Ballistic impact onto flexible woven textile fabrics is a complicated multi-scale problem given the structural hierarchy of the materials, anisotropic material behavior, projectile geometry–fabric interactions, impact velocity and boundary conditions. Although this subject has been an active area of research for decades, the fundamental mechanisms, such as material failure, dynamic response and multi-axial loading occurring at the lower length scales during impact, are not well understood. This paper reviews the recent advances in modeling and experiments of Kevlar ballistic fibrils, fibers, yarns and flexible woven textile fabrics pertinent to the deformation modes occurring during impact and serves to identify topics worthy of further investigation that will advance the basic understanding of the phenomena governing transverse impact. This review also explores aspects such as homogeneous versus heterogeneous behavior of yarns consisting of individual fibers and the inelastic transverse behavior of the fiber, which is not considered in the previous review papers on this topic.
KimJMcDonoughWGBlairW. The modified-single fiber test: a methodology for monitoring ballistic performance. J Appl Polym Sci2008; 108: 876–886.
2.
KrishnanKSockalingamSBansalS. Numerical simulation of ceramic composite armor subjected to ballistic impact. Composites Part B2010; 41: 583–593.
3.
ShardaJDeenadayaluCMobasherB. Modeling of multilayer composite fabrics for gas turbine engine containment systems. J Aerosp Eng2006; 19: 38–45.
4.
ChocronSFigueroaEKingN. Modeling and validation of full fabric targets under ballistic impact. Composites Sci Technol2010; 70: 2012–2022.
5.
NilakantanGMerrillRLKeefeM. Experimental investigation of the role of frictional yarn pull-out and windowing on the probabilistic impact response of Kevlar fabrics. Composites Part B2015; 68: 215–229.
6.
Nilakantan G, Keefe M, Gillespie JW Jr, et al. An experimental and numerical study of the impact response (V50) of flexible plain weave fabrics: Accounting for statistical distributions of yarn strength. In: the 1st joint American-Canadian international conference on composites and the 24th annual ASC technical conference, University of Delaware, Newark, USA, September 2009.
7.
SockalingamSGillespieJWJrKeefeMFiber-level tow modeling of Kevlar KM2 subjected to high velocity impact. In: AlbersEBeckwithRCatesSW (eds). SAMPE, USA: Seattle, WA, 2014, pp. 2–5.
8.
NortholtMVan AartsenJ. On the crystal and molecular structure of poly‐(p‐phenylene terephthalamide). J Polym Sci Polym Lett1973; 11: 333–337.
9.
NortholtM. X-ray diffraction study of poly (p-phenylene terephthalamide) fibres. Eur Polym J1974; 10: 799–804.
10.
TashiroKKobayashiMTadokoroH. Elastic moduli and molecular structures of several crystalline polymers, including aromatic polyamides. Macromolecules1977; 10: 413–420.
11.
YangHH. Kevlar aramid fiber, New York: Wiley, 1993.
12.
BunnCW. The crystal structure of long-chain normal paraffin hydrocarbons. The “shape” of the< CH2 group. Trans Faraday Soc1939; 35: 482–491.
13.
BankMKrimmS. Lattice‐frequency studies of crystalline and fold structure in polyethylene. J Appl Phys1968; 39: 4951–4958.
14.
SetoTHaraTTanakaK. Phase transformation and deformation processes in oriented polyethylene. Jpn J Appl Phys1968; 7: 31–31.
15.
BassettDBlockSPiermariniG. A high‐pressure phase of polyethylene and chain‐extended growth. J Appl Phys1974; 45: 4146–4150.
16.
PrevorsekDCKwonYDChinHB. Analysis of the temperature rise in the projectile and extended chain polyethylene fiber composite armor during ballistic impact and penetration. Polym Eng Sci1994; 34: 141–52.
17.
CheesemanBABogettiTA. Ballistic impact into fabric and compliant composite laminates. Compos Struct2003; 61: 161–173.
18.
TabieiANilakantanG. Ballistic impact of dry woven fabric composites: a review. Appl Mech Rev2008; 61: 010801–010801.
19.
DavidNGaoXZhengJ. Ballistic resistant body armor: contemporary and prospective materials and related protection mechanisms. Appl Mech Rev2009; 62: 050802–050802.
20.
HaqueBZGGillespieJW. A new penetration equation for ballistic limit analysis. J Thermoplast Compos Mater2013; 28: 0892705713495430–0892705713495430.
21.
SmithJCMcCrackinFLSchieferHF. Stress-strain relationships in yarns subjected to rapid impact loading: part V: wave propagation in long textile yarns impacted transversely. Text Res J1958; 28: 288–302.
22.
SmithJCBlandfordJMSchieferHF. Stress-strain relationships in yarns subjected to rapid impact loading part VI: velocities of strain waves resulting from impact. Text Res J1960; 30: 752–760.
23.
MamivandMLiaghatGH. A model for ballistic impact on multi-layer fabric targets. Int J Impact Eng2010; 37: 806–812.
WangL. Foundations of stress waves, Oxford: Elsevier, 2011.
26.
SongBParkHLuW. Transverse impact response of a linear elastic ballistic fiber yarn. J Appl Mech2011; 78: 051023-1–051023-9.
27.
WalkerJDChocronS. Why impacted yarns break at lower speed than classical theory predicts. J Appl Mech2011; 78: 051021–051021.
28.
ChocronSKirchdoerferTKingN. Modeling of fabric impact with high speed imaging and nickel-chromium wires validation. J Appl Mech2011; 78: 051007–051007.
29.
Leigh PhoenixSPorwalPK. A new membrane model for the ballistic impact response and V50 performance of multi-ply fibrous systems. Int J Solids Struct2003; 40: 6723–6765.
30.
PorwalPKPhoenixSL. Modeling system effects in ballistic impact into multi-layered fibrous materials for soft body armor. Int J Fract2005; 135: 217–249.
31.
Cunniff PM. Dimensionless parameters for optimization of textile-based body armor systems. In: proceedings of the 18th international symposium on ballistics, San Antonio, Texas, 1999, pp.1303–1310.
32.
AfshariMChenPKotekR. Relationship between tensile properties and ballistic performance of poly (ethylene naphthalate) woven and nonwoven fabrics. J Appl Polym Sci2012; 125: 2271–2280.
33.
KarthikeyanKRussellBFleckN. The effect of shear strength on the ballistic response of laminated composite plates. Eur J Mech A Solids2013; 42: 35–53.
34.
Standard N. I. J. 0101.06:2008. Ballistic resistance of body armor.
35.
DongZSunCT. Testing and modeling of yarn pull-out in plain woven Kevlar fabrics. Composites Part A2009; 40: 1863–1869.
36.
CunniffPM. An analysis of the system effects in woven fabrics under ballistic impact. Text Res J1992; 62: 495–509.
37.
ChocronSRanjan SamantKNichollsAE. Measurement of strain in fabrics under ballistic impact using embedded nichrome wires. Part I: technique. Int J Impact Eng2009; 36: 1296–1302.
38.
ChocronSAndersonCEJrSamantKR. Measurement of strain in fabrics under ballistic impact using embedded nichrome wires, part II: results and analysis. Int J Impact Eng2010; 37: 69–81.
39.
ChocronSKingNBiggerR. Impacts and waves in Dyneema® HB80 strips and laminates. J Appl Mech2013; 80: 031806–031806.
40.
TanVBCLimCTCheongCH. Perforation of high-strength fabric by projectiles of different geometry. Int J Impact Eng2003; 28: 207–222.
41.
TalebiHWongSVHamoudaAMS. Finite element evaluation of projectile nose angle effects in ballistic perforation of high strength fabric. Compos Struct2009; 87: 314–320.
42.
MontgomeryTGradyPTomasinoC. The effects of projectile geometry on the performance of ballistic fabrics. Text Res J1982; 52: 442–450.
43.
LimCTanVCheongC. Perforation of high-strength double-ply fabric system by varying shaped projectiles. Int J Impact Eng2002; 27: 577–591.
44.
ProsserRACohenSHSegarsRA. Heat as a factor in the penetration of cloth ballistic panels by 0.22 caliber projectiles. Text Res J2000; 70: 709–722.
45.
TanVLimCCheongC. Perforation of high-strength fabric by projectiles of different geometry. Int J Impact Eng2003; 28: 207–222.
46.
ChenXZhuFWellsG. An analytical model for ballistic impact on textile based body armour. Composites Part B2013; 45: 1508–1514.
47.
ShimVGuoYTanV. Response of woven and laminated high-strength fabric to oblique impact. Int J Impact Eng2012; 48: 87–97.
48.
Shockey DA, Erlich DC and Simons JW. Lightweight fragment barriers for commercial aircraft. In: proceedings of the 18th international symposium on ballistics, San Antonio, TX, 15–19 November 1999, pp.1192–1199.
49.
ZengXSShimVPWTanVBC. Influence of boundary conditions on the ballistic performance of high-strength fabric targets. Int J Impact Eng2005; 32: 631–642.
50.
ParsonsEMWeerasooriyaTSarvaS. Impact of woven fabric: experiments and mesostructure-based continuum-level simulations. J Mech Phys Solids2010; 58: 1995–2021.
51.
ShimekMEFahrentholdEP. Effects of weave type on ballistic performance of fabrics. AIAA J2012; 50: 2558–2565.
52.
KędzierskiPPopławskiAGieletaR. Experimental and numerical investigation of fabric impact behavior. Composites Part B2014; 69: 452–459.
53.
LimJSLeeBHLeeCB. Effect of the weaving density of aramid fabrics on their resistance to ballistic impacts. Engineering2012; 4: 944–944.
54.
LimJS. Ballistic behavior of Heracron®-based composites: effect of the number multifilaments on high-speed projectiles. Model Numer Simulat Mater Sci2013; 3: 84–84.
55.
ChenXZhouYWellsG. Numerical and experimental investigations into ballistic performance of hybrid fabric panels. Composites Part B2014; 58: 35–42.
56.
DongZManimalaJMSunC. Mechanical behavior of silica nanoparticle-impregnated Kevlar fabrics. J Mech Mater Struct2010; 5: 529–548.
57.
ShimVPWLimCTFooKJ. Dynamic mechanical properties of fabric armour. Int J Impact Eng2001; 25: 1–15.
58.
ZhuDMobasherBRajanSD. Dynamic tensile testing of Kevlar 49 fabrics. J Mater Civ Eng2010; 23: 230–239.
59.
PhoenixSLSkeltonJ. Transverse compressive moduli and yield behavior of some orthotropic, high-modulus filaments. Text Res J1974; 44: 934–940.
60.
Raftenburg MN, Scheidler NJ and Moy P. Transverse compression response of a multi-ply Kevlar vest. Technical Report ARL-TR-3343. Army Research Laboratory. Aberdeen Proving Ground, MD, 2004.
61.
ManimalaJMSunC. Investigation of failure in Kevlar fabric under transverse indentation using a homogenized continuum constitutive model. Text Res J2014; 84: 388–398.
62.
LomovSVWillemsAVerpoestI. Picture frame test of woven composite reinforcements with a full-field strain registration. Text Res J2006; 76: 243–252.
63.
ZhuDMobasherBVaidyaA. Mechanical behaviors of Kevlar 49 fabric subjected to uniaxial, biaxial tension and in-plane large shear deformation. Composites Sci Technol2013; 74: 121–130.
64.
BadelPVidal-SalléEBoisseP. Computational determination of in-plane shear mechanical behaviour of textile composite reinforcements. Comput Mater Sci2007; 40: 439–448.
65.
Ha-MinhCImadAKanitT. Numerical analysis of a ballistic impact on textile fabric. Int J Mech Sci2013; 69: 32–39.
66.
SongBLuW. Effect of twist on transverse impact response of ballistic fiber yarns. Int J Impact Eng2015; 85: 1–4.
67.
BazhenovSDukhovskiiIKovalevP. The fracture of SVM aramide fibers upon a high-velocity transverse impact. Polym Sci Ser A Chem Phys2001; 43: 61–71.
68.
CarrD. Failure mechanisms of yarns subjected to ballistic impact. J Mater Sci Lett1999; 18: 585–588.
69.
Field JE and Sun Q. High-speed photographic study of impact on fibers and woven fabrics. In: 19th international congress on high-speed photography and photonics, International Society for Optics and Photonics, 1991, pp.703–712.
70.
Heru Utomo B and Broos J. Dynamic material behavior determination using single fiber impact. In: 25th conference and exposition on structural dynamics (IMAC-XXV), Orlando, Florida, USA, 19–22 February 2007.
71.
Mulkern TJ and Raftenberg MN. Kevlar KM2 yarn and fabric strength under quasi-static tension Technical Report ARL-TR-2865. Army Research Laboratory. Aberdeen Proving Ground, MD, 2002.
72.
NilakantanGObaidAAKeefeM. Experimental evaluation and statistical characterization of the strength and strain energy density distribution of Kevlar KM2 yarns: exploring length-scale and weaving effects. J Compos Mater2011; 45: 1749–1769.
73.
TanVZengXShimV. Characterization and constitutive modeling of aramid fibers at high strain rates. Int J Impact Eng2008; 35: 1303–1313.
74.
ZhuDMobasherBErniJ. Strain rate and gage length effects on tensile behavior of Kevlar 49 single yarn. Composites Part A2012; 43: 2021–2029.
75.
DoorakiBFNemesJBolducM. Study of parameters affecting the strength of yarns. J Phys IV2006; 134: 1183–1188.
76.
LanguerandDZhangHMurthyN. Inelastic behavior and fracture of high modulus polymeric fiber bundles at high strain-rates. Mater Sci Eng A2009; 500: 216–224.
77.
KirkwoodKMKirkwoodJELeeYS. Yarn pull-out as a mechanism for dissipating ballistic impact energy in Kevlar® KM-2 fabric part I: quasi-static characterization of yarn pull-out. Text Res J2004; 74: 920–928.
78.
KirkwoodJEKirkwoodKMLeeYS. Yarn pull-out as a mechanism for dissipating ballistic impact energy in Kevlar® KM-2 fabric part II: predicting ballistic performance. Text Res J2004; 74: 939–948.
79.
ZhuDSoranakomCMobasherB. Experimental study and modeling of single yarn pull-out behavior of Kevlar® 49 fabric. Composites Part A2011; 42: 868–879.
80.
BilisikK. Properties of yarn pull-out in para-aramid fabric structure and analysis by statistical model. Composites Part A2011; 42: 1930–1942.
81.
GawandiAThostensonETGilllespieJWJr. Tow pullout behavior of polymer-coated Kevlar fabric. J Mater Sci2011; 46: 77–89.
82.
NilakantanGGillespieJW. Yarn pull-out behavior of plain woven Kevlar fabrics: effect of yarn sizing, pullout rate, and fabric pre-tension. Compos Struct2013; 101: 215–224.
83.
GuoZHongJZhengJ. Loading rate effects on dynamic out-of-plane yarn pull-out. Text Res J2014; 84: 1708–1719.
84.
GuoZHongJZhengJ. Out-of-plane effects on dynamic pull-out of p-phenylene terephthalamide yarns. Text Res J2014; 85: 140–149.
85.
RaoYFarrisRJ. A modeling and experimental study of the influence of twist on the mechanical properties of high‐performance fiber yarns. J Appl Polym Sci2000; 77: 1938–1949.
86.
ChuYChenXWangQ. An investigation on sol-gel treatment to aramid yarn to increase inter-yarn friction. Appl Surf Sci2014; 320: 710–717.
87.
ChengMChenWWeerasooriyaT. Experimental investigation of the transverse mechanical properties of a single Kevlar® KM2 fiber. Int J Solids Struct2004; 41: 6215–6232.
88.
ChengMChenWWeerasooriyaT. Mechanical properties of Kevlar® KM2 single fiber. J Eng Mater Technol2005; 127: 197–203.
89.
LealAADeitzelJMGillespieJW. Compressive strength analysis for high performance fibers with different modulus in tension and compression. J Compos Mater2009; 43: 661–674.
Kim J, Heckert N, McDonough W, et al. Statistical characterization of single PPTA fiber tensile properties from high strain rate tests. In: Song B, Casem D and Kimberley J (eds) Dynamic behavior of materials, volume 1. 2015, pp.5–8. Bethel, CT: Springer International Publishing.
92.
LimJChenWWZhengJQ. Dynamic small strain measurements of Kevlar® 129 single fibers with a miniaturized tension Kolsky bar. Polym Test2010; 29: 701–705.
93.
LimJZhengJMastersK. Mechanical behavior of A265 single fibers. J Mater Sci2010; 45: 652–661.
94.
HudspethMClausBParabN. In situ visual observation of fracture processes in several high-performance fibers. J Dyn Behav Mater2015; 1: 55–64.
95.
KimJHAlan HeckertNLeighSD. Statistical analysis of PPTA fiber strengths measured under high strain rate condition. Composites Sci Technol2014; 98: 93–99.
96.
LimJZhengJQMastersK. Effects of gage length, loading rates, and damage on the strength of PPTA fibers. Int J Impact Eng2011; 38: 219–227.
97.
SchwartzPNetravaliASembachS. Effects of strain rate and gauge length on the failure of ultra-high strength polyethylene fibers. Text Res J1986; 56: 502–508.
98.
KawabataS. Measurement of the transverse mechanical properties of high-performance fibres. J Text Inst1990; 81: 432–447.
99.
SingletaryJDavisHRamasubramanianMK. The transverse compression of PPTA fibers part I single fiber transverse compression testing. J Mater Sci2000; 35: 573–581.
100.
SingletaryJDavisHSongY. The transverse compression of PPTA fibers Part II Fiber transverse structure. J Mater Sci2000; 35: 583–592.
101.
RuanFBaoL. Mechanical enhancement of UHMWPE fibers by coating with carbon nanoparticles. Fibers Polym2014; 15: 723–728.
102.
GuoZCasemDHudspethM. Transverse compression of two high-performance ballistic fibers. Text Res J2015, pp. 1–10.
103.
Wollbrett‐BlitzJJoannèsSBruantR. Multiaxial mechanical behavior of aramid fibers and identification of skin/core structure from single fiber transverse compression testing. J Polym Sci Part B Polym Phys2015; 54: 374–384.
104.
LealAADeitzelJMGillespieJW. Assessment of compressive properties of high performance organic fibers. Composites Sci Technol2007; 67: 2786–2794.
105.
M’Ewen E.XLI. Stresses in elastic cylinders in contact along a generatrix (including the effect of tangential friction). Philos Mag Ser 71949; 40: 454–459.
106.
HadleyDWWardIMWardJ. The transverse compression of anisotropic fibre monofilaments. Proc R Soc London Ser A1965; 285: 275–286.
107.
KotaniTSweeneyJWardIM. The measurement of transverse mechanical properties of polymer fibres. J Mater Sci1994; 29: 5551–5558.
108.
PinnockPRWardIMWolfeJM. The compression of anisotropic fibre monofilaments. II. Proc R Soc London Ser A1966; 291: 267–278.
109.
TimoshenkoSGoodierJN. Theory of elasticity, New York: McGraw-Hill, 1951.
110.
ObaidAAYarlagaddaSGillespieJWJr. Combined effects of Kink bands and hygrothermal conditioning on tensile strength of polyarylate LCP and aramid fibers. J Compos Mater2015; 50: 339–350.
111.
KollárLPSpringerGS. Mechanics of composite structures, Cambridge: Cambridge University Press, 2003.
112.
TsaiCDanielI. Determination of shear modulus of single fibers. Exp Mech1999; 39: 284–286.
113.
Sanborn BD and Weerasooriya T. Effect of strain rates and pre-twist on tensile strength of Kevlar KM2 single fiber. Technical Report ARL-TR-6403. Army Research Laboratory. Aberdeen Proving Ground, MD, 2013.
114.
SanbornBWeerasooriyaT. Quantifying damage at multiple loading rates to Kevlar KM2 fibers due to weaving, finishing, and pre-twist. Int J Impact Eng2014; 71: 50–59.
115.
HudspethMNieXChenW. Dynamic failure of Dyneema SK76 single fibers under biaxial shear/tension. Polymer2012; 53: 5568–5574.
116.
HudspethMLiDSpatolaJ. The effects of off-axis transverse deflection loading on the failure strain of various high-performance fibers. Text Res J.. 2016; 86(9): 897–910.
117.
HudspethMChenWZhengJ. Why the Smith theory over-predicts instant rupture velocities during fiber transverse impact. Text Res J.. Epub ahead of print 2015. DOI: 10.1177/0040517515586158.
118.
RaoYWaddonAJFarrisRJ. The evolution of structure and properties in poly(p-phenylene terephthalamide) fibers. Polymer2001; 42: 5925–5935.
119.
McAllisterQPGillespieJWVanLandinghamMR. Evaluation of the three-dimensional properties of Kevlar across length scales. J Mater Res2012; 27: 1824–1837.
120.
McAllisterQPGillespieJWJrVanLandinghamMR. The influence of surface microstructure on the scratch characteristics of Kevlar fibers. J Mater Sci2013; 48: 292–1302.
121.
LiSMcGhieATangS. Comparative study of the internal structures of Kevlar and spider silk by atomic force microscopy. J Vacuum Sci Technol A1994; 12: 1891–1894.
122.
McAllister QP. The energy dissipative mechanisms of the particle-fiber interface in a textile composite. PhD Dissertation, University of Delaware, 2013.
123.
ColeDPStrawheckerKE. An improved instrumented indentation technique for single microfibers. J Mater Res2014; 29: 1104–1112.
124.
McAllisterQPGillespieJWVanLandinghamMR. The energy dissipative mechanisms of particle-fiber interactions in a textile composite. J Compos Mater2013; 48: 3553–3567.
125.
McAllisterQPGillespieJWJrVanLandinghamMR. The sub-micron scale energy dissipative deformation mechanisms of Kevlar fibrils. J Mater Sci2013; 48: 6245–6261.
TanVTayTTeoW. Strengthening fabric armour with silica colloidal suspensions. Int J Solids Struct2005; 42: 1561–1576.
128.
LaBarreECalderon-ColonXMorrisM. Effect of a carbon nanotube coating on friction and impact performance of Kevlar. J Mater Sci2015; 50: 5431–5442.
129.
McDanielPBDeitzelJMGillespieJW. Structural hierarchy and surface morphology of highly drawn ultra high molecular weight polyethylene fibers studied by atomic force microscopy and wide angle X-ray diffraction. Polymer2015; 69: 148–158.
130.
PenningsA. Bundle‐like nucleation and longitudinal growth of fibrillar polymer crystals from flowing solutions. J Polym Sci Polym Symposia1977; 59: 55–86.
131.
StrawheckerKEColeDP. Morphological and local mechanical surface characterization of ballistic fibers via AFM. J Appl Polym Sci2014; 131: 40880 (1–12)–40880 (1–12).
132.
MarissenR. Design with ultra strong polyethylene fibers. Mater Sci Appl2011; 2: 319–319.
133.
IvanovITabieiA. Loosely woven fabric model with viscoelastic crimped fibres for ballistic impact simulations. Int J Numer Methods Eng2004; 61: 1565–1583.
134.
KingMJJearanaisilawongPSocrateS. A continuum constitutive model for the mechanical behavior of woven fabrics. Int J Solids Struct2005; 42: 3867–3896.
135.
ParsonsEMKingMJSocrateS. Modeling yarn slip in woven fabric at the continuum level: simulations of ballistic impact. J Mech Phys Solids2013; 61: 265–292.
136.
ShahkaramiAVaziriR. A continuum shell finite element model for impact simulation of woven fabrics. Int J Impact Eng2007; 34: 104–119.
137.
LimCTShimVPWNgYH. Finite-element modeling of the ballistic impact of fabric armor. Int J Impact Eng2003; 28: 13–31.
138.
BansalSMobasherBRajanS. Development of fabric constitutive behavior for use in modeling engine fan blade-out events. J Aerospace Eng2009; 22: 249–259.
139.
StahleckerZMobasherBRajanSD. Development of reliable modeling methodologies for engine fan blade out containment analysis. Part II: finite element analysis. Int J Impact Eng2009; 36: 447–459.
140.
NadlerBPapadopoulosPSteigmannDJ. Multiscale constitutive modeling and numerical simulation of fabric material. Int J Solids Struct2006; 43: 206–221.
GrujicicMBellWCArakereG. Development of a meso-scale material model for ballistic fabric and its use in flexible-armor protection systems. J Mater Eng Perform2010; 19: 22–39.
143.
ErolOWetzelEDKeefeM. Simulation of a textile sleeve on a manikin arm undergoing elbow flexion: effect of arm-sleeve friction. J Text Inst2014; 106: 1135–1146.
144.
DuanYKeefeMBogettiTA. Modeling friction effects on the ballistic impact behavior of a single-ply high-strength fabric. Int J Impact Eng2005; 31: 996–1012.
145.
NilakantanGKeefeMBogettiTA. On the finite element analysis of woven fabric impact using multiscale modeling techniques. Int J Solids Struct2010; 47: 2300–2315.
146.
WangYMiaoYSwensonD. Digital element approach for simulating impact and penetration of textiles. Int J Impact Eng2010; 37: 552–560.
147.
GrujicicMHariharanAPanduranganB. Fiber-level modeling of dynamic strength of Kevlar KM2 ballistic fabric. J Mater Eng Perform2012; 21: 1107–1119.
148.
NilakantanG. Filament-level modeling of Kevlar KM2 yarns for ballistic impact studies. Compos Struct2013; 104: 1–13.
149.
HudspethMAgarwalAAndrewsB. Degradation of yarns recovered from soft-armor targets subjected to multiple ballistic impacts. Composites Part A2014; 58: 98–106.
150.
FreestonWDClausWD. Strain-wave reflections during ballistic impact of fabric panels. Text Res J1973; 43: 348–351.
151.
RoylanceD. Wave propagation in a viscoelastic fiber subjected to transverse impact. J Appl Mech1973; 40: 143–148.
152.
Cunniff P, Ting CTJ and Roylance D. Numerical characterization of the effects of transverse yarn interaction on textile ballistic response, http://web.mit.edu/roylance/www/Ting_98.pdf (1998, accessed 3 November 2015).
153.
TanVChingT. Computational simulation of fabric armour subjected to ballistic impacts. Int J Impact Eng2006; 32: 1737–1751.
154.
ShimVPWTanVBCTayTE. Modelling deformation and damage characteristics of woven fabric under small projectile impact. Int J Impact Eng1995; 16: 585–605.
155.
ZengXTanVShimV. Modelling inter‐yarn friction in woven fabric armour. Int J Numer Methods Eng2006; 66: 1309–1330.
156.
NovotnyWRCepušEShahkaramiA. Numerical investigation of the ballistic efficiency of multi-ply fabric armours during the early stages of impact. Int J Impact Eng2007; 34: 71–88.
157.
Blankenhorn G, Schweizerhof K and Finckh H. Improved numerical investigations of a projectile impact on a textile structure. In: fourth European LS-DYNA users conference, 2003.
158.
RaoMPDuanYKeefeM. Modeling the effects of yarn material properties and friction on the ballistic impact of a plain-weave fabric. Compos Struct2009; 89: 556–566.
159.
NilakantanGWetzelEDBogettiTA. A deterministic finite element analysis of the effects of projectile characteristics on the impact response of fully clamped flexible woven fabrics. Compos Struct2013; 95: 191–201.
DuanYKeefeMBogettiT. A numerical investigation of the influence of friction on energy absorption by a high-strength fabric subjected to ballistic impact. Int J Impact Eng2006; 32: 1299–1312.
162.
DuanYKeefeMBogettiTA. Modeling the role of friction during ballistic impact of a high-strength plain-weave fabric. Compos Struct2005; 68: 331–337.
163.
BarauskasRAbraitien ėA. Computational analysis of impact of a bullet against the multilayer fabrics in LS-DYNA. Int J Impact Eng2007; 34: 1286–1305.
GogineniSGaoXDavidN. Ballistic impact of Twaron CT709® plain weave fabrics. Mech Adv Mater Struct2012; 19: 441–452.
166.
GuB. Ballistic penetration of conically cylindrical steel projectile into plain-woven fabric target–a finite element simulation. J Compos Mater2004; 38: 2049–2074.
167.
SunDChenXLewisE. Finite element simulation of projectile perforation through a ballistic fabric. Text Res J2012; 83: 1489–1499.
168.
JiaXHuangZZuX. Effect of mesoscale and multiscale modeling on the performance of Kevlar woven fabric subjected to ballistic impact: a numerical study. Appl Compos Mater2013; 20: 1195–1214.
169.
Yen C, Scott B, Dehmer P, et al. A comparison between experiment and numerical simulation of fabric ballistic impact. In: proceedings of the 23rd international ballistic symposium, Tarragona, Spain, 2007.
170.
JiangYTabieiASimitsesGJ. A novel micromechanics-based approach to the derivation of constitutive equations for local/global analysis of a plain-weave fabric composite. Composites Sci Technol2000; 60: 1825–1833.
171.
ZohdiTPowellD. Multiscale construction and large-scale simulation of structural fabric undergoing ballistic impact. Comput Methods Appl Mech Eng2006; 195: 94–109.
172.
ZohdiT. Microfibril-based estimates of the ballistic limit of multilayered fabric shielding. Int J Fract2009; 158: 81–88.
173.
XiaWAdeebSMNadlerB. Ballistic performance study of fabric armor based on numerical simulations with multiscale material model. Int J Numer Methods Eng2011; 87: 1007–1024.
174.
XiaWNadlerB. Three-scale modeling and numerical simulations of fabric materials. Int J Eng Sci2011; 49: 229–239.
175.
NilakantanGKeefeMWetzelED. Computational modeling of the probabilistic impact response of flexible fabrics. Compos Struct2011; 93: 3163–3174.
176.
NilakantanGKeefeMWetzelED. Effect of statistical yarn tensile strength on the probabilistic impact response of woven fabrics. Composites Sci Technol2012; 72: 320–329.
177.
GasserABoissePHanklarS. Mechanical behaviour of dry fabric reinforcements. 3D simulations versus biaxial tests. Comput Mater Sci2000; 17: 7–20.
178.
Durville D. Finite element simulation of the mechanical behaviour of textile composites at the mesoscopic scale of individual fibers. In: textile composites and inflatable structures II, Springer Netherlands, 2008.
179.
YuyangMAoJAn YuYEnergy loss due to transverse plastic deformation of fibers in textile fabric impact processes. In: LiuD (ed). Dynamic effects in composites2012, p.103. Lancaster: DEStech Publications, Inc.
180.
Sockalingam S, Gillespie JW Jr and Keefe M. Modeling the transverse compression response of Kevlar KM2. In: proceedings of the American Society for Composites (ASC) 28th technical conference, College Park, PA, USA, 2013.
181.
SockalingamSGillespieJWJrKeefeM. On the transverse compression response of Kevlar KM2 using fiber-level finite element model. Int J Solids Struct2014; 51: 2504–2517.
182.
SockalingamSGillespieJWJrKeefeM. Dynamic modeling of Kevlar KM2 single fiber subjected to transverse impact. Int J Solids Struct2015; 67–68: 297–310.
183.
RecchiaSZhengJQHornerS. Multiscale modeling of randomly interwoven fibers for prediction of KM2 Kevlar yarn strength and damage. Acta Mech2015; 226: 1–10.
184.
SockalingamSBrembleRGillespieJWJr. Transverse compression behavior of Kevlar KM2 single fiber. Composites Part A2016; 81: 271–281.
185.
AllenMPTildesleyDJ. Computer simulation of liquids, Oxford: Oxford University Press, 1987.
186.
ChenCDepaPMaranasJK. Comparison of explicit atom, united atom, and coarse-grained simulations of poly (methyl methacrylate). J Chem Phys2008; 128: 124906–1-12.
187.
GrujicicMBellWGlomskiP. Filament-level modeling of aramid-based high-performance structural materials. J Mater Eng Perform2011; 20: 1401–1413.
188.
GrujicicMGlomskiPPanduranganB. Multi-length scale computational derivation of Kevlar® yarn-level material model. J Mater Sci2011; 46: 4787–4802.
189.
GrujicicMYavariRRamaswamiS. Molecular-level study of the effect of prior axial compression/torsion on the axial-tensile strength of PPTA fibers. J Mater Eng Perform2013; 22: 3269–3287.
190.
SunH. COMPASS: an ab initio force-field optimized for condensed-phase applications overview with details on alkane and benzene compounds. J Phys Chem B1998; 102: 7338–7364.
191.
GreenhalghEBloodworthVIannucciL. Fractographic observations on Dyneema® composites under ballistic impact. Composites Part A2013; 44: 51–62.
192.
Chowdhury SC, Sockalingam S and Gillespie JW Jr. Molecular dynamics modeling of compression kinking in Kevlar. In: SAMPE conference proceedings, Baltimore, MD, USA, 18–21 May 2015.
193.
MayoJWetzelE. Cut resistance and failure of high-performance single fibers. Text Res J2014; 84: 1233–1246.
194.
Thomas JA, Shanaman MT, Lomicka CL, et al. Multiscale modeling of high-strength fibers and fabrics. In: SPIE defense, security, and sensing, International Society for Optics and Photonics, 2012.
195.
LomickaCThomasJLaBarreEImproving ballistic fiber strength: insights from experiment and simulation. In: SongBCasemDKimberleyJ (eds). Dynamic behavior of materials, volume 12014, p.187–193. Bethel: CT Springer International Publishing.
196.
Recchia SS, Pelegri A, Clawson JK, et al. A hierarchical model for Kevlar fiber failure. In: ASME 2013 international mechanical engineering congress and exposition, American Society of Mechanical Engineers, 2013.
197.
Chowdhury SC, Staniszewski J, Martz EM, et al. A computational approach for linking molecular dynamics to finite element simulation of polyethylene fibers. In: American Society of Composites - 30th technical conference, East Lansing, MI, USA, 28-30 September 2015.
198.
BoydRHGeeRHHanJ. Conformational dynamics in bulk polyethylene: a molecular dynamics simulation study. J Chem Phys1994; 101: 788–797.
199.
BrownDClarkeJH. Molecular dynamics simulation of an amorphous polymer under tension. 1. Phenomenology. Macromolecules1991; 24: 2075–2082.
200.
RottlerJRobbinsMO. Growth, microstructure, and failure of crazes in glassy polymers. Phys Rev E2003; 68: 011801–011801.
201.
YamamotoT. Molecular dynamics in fiber formation of polyethylene and large deformation of the fiber. Polymer2013; 54: 3086–3097.
202.
CurgulSVan VlietKJRutledgeGC. Molecular dynamics simulation of size-dependent structural and thermal properties of polymer nanofibers. Macromolecules2007; 40: 8483–8489.
203.
HossainDTschoppMWardD. Molecular dynamics simulations of deformation mechanisms of amorphous polyethylene. Polymer2010; 51: 6071–6083.
204.
MattssonTRLaneJMDCochraneKR. First-principles and classical molecular dynamics simulation of shocked polymers. Phys Rev B2010; 81: 054103–054103.
205.
ChantawansriTLSirkTWByrdEF. Shock Hugoniot calculations of polymers using quantum mechanics and molecular dynamics. J Chem Phys2012; 137: 204901–204901.
206.
SillingSA. Reformulation of elasticity theory for discontinuities and long-range forces. J Mech Phys Solids2000; 48: 175–209.
207.
XuJAskariAWecknerO. Peridynamic analysis of impact damage in composite laminates. J Aerosp Eng2008; 21: 187–194.
