Abstract
Previous experimental investigations reported in the open literature have indicated that applying polyurea external coatings and/or internal linings can substantially improve ballistic penetration resistance and blast survivability of buildings, vehicles, and laboratory/field test-plates, as well as the blast-mitigation capacity of combat helmets. The protective role of polyurea coatings/linings has been linked to polyurea microstructure, which consists of discrete hard-domains distributed randomly within a compliant/soft matrix. When this protective role is investigated computationally, the availability of reliable, high-fidelity constitutive models for polyurea is vitally important. In the present work, a comprehensive overview and a critical assessment of a polyurea material constitutive model, recently proposed by Shim and Mohr (Int J Plast 27:868-886, 2011), are carried out. The review revealed that this model can accurately account for the experimentally measured uniaxial-stress versus strain data obtained under monotonic and multistep compressive loading/unloading conditions, as well as under stress relaxation conditions. On the other hand, by combining analytical and finite-element procedures with the material model in order to define the basic shock-Hugoniot relations for this material, it was found that the computed shock-Hugoniot relations differ significantly from their experimental counterparts. Potential reasons for the disagreement between the computed and experimental shock-Hugoniot relations are identified.
Similar content being viewed by others
References
M. Grujicic, T. He, and B. Pandurangan, Development and Parameterization of an Equilibrium Material Model for Segmented Polyurea, Multidiscip. Model. Mater. Struct., 2011, 7, p 96–114
M. Grujicic, T. He, B. Pandurangan, F.R. Svingala, G.S. Settles, and M.J. Hargather, Experimental Characterization and Material-Model Development for Microphase-Segregated Polyurea: An Overview, J. Mater. Eng. Perform., 2011, 21, p 2–16
M. Grujicic, B. Pandurangan, T. He, B.A. Cheeseman, C.-F. Yen, and C.L. Randow, Computational Investigation of Impact Energy Absorption Capability of Polyurea Coatings via Deformation-Induced Glass Transition, Mater. Sci. Eng. A, 2010, 527, p 7741–7751
M. Grujicic, B. Pandurangan, G. Arakere, W.C. Bell, T. He, and X. Xie, Material-Modeling and Structural-Mechanics Aspects of the Traumatic Brain Injury Problem, Multidiscip. Model. Mater. Struct., 2010, 6, p 335–363
M. Grujicic, T. He, B. Pandurangan, J. Runt, J. Tarter, and G. Dillon, Development and Parameterization of a Time-Invariant (Equilibrium) Material Model for Segmented Elastomeric Polyureas, J. Mater. Des. Appl., 2011, 225, p 182–194
M. Grujicic, W.C. Bell, B. Pandurangan, and T. He, Blast-Wave Impact-Mitigation Capability of Polyurea When Used as Helmet Suspension Pad Material, Mater. Des., 2010, 31, p 4050–4065
M. Grujicic, W.C. Bell, B. Pandurangan, and P.S. Glomski, Fluid/Structure Interaction Computational Investigation of the Blast-Wave Mitigation Efficacy of the Advanced Combat Helmet, J. Mater. Eng. Perform., 2011, 20, p 877–893
M. Grujicic, B. Pandurangan, A.E. King, J. Runt, J. Tarter, and G. Dillon, Multi-Length Scale Modeling and Analysis of Microstructure Evolution and Mechanical Properties in Polyurea, J. Mater. Sci., 2011, 46, p 1767–1779
M. Grujicic, B. Pandurangan, W.C. Bell, B.A. Cheeseman, C.-F. Yen, and C.L. Randow, Molecular-Level Simulations of Shock Generation and Propagation in Polyurea, Mater. Sci. Eng. A, 2011, 528, p 3799–3808
M. Grujicic, A. Arakere, B. Pandurangan, A. Grujicic, A.A. Littlestone, and R.S. Barsoum, Computational Investigation of Shock-Mitigation Efficacy of Polyurea when used in a Combat Helmet: A Core Sample Analysis, Multidiscip. Model. Mater. Struct., 2012, 8, p 297–331
M. Grujicic, B.P. d’Entremont, B. Pandurangan, A. Grujicic, M. LaBerge, J. Runt, J. Tarter, and G. Dillon, A Study of the Blast-induced Brain White-Matter Damage and the Associated Diffuse Axonal Injury, Multidiscip. Model. Mater. Struct., 2012, 8, p 213–245
A. Grujicic, M. LaBerge, M. Grujicic, B. Pandurangan, J. Runt, J. Tarter, and G. Dillon, Potential Improvements in Shock-Mitigation Efficacy of a Polyurea-Augmented Advanced Combat Helmet: A Computational Investigation, J. Mater. Eng. Perform., 2012, 21, p 1562–1579
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., 2012, 21, p 2024–2037
M. Grujicic and B. Pandurangan, Meso-Scale Analysis of Segmental Dynamics in Micro-Phase Segregated Polyurea, J. Mater. Sci., 2012, 47, p 3876–3889
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., 2012, 47, p 8197–8215
M. Grujicic, J.S. Snipes, S. Ramaswami, R. Yavari, J. Runt, J. Tarter, and G. Dillon, Coarse-Grained Molecular-Level Analysis of Polyurea Properties and Shock-Mitigation Potential, J. Mater. Eng. Perform., 2013, 22, p 1964–1981
T. Choi, D. Fragiadakis, C.M. Roland, and J. Runt, Microstructure and Segmental Dynamics of Polyurea Under Uniaxial Deformation, Macromolecules, 2012, 45, p 3581–3589
A. Castagna, A. Pangon, T. Choi, G. Dillon, and J. Runt, The Role of Soft Segment Molecular Weight on Microphase Separation and Dynamics in Bulk Polymerized Poly(tetramethylene oxide) Based Polyureas, Macromolecules, 2012, 45, p 8438–8444
M. Grujicic, H. Marvi, G. Arakere, W.C. Bell, and I. Haque, The Effect of Up-Armoring the High-Mobility Multi-Purpose Wheeled Vehicle (HMMWV) on the Off-Road Vehicle Performance, Multidiscip. Model. Mater. Struct., 2010, 6(2), p 229–256
M. Grujicic, W.C. Bell, G. Arakere, and I. Haque, Finite Element Analysis of the Effect of Up-Armoring on the Off-Road Braking and Sharp-Turn Performance of a High-Mobility Multi-Purpose Wheeled Vehicle (HMMWV), J. Automob. Eng., 2009, 223(D11), p 1419–1434
M. Grujicic, G. Arakere, H.K. Nallagatla, W.C. Bell, and I. Haque, Computational Investigation of Blast Survivability and Off-Road Performance of an Up-Armored High-Mobility Multi-Purpose Wheeled Vehicle (HMMWV), J. Automob. Eng., 2009, 223, p 301–325
V.F. Nesterenko, Shock (Blast) Mitigation by “Soft” Condensed Matter, MRS Symp. Proc., 2002, 759, p MM 4.3.1–MM 4.3.12
A.J. Ryan, Spinodal Decomposition During Bulk Copolymerization: Reaction Injection Molding, Polymer, 1990, 31, p 707–712
Y.A. Bahei-El-Din, G.J. Dvorak, and O.J. Fredricksen, A Blast-Tolerant Sandwich Plate Design with a Polyurea Interlayer, Int. J. Solids Struct., 2006, 43, p 7644–7658
S.M. Walsh, R.R. Scott, and D.M. Spagnuolo, The Development of a Hybrid Thermoplastic Ballistic Material with Application to Helmets, ARL-TR-3700, Army Research Laboratory, December 2005
S.A. Tekalur, A. Shukla, and K. Shivakumar, Blast Resistance of Polyurea-based Layered Composite Materials, Compos. Struct., 2008, 84, p 271–281
M. Grujicic, B. Pandurangan, and B.A. Cheeseman, A Computational Analysis of Detonation of Buried Mines, Multidiscip. Model. Mater. Struct., 2006, 2, p 363–387
M. Grujicic, B. Pandurangan, and B.A. Cheeseman, The Effect of Degree of Saturation of Sand on Detonation Phenomena Associated with Shallow-Buried and Ground-Laid Mines, Shock Vib., 2006, 13, p 41–62
M. Grujicic, B. Pandurangan, Y. Huang, B.A. Cheeseman, W.N. Roy, and R.R. Skaggs, Impulse Loading Resulting from Shallow Buried Explosives in Water-Saturated Sand, J. Mater. Des. Appl., 2007, 221, p 21–35
M. Grujicic, B. Pandurangan, J.D. Summers, B.A. Cheeseman, and W.N. Roy, Application of the Modified Compaction Material Model to Soil with Various Degrees of Water Saturation, Shock Vib., 2008, 15, p 79–99
M. Grujicic, B. Pandurangan, I. Haque, B.A. Cheeseman, W.N. Roy, and R.R. Skaggs, A Computational Analysis of Mine-Blast Survivability of a Soft-Skin Vehicle, Multidiscip. Model. Mater. Struct., 2007, 3, p 431–460
M. Grujicic, B. Pandurangan, G.M. Mocko, S.T. Hung, B.A. Cheeseman, W.N. Roy, and R.R. Skaggs, A Combined Multi-Material Euler/Lagrange Computational Analysis of Blast Loading Resulting from Detonation of Buried Landmines, Multidiscip. Model. Mater. Struct., 2008, 4, p 105–124
M. Grujicic, B. Pandurangan, R. Qiao, B.A. Cheeseman, W.N. Roy, R.R. Skaggs, and R. Gupta, Parameterization of the Porous-Material Model for Sand with Different Levels of Water Saturation, Soil Dyn. Earthq. Eng., 2008, 28, p 20–35
M. Grujicic, B. Pandurangan, N. Coutris, B.A. Cheeseman, W.N. Roy, and R.R. Skaggs, Derivation and Validation of a Material Model for Clayey Sand for Use in Landmine Detonation Computational Analysis, Multidiscip. Model. Mater. Struct., 2009, 5(4), p 311–344
M. Grujicic, B. Pandurangan, N. Coutris, B.A. Cheeseman, W.N. Roy, and R.R. Skaggs, Computer-Simulations Based Development of a High Strain-Rate, Large-Deformation, High-Pressure Material Model for STANAG 4569 Sandy Gravel, Soil Dyn. Earthq. Eng., 2008, 28, p 1045–1062
M. Grujicic, B. Pandurangan, N. Coutris, B.A. Cheeseman, W.N. Roy, and R.R. Skaggs, Derivation, Parameterization and Validation of a Sandy-Clay Material Model for Use in Landmine Detonation Computational Analyses, J. Mater. Eng. Perform., 2010, 10(3), p 434–450
M. Grujicic, T. He, B. Pandurangan, W.C. Bell, N. Coutris, B.A. Cheeseman, W.N. Roy, and R.R. Skaggs, Development, Parameterization and Validation of a Visco-Plastic Material Model for Sand with Different Levels of Water Saturation, J. Mater. Des. Appl., 2009, 223, p 63–81
H.J. Qi and M.C. Boyce, Stress-Strain Behavior of Thermoplastic Polyurethanes, Mech. Mater., 2005, 37, p 817–839
A.V. Amirkhizi, J. Isaacs, J. McGee, and S. Nemat-Nasser, An Experimentally-based Viscoelastic Constitutive Model for Polyurea, Including Pressure and Temperature Effects, Philos. Mag., 2006, 86, p 5847–5866
C. Li and J. Lua, A Hyper-Viscoelastic Constitutive Model for Polyurea, Mater. Lett., 2009, 63, p 877–880
T. Jiao, R.J. Clifton, and S.E. Grunschel, Pressure-Sensitivity and Constitutive Modeling of an Elastomer at High Strain Rates, 16th APS Topical Conference on Shock Compression of Condensed Matter, June 28–July 3, 2009
T.M. El Sayed, “Constitutive Models for Polymers and Soft Biological Tissues,” Ph.D. Thesis, California Institute of Technology, 2008
W. Mock, S. Bartyczak, G. Lee, J. Fedderlym, and K. Jordan, Dynamic Properties of Polyurea 1000, Shock Compression of Condensed Matter, American Institute for Physics, 2009, p 1241–1244
J. Shim and D. Mohr, Rate Dependent Finite Strain Constitutive Model of Polyurea, Int. J. Plast., 2011, 27, p 868–886
L.M. Yang, V.P.W. Shim, and C.T. Lim, A Visco-Hyperelastic Approach to Modeling the Constitutive Behavior of Rubber, Int. J. Impact Eng., 2000, 24, p 545–560
V.P.W. Shim, L.M. Yang, C.T. Lim, and P.H. Law, A Visco-Hyperelastic Constitutive Model to Characterize Both Tensile and Compressive Behavior of Rubber, J. Appl. Polym. Sci., 2004, 92, p 523–531
M.S. Hoo Fatt and X. Ouyang, Integral-based Constitutive Equation for Rubber at High Strain Rates, Int. J. Solids Struct., 2007, 44, p 6491–6506
J.S. Bergström and M.C. Boyce, Constitutive Modeling of the Large Strain Time-Dependent Behavior of Elastomers, J. Mech. Phys. Solids, 1998, 46, p 931–954
N. Huber and C. Tsakmakis, Finite Deformation Viscoelasticity Laws, Mech. Mater., 2000, 32, p 1–18
Y. Tomita, K. Azuma, and M. Naito, Computational Evaluation of Strain-Rate-Dependent Deformation Behavior of Rubber and Carbon-Black-Filled Rubber Under Monotonic and Cyclic Straining, Int. J. Mech. Sci., 2008, 50, p 856–868
M. Johlitz, H. Steeb, S. Diebels, A. Chatzouridou, J. Batal, and W. Possart, Experimental and Theoretical Investigation of Nonlinear Viscoelastic Polyurethane Systems, J. Mater. Sci., 2007, 42, p 9894–9904
E.M. Arruda and M.C. Boyce, A 3-Dimensional Constitutive Model for the Large Stretch Behavior of Rubber Elastic Materials, J. Mech. Phys. Solids, 1993, 41, p 389–412
C.M. Roland, Network Recovery from Uniaxial Extension I: Elastic Equilibrium, Rubber Chem. Technol., 1989, 62, p 863–879
A.R. Johnson, C.J. Quigley, and C.E. Freese, A Viscohyperelastic Finite Element Model for Rubber, Comput. Methods Appl. Mech. Eng., 1995, 127, p 163–180
S.J. Quintavalla and S.H. Johnson, Extension of the Bergstrom-Boyce Model to High Strain Rates, Rubber Chem. Technol., 2004, 77, p 972–981
J.S. Bergström and L.B. Hilbert, A Constitutive Model of Predicting the Large Deformation Thermomechanical Behavior of Fluoropolymers, Mech. Mater., 2005, 37, p 899–913
P. Areias and K. Matous, Finite Element Formulation for Modeling Nonlinear Viscoelastic Elastomers, Comput. Methods Appl. Mech. Eng., 2008, 197, p 4702–4717
A.F.M.S. Amin, M.S. Alam, and Y. Okui, An Improved Hyperelasticity Relation in Modeling Viscoelasticity Response of Natural and High Damping Rubbers in Compression: Experiments, Parameter Identification and Numerical Verification, Mech. Mater., 2002, 34, p 75–95
G. Palm, R.B. Dupaix, and J. Castro, Large Strain Mechanical Behavior of Poly(methyl methacrylate) (PMMA) Near the Glass Transition Temperature, J. Eng. Mater. Technol., 2006, 128, p 559–563
A. Khan and H. Zhang, Finite Deformation of a Polymer: Experiments and Modeling, Int. J. Plast., 2001, 17, p 1167–1188
O.U. Colak, Modeling Deformation Behavior of Polymers with Viscoplasticity Theory Based on Overstress, Int. J. Plast., 2005, 21, p 145–160
A.F.M.S. Amin, A. Lion, S. Sekita, and Y. Okui, Nonlinear Dependence of Viscosity in Modeling the Rate-Dependent Response of Natural and High Damping Rubbers in Compression and Shear: Experimental Identification and Numerical Verification, Int. J. Plast., 2006, 22, p 1610–1657
A.S. Khan, O. Lopez-Pamies, and R. Kazmi, Thermo-Mechanical Large Deformation Response and Constitutive Modeling of Viscoelastic Polymers Over a Wide Range of Strain Rates and Temperatures, Int. J. Plast., 2006, 22, p 581–601
M.S. Hoo Fatt and X. Ouyang, Three-Dimensional Constitutive Equations for Styrene Butadiene Rubber at High Strain Rates, Mech. Mater., 2008, 40, p 1–16
L. Anand and N.M. Ames, On Modeling the Micro-Indentation Response of an Amorphous Polymer, Int. J. Plast., 2006, 22, p 1123–1170
M.E. Gurtin, E. Fried, and L. Anand, The Mechanics and Thermodynamics of Continua, Cambridge University Press, New York, NY, 2010, p 293
MATLAB, Version 8.0.0.783, R2012b, The MathWorks Inc., MA
ABAQUS Version 6.10EF, User Documentation, Dassault Systems, 2011
M. Grujicic, B. Pandurangan, W.C. Bell, and S. Bagheri, Shock-Wave Attenuation and Energy-Dissipation Potential of Granular Materials, J. Mater. Eng. Perform., 2012, 21, p 167–179
L. Davison, Fundamentals of Shock-Wave Propagation in Solids, Springer-Verlag, Heidelberg, 2008, ISBN 978-3-540-74568-6
M. Grujicic, B. Pandurangan, J.S. Snipes, C-F.Yen, and B.A. Cheeseman, Multi-Length Scale Enriched Continuum-Level Material Model for Kevlar®-Fiber Reinforced Polymer-Matrix Composites, J. Mater. Eng. Perform., 2013, 22, p 681–695
Acknowledgments
The material presented in this paper is based on work supported by the Office of Naval Research (ONR) research contract entitled “Elastomeric Polymer-By-Design to Protect the Warfighter Against Traumatic Brain Injury by Diverting the Blast Induced Shock Waves from the Head,” Contract Number 4036-CU-ONR-1125 as funded through the Pennsylvania State University. The authors are indebted to Dr. Roshdy Barsoum of ONR for continuing support and interest in the present work.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Grujicic, M., Snipes, J.S., Galgalikar, R. et al. Material-Model-Based Determination of the Shock-Hugoniot Relations in Nanosegregated Polyurea. J. of Materi Eng and Perform 23, 357–371 (2014). https://doi.org/10.1007/s11665-013-0769-7
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11665-013-0769-7