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High-Strain-Rate Behavior of a Viscoelastic Gel Under High-Velocity Microparticle Impact

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Abstract

Background

Impact experiments, routinely performed at the macroscale, have long been used to study mechanical properties of materials. Microscale high-velocity impact, relevant to applications such as ballistic drug delivery has remained largely unexplored at the level of a single impact event.

Objective

In this work, we study the mechanical behavior of polymer gels subjected to high-velocity microparticle impact, with strain rates up to 107 s−1, through direct visualization of the impact dynamics.

Methods

In an all-optical laser-induced particle impact test, 10–24 μm diameter steel microparticles are accelerated through a laser ablation process to velocities ranging from 50 to 1000 m/s. Impact events are monitored using a high-speed multi-frame camera with nanosecond time resolution.

Results

We measure microparticle trajectories and extract both maximum and final penetration depths for a range of particle sizes, velocities, and gel concentrations. We propose a modified Clift-Gauvin model and demonstrate that it adequately describes both individual trajectories and penetration depths. The model parameters, namely, the apparent viscosity and impact resistance, are extracted for a range of polymer concentrations.

Conclusions

Laser-induced microparticle impact test makes it possible to perform reproducible measurements of the single particle impact dynamics on gels and provides a quantitative basis for understanding these dynamics. We show that the modified Clift-Gauvin model, which accounts for the velocity dependence of the drag coefficient, offers a better agreement with the experimental data than the more commonly-used Poncelet model. Microscale ballistic impact imaging performed with high temporal and spatial resolution can serve as direct input for simulations of high-velocity impact responses and high strain rate deformation in gels and other soft materials.

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References

  1. Christiansen EL, Nagy K, Lear DM, Prior TG (2009) Space station MMOD shielding. Acta Astronaut 65:921–929. https://doi.org/10.1016/j.actaastro.2008.01.046

    Article  Google Scholar 

  2. Christiansen EL, Hyde JL, Bernhard RP (2004) Space shuttle debris and meteoroid impacts. Adv Sp Res 34:1097–1103. https://doi.org/10.1016/j.asr.2003.12.008

    Article  Google Scholar 

  3. Parsi M, Najmi K, Najafifard F, Hassani S, McLaury BS, Shirazi SA (2014) A comprehensive review of solid particle erosion modeling for oil and gas wells and pipelines applications. J Nat Gas Sci Eng 21:850–873. https://doi.org/10.1016/j.jngse.2014.10.001

    Article  Google Scholar 

  4. Pepi M, Squillacioti R, Pfledderer L, Phelps A (2012) Solid particle Erosion testing of helicopter rotor blade materials. J Fail Anal Prev 12:96–108. https://doi.org/10.1007/s11668-011-9531-3

    Article  Google Scholar 

  5. Tilly GP (1969) Erosion caused by airborne particles. Wear 14:63–79. https://doi.org/10.1016/0043-1648(69)90035-0

    Article  Google Scholar 

  6. Moridi A, Hassani-Gangaraj SM, Guagliano M, Dao M (2014) Cold spray coating: review of material systems and future perspectives. Surf Eng 30:369–395. https://doi.org/10.1179/1743294414Y.0000000270

    Article  Google Scholar 

  7. Kendall M, Mitchell T, Wrighton-Smith P (2004) Intradermal ballistic delivery of micro-particles into excised human skin for pharmaceutical applications. J Biomech 37:1733–1741. https://doi.org/10.1016/j.jbiomech.2004.01.032

    Article  Google Scholar 

  8. Hill PF, Edwards DP, Bowyer GW (2001) Small fragment wounds: biophysics, pathophysiology and principles of management. J R Army Med Corps 147:41–51. https://doi.org/10.1136/jramc-147-01-04

    Article  Google Scholar 

  9. Hisley DM, Gurganus JC, Drysdale AW (2011) Experimental methodology using digital image correlation to assess ballistic helmet blunt trauma. J Appl Mech 78:051022. https://doi.org/10.1115/1.4004332

    Article  Google Scholar 

  10. Salisbury CP, Cronin DS (2009) Mechanical properties of ballistic gelatin at high deformation rates. Exp Mech 49:829–840. https://doi.org/10.1007/s11340-008-9207-4

    Article  Google Scholar 

  11. Miller DL, Smith NB, Bailey MR, Czarnota GJ, Hynynen K, Makin IRS, Bioeffects Committee of the American Institute of Ultrasound in Medicine (2012) Overview of therapeutic ultrasound applications and safety considerations. J Ultrasound Med 31:623–634. https://doi.org/10.7863/jum.2012.31.4.623

    Article  Google Scholar 

  12. Mancia L, Vlaisavljevich E, Xu Z, Johnsen E (2017) Predicting tissue susceptibility to mechanical cavitation damage in therapeutic ultrasound. Ultrasound Med Biol 43:1421–1440. https://doi.org/10.1016/j.ultrasmedbio.2017.02.020

    Article  Google Scholar 

  13. Lee T, Luo W, Li Q, Demirci H, Guo LJ (2017) Laser-induced focused ultrasound for cavitation treatment: toward high-precision invisible sonic scalpel. Small 13:1–10. https://doi.org/10.1002/smll.201701555

    Article  Google Scholar 

  14. Gama BA, Lopatnikov SL, Gillespie JW (2004) Hopkinson bar experimental technique: a critical review. Appl Mech Rev 57:223–250

    Article  Google Scholar 

  15. Richler D, Rittel D (2014) On the testing of the dynamic mechanical properties of soft gelatins. Exp Mech 54:805–815. https://doi.org/10.1007/s11340-014-9848-4

    Article  Google Scholar 

  16. Song B, Chen W (2004) Dynamic stress equilibration in split Hopkinson pressure bar tests on soft materials. Exp Mech 44:300–312. https://doi.org/10.1177/0014485104041543

    Article  Google Scholar 

  17. Toyoda Y, Gupta YM (2014) Shockless and shock wave compression of ballistic gel to 1.3 GPa. J Appl Phys 116:. https://doi.org/10.1063/1.4898679

  18. Estrada JB, Barajas C, Henann DL, Johnsen E, Franck C (2018) High strain-rate soft material characterization via inertial cavitation. J Mech Phys Solids 112:291–317. https://doi.org/10.1016/j.jmps.2017.12.006

    Article  Google Scholar 

  19. Panzer MB, Myers BS, Capehart BP, Bass CR (2012) Development of a finite element model for blast brain injury and the effects of CSF cavitation. Ann Biomed Eng 40:1530–1544. https://doi.org/10.1007/s10439-012-0519-2

    Article  Google Scholar 

  20. Marjoribanks RS, Dille C, Schoenly JE, McKinney L, Mordovanakis A, Kaifosh P, Forrester P, Qian Z, Covarrubias A, Feng Y, Lilge L (2012) Ablation and thermal effects in treatment of hard and soft materials and biotissues using ultrafast-laser pulse-train bursts. Photonics Lasers Med 1:155–169. https://doi.org/10.1515/plm-2012-0020

    Article  Google Scholar 

  21. Lee J-H, Veysset D, Singer JP, Retsch M, Saini G, Pezeril T, Nelson KA, Thomas EL (2012) High strain rate deformation of layered nanocomposites. Nat Commun 3:1164. https://doi.org/10.1038/ncomms2166

    Article  Google Scholar 

  22. Veysset D, Hsieh AJ, Kooi S, Maznev AA, Masser KA, Nelson KA (2016) Dynamics of supersonic microparticle impact on elastomers revealed by real-time multi-frame imaging. Sci Rep 6:25577. https://doi.org/10.1038/srep25577

    Article  Google Scholar 

  23. Hassani-Gangaraj M, Veysset D, Nelson KA, Schuh CA (2018) In-situ observations of single micro-particle impact bonding. Scr Mater 145:9–13. https://doi.org/10.1016/j.scriptamat.2017.09.042

    Article  Google Scholar 

  24. Hassani-Gangaraj M, Veysset D, Nelson KA, Schuh CA (2017) Melting can hinder impact-induced adhesion. Phys Rev Lett 119:175701. https://doi.org/10.1103/PhysRevLett.119.175701

    Article  Google Scholar 

  25. Xie W, Alizadeh-Dehkharghani A, Chen Q, Champagne VK, Wang X, Nardi AT, Kooi S, Müftü S, Lee JH (2017) Dynamics and extreme plasticity of metallic microparticles in supersonic collisions /639/166/988 /639/301/1023/1026 /639/301/930/12 /128 article. Sci Rep 7:1–9. https://doi.org/10.1038/s41598-017-05104-7

    Article  Google Scholar 

  26. Hassani-Gangaraj M, Veysset D, Nelson KA, Schuh CA (2019) Impact-bonding with aluminum, silver, and Gold microparticles: toward understanding the role of native oxide layer. Appl Surf Sci 476:528–532. https://doi.org/10.1016/j.apsusc.2019.01.111

    Article  Google Scholar 

  27. Hassani-Gangaraj M, Veysset D, Nelson KA, Schuh CA (2018) Melt-driven erosion in microparticle impact. Nat Commun 9:5077. https://doi.org/10.1038/s41467-018-07509-y

    Article  Google Scholar 

  28. Veysset D, Hsieh AJ, Kooi SE, Nelson KA (2017) Molecular influence in high-strain-rate microparticle impact response of poly(urethane urea) elastomers. Polymer 123:30–38. https://doi.org/10.1016/j.polymer.2017.06.071

    Article  Google Scholar 

  29. Hsieh AJ, Veysset D, Miranda DF, Kooi SE, Runt J, Nelson KA (2018) Molecular influence in the glass/polymer interface design: the role of segmental dynamics. Polymer 146:222–229. https://doi.org/10.1016/j.polymer.2018.05.034

    Article  Google Scholar 

  30. Wu Y-CM HW, Sun Y et al (2019) Unraveling the high strain-rate dynamic stiffening in select model polyurethanes − the role of intermolecular hydrogen bonding. Polymer 168:218–227. https://doi.org/10.1016/j.polymer.2019.02.038

    Article  Google Scholar 

  31. Sun Y, Wu Y-CM, Veysset D, Kooi SE, Hu W, Swager TM, Nelson KA, Hsieh AJ (2019) Molecular dependencies of dynamic stiffening and strengthening through high strain rate microparticle impact of polyurethane and polyurea elastomers. Appl Phys Lett 115:093701. https://doi.org/10.1063/1.5111964

    Article  Google Scholar 

  32. Lee J-H, Loya PE, Lou J, Thomas EL (2014) Dynamic mechanical behavior of multilayer graphene via supersonic projectile penetration. Science 346:1092–1096. https://doi.org/10.1126/science.1258544

    Article  Google Scholar 

  33. Xie W, Tadepalli S, Park SH, Kazemi-Moridani A, Jiang Q, Singamaneni S, Lee JH (2018) Extreme mechanical behavior of nacre-mimetic Graphene-oxide and silk Nanocomposites. Nano Lett 18:987–993. https://doi.org/10.1021/acs.nanolett.7b04421

    Article  Google Scholar 

  34. Hyon J, Lawal O, Fried O, Thevamaran R, Yazdi S, Zhou M, Veysset D, Kooi SE, Jiao Y, Hsiao MS, Streit J, Vaia RA, Thomas EL (2018) Extreme energy absorption in glassy polymer thin films by supersonic micro-projectile impact. Mater Today 21:817–824. https://doi.org/10.1016/j.mattod.2018.07.014

    Article  Google Scholar 

  35. Veysset D, Kooi SE, Мaznev AA, Tang S, Mijailovic AS, Yang YJ, Geiser K, van Vliet KJ, Olsen BD, Nelson KA (2018) High-velocity micro-particle impact on gelatin and synthetic hydrogel. J Mech Behav Biomed Mater 86:71–76. https://doi.org/10.1016/j.jmbbm.2018.06.016

    Article  Google Scholar 

  36. Liu K, Jiang M, Wu Z, Li Z, Ning J (2019) A mechanical model for spherical fragments penetrating gelatine. Int J Impact Eng 131:27–38. https://doi.org/10.1016/j.ijimpeng.2019.04.022

    Article  Google Scholar 

  37. Clift R, Gauvin WH (1971) Motion of entrained particles in gas streams. Can J Chem Eng 49:439–448. https://doi.org/10.1002/cjce.5450490403

    Article  Google Scholar 

  38. Mrozek RA, Leighliter B, Gold CS, Beringer IR, Yu JH, VanLandingham MR, Moy P, Foster MH, Lenhart JL (2015) The relationship between mechanical properties and ballistic penetration depth in a viscoelastic gel. J Mech Behav Biomed Mater 44:109–120. https://doi.org/10.1016/j.jmbbm.2015.01.001

    Article  Google Scholar 

  39. Hassani-Gangaraj M, Veysset D, Nelson KA, Schuh CA (2016) Supersonic impact of metallic micro-particles. arXiv:161208081

  40. Al Khalil M, Frissane H, Taddei L et al (2019) SPH-based method to simulate penetrating impact mechanics into ballistic gelatin: toward an understanding of the perforation of human tissue. Extrem Mech Lett 29:100479. https://doi.org/10.1016/j.eml.2019.100479

    Article  Google Scholar 

  41. Meng S, Taddei L, Lebaal N, Veysset D, Roth S (2020) Modeling micro-particles impacts into ballistic gelatine using smoothed particles hydrodynamics method. Extrem Mech Lett 39:100852. https://doi.org/10.1016/j.eml.2020.100852

    Article  Google Scholar 

  42. Akers B, Belmonte A (2006) Impact dynamics of a solid sphere falling into a viscoelastic micellar fluid. J Nonnewton Fluid Mech 135:97–108. https://doi.org/10.1016/j.jnnfm.2006.01.004

    Article  Google Scholar 

  43. Ansley RW, Smith TN (1967) Motion of spherical particles in a Bingham plastic. AICHE J 13:1193–1196. https://doi.org/10.1002/aic.690130629

    Article  Google Scholar 

  44. Luu L-H, Forterre Y (2009) Drop impact of yield-stress fluids. J Fluid Mech 632:301–327. https://doi.org/10.1017/S0022112009007198

    Article  MATH  Google Scholar 

  45. Ovarlez G, Cohen-Addad S, Krishan K, Goyon J, Coussot P (2013) On the existence of a simple yield stress fluid behavior. J Nonnewton Fluid Mech 193:68–79. https://doi.org/10.1016/j.jnnfm.2012.06.009

    Article  Google Scholar 

  46. Tabuteau H, Coussot P, de Bruyn JR (2007) Drag force on a sphere in steady motion through a yield-stress fluid. J Rheol (N Y N Y) 51:125–137. https://doi.org/10.1122/1.2401614

    Article  Google Scholar 

  47. De Bruyn JR, Walsh AM (2004) Penetration of spheres into loose granular media. Can J Phys 82:439–446. https://doi.org/10.1139/p04-025

    Article  Google Scholar 

  48. Goossens WRA (2019) Review of the empirical correlations for the drag coefficient of rigid spheres. Powder Technol 352:350–359. https://doi.org/10.1016/j.powtec.2019.04.075

    Article  Google Scholar 

  49. Yoshitake Y, Mitani S, Sakai K, Takagi K (2008) Surface tension and elasticity of gel studied with laser-induced surface-deformation spectroscopy. Phys Rev E - Stat Nonlinear, Soft Matter Phys 78:1–7. https://doi.org/10.1103/PhysRevE.78.041405

    Article  Google Scholar 

  50. Nakamura T, Hattori M, Kawasaki H et al (1996) Surface tension of the polymer network of a gel. Phys Rev E - Stat Physics, Plasmas, Fluids, Relat Interdiscip Top 54:1663–1668

    Google Scholar 

  51. Jin Y, Mai R, Wu C, Han R, Li B (2018) Comparison of ballistic impact effects between biological tissue and gelatin. J Mech Behav Biomed Mater 78:292–297. https://doi.org/10.1016/j.jmbbm.2017.11.033

    Article  Google Scholar 

  52. Liu M, Hwang HY, Tao H, et al (2012) Terahertz-field-induced insulator-to-metal transition in vanadium dioxide metamaterial. Nature 1–4. https://doi.org/10.1038/nature11231

  53. Dehn J (1987) A unified theory of penetration. Int J Impact Eng 5:239–248. https://doi.org/10.1016/0734-743X(87)90041-8

    Article  Google Scholar 

  54. Liu L, Fan Y, Li W, Liu H (2012) Cavity dynamics and drag force of high-speed penetration of rigid spheres into 10wt% gelatin. Int J Impact Eng 50:68–75. https://doi.org/10.1016/j.ijimpeng.2012.06.004

    Article  Google Scholar 

  55. Segletes SB (2008) Modeling the penetration behavior of rigid spheres into ballistic gelatin. ART-TR-4393

  56. Cross MM (1979) Relation between viscoelasticity and shear-thinning behaviour in liquids. Rheol Acta 18:609–614. https://doi.org/10.1007/BF01520357

    Article  Google Scholar 

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Acknowledgments

DV thanks Drs. Bianca Giovanardi and Anwar Koshakji for fruitful discussions. This material is based upon work supported by the U. S. Army Research Office through the Institute for Soldier Nanotechnologies, under Cooperative Agreement Number W911NF-18-2-0048.

Additional image sequences can be found in the supplementary information (Figs. 5-12). The data that support the findings of this work are available from the corresponding author upon request.

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Authors and Affiliations

  1. Institute for Soldier Nanotechnologies, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    D. Veysset, Y. Sun, J. Lem, S. E. Kooi, A. A. Maznev & K. A. Nelson

  2. Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Y. Sun, J. Lem, A. A. Maznev & K. A. Nelson

  3. U.S. Army Research Laboratory, CCDC ARL, Aberdeen Proving Ground, MD, 21005-5069, USA

    S. T. Cole, R. A. Mrozek & J. L. Lenhart

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  1. D. Veysset
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Correspondence to D. Veysset.

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Veysset, D., Sun, Y., Lem, J. et al. High-Strain-Rate Behavior of a Viscoelastic Gel Under High-Velocity Microparticle Impact. Exp Mech 60, 1179–1186 (2020). https://doi.org/10.1007/s11340-020-00639-9

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