
8. Omidvar, M., Malioche, J.D., Bless, S., Iskander, M.: Phenomenology of rapid projectile penetration into granular soils. Int. J. Impact Eng. 85,
60–82 (2015)
9. Iskander, M., Bless, S., Omidvar, M.: Rapid Penetration into Granular Media: Visualizing the Fundamental Physics of Rapid Earth Penetration.
Elsevier, San Diego, CA (2015)
10. Omidvar, M., Bless, S., Iskander, M.: Recent insights into penetration of sand and similar granular materials. In: Shock Phenomena in Granular
and Porous Materials, pp. 137–163. Springer, Cham (2019)
11. Bless, S., Omidvar, M., Iskander, M.: Poncelet coefficients for dry sand. AIP Conf. Proc. 1979. 1, 110001 (2018)
12. Penumadu, D., Kim, F.: Multimodel radiation-based tomography and diffraction of granular materials using neutrons and photons and instrumented penetration mechanics. In: Iskander, M., Bless, S., Omidvar, M. (eds.) Rapid Penetration into Granular Media. Elsevier, San Diego,
CA (2015)
13. Parab, N.D., Claus, B., Hudspeth, M.C., Black, J.T., Mondal, A.J., Sun, J., Fezzas, K., Xiao, X., Luo, S.N., Chen, W.: Experimental assessment
of fracture in individual sand particles at different loading rates. Int. J. Impact Eng. 68, 8–14 (2014)
6 Observations of Velocity-Dependent Drag and Bearing Stress in Sand Penetration