Abstract: This paper presents a numerical study to improve the understanding of the complex subject of penetration and perforation of concrete targets impacted by low-velocity projectiles. The main focus is on the damage mechanisms and the major factors that account for the target resistance of the concrete. An improved continuous surface cap model recently proposed was employed. The model was first equipped with element erosion criteria and was adequately validated by comparisons with ballistic experiments. Comprehensive numerical simulations were carried out where the individual influence of tensile, shear, and volumetric behaviors (pore collapse) of a concrete target on its ballistic performance was investigated. Results demonstrated that cratering on the front face and scabbing on the rear face of the concrete target were mainly dominated by its tensile behavior. The major target resistance came from the second tunneling stage which was primarily governed by the shear and volumetric behaviors of the concrete. Particularly, this study captured the pore collapse-induced damage phenomenon during the high-pressure tunneling stage, which has been extensively reported in experiments but has usually been neglected in previous numerical investigations.

弹体低速侵彻混凝土材料的数值模拟研究：靶体损伤机理及阻力机制新见解

[1]BatzleML, SimmonsG, SiegfriedRW, 1980. Microcrack closure in rocks under stress: direct observation. Journal of Geophysical Research: Solid Earth, 85(B12)‍:‍7072-7090.

[2]BeppuM, MiwaK, ItohM, et al., 2008. Damage evaluation of concrete plates by high-velocity impact. International Journal of Impact Engineering, 35(12):1419-1426.

[3]ChenXW, LiXL, HuangFL, et al., 2008. Normal perforation of reinforced concrete target by rigid projectile. International Journal of Impact Engineering, 35(10):1119-1129.

[4]CuiJ, HaoH, ShiYC, et al., 2017. Experimental study of concrete damage under high hydrostatic pressure. Cement and Concrete Research, 100:140-152.

[5]de MaioU, GrecoF, LeonettiL, et al., 2022. A cohesive fracture model for predicting crack spacing and crack width in reinforced concrete structures. Engineering Failure Analysis, 139:106452.

[6]DurbanD, MasriR, 2004. Dynamic spherical cavity expansion in a pressure sensitive elastoplastic medium. International Journal of Solids and Structures, 41(20):‍5697-5716.

[7]FengJ, SongML, SunWW, et al., 2018. Thick plain concrete targets subjected to high speed penetration of 30CrMnSiNi2A steel projectiles: tests and analyses. International Journal of Impact Engineering, 122:305-317.

[8]ForquinP, AriasA, ZaeraR, 2008. Role of porosity in controlling the mechanical and impact behaviours of cement-based materials. International Journal of Impact Engineering, 35(3):133-146.

[9]ForquinP, SallierL, PontiroliC, 2015. A numerical study on the influence of free water content on the ballistic performances of plain concrete targets. Mechanics of Materials, 89:176-189.

[10]ForrestalMJ, AltmanBS, CargileJD, et al., 1994. An empirical equation for penetration depth of ogive-nose projectiles into concrete targets. International Journal of Impact Engineering, 15(4):395-405.

[11]ForrestalMJ, FrewDJ, HanchakSJ, et al., 1996. Penetration of grout and concrete targets with ogive-nose steel projectiles. International Journal of Impact Engineering, 18(5):465-476.

[12]GoswamiA, AdhikarySD, LiB, 2019. Predicting the punching shear failure of concrete slabs under low velocity impact loading. Engineering Structures, 184:37-51.

[13]HanchakSJ, ForrestalMJ, YoungER, et al., 1992. Perforation of concrete slabs with 48 MPa (7 ksi) and 140 MPa (20 ksi) unconfined compressive strengths. International Journal of Impact Engineering, 12(1):1-7.

[14]HolmquistTJ, JohnsonGR, CookWH, 1993. A computational constitutive model for concrete subjected to large strains, high strain rates, and high pressures. Proceedings of the 14th International Symposium on Ballistics, p.591-600.

[15]HouZG, 2006. Research on Concrete Strength Under Triaxial Stresses. MS Thesis, Hebei University of Technology, Tianjin, China(in Chinese).

[16]HuangFL, WuHJ, JinQK, et al., 2005. A numerical simulation on the perforation of reinforced concrete targets. International Journal of Impact Engineering, 32(1-4):‍173-187.

[17]HuangXP, KongXZ, ChenZY, et al., 2020. A computational constitutive model for rock in hydrocode. International Journal of Impact Engineering, 145:103687.

[18]HuangXP, KongXZ, ChenZY, et al., 2021. A plastic-damage model for rock-like materials focused on damage mechanisms under high pressure. Computers and Geotechnics, 137:104263.

[19]KongXZ, FangQ, WuH, et al., 2016. Numerical predictions of cratering and scabbing in concrete slabs subjected to projectile impact using a modified version of HJC material model. International Journal of Impact Engineering, 95:61-71.

[20]KongXZ, WuH, FangQ, et al., 2017a. Rigid and eroding projectile penetration into concrete targets based on an extended dynamic cavity expansion model. International Journal of Impact Engineering, 100:13-22.

[21]KongXZ, WuH, FangQ, et al., 2017b. Projectile penetration into mortar targets with a broad range of striking velocities: test and analyses. International Journal of Impact Engineering, 106:18-29.

[22]KongXZ, FangQ, ChenL, et al., 2018. A new material model for concrete subjected to intense dynamic loadings. International Journal of Impact Engineering, 120:60-78.

[23]LeppänenJ, 2006. Concrete subjected to projectile and fragment impacts: modelling of crack softening and strain rate dependency in tension. International Journal of Impact Engineering, 32(11):1828-1841.

[24]LiJZ, LvZJ, ZhangHS, et al., 2013. Perforation experiments of concrete targets with residual velocity measurements. International Journal of Impact Engineering, 57:1-6.

[25]LiQM, ReidSR, WenHM, et al., 2005. Local impact effects of hard missiles on concrete targets. International Journal of Impact Engineering, 32(1-4):224-284.

[26]LiuJ, WuCQ, LiJ, et al., 2021. Projectile impact resistance of fibre-reinforced geopolymer-based ultra-high performance concrete (G-UHPC). Construction and Building Materials, 290:123189.

[27]MasriR, DurbanD, 2005. Dynamic spherical cavity expansion in an elastoplastic compressible Mises solid. Journal of Applied Mechanics, 72(6):887-898.

[28]NguyenKD, ThanhCL, VogelF, et al., 2022. Crack propagation in quasi-brittle materials by fourth-order phase-field cohesive zone model. Theoretical and Applied Fracture Mechanics, 118:103236.

[29]RajputA, IqbalMA, GuptaNK, 2018. Ballistic performances of concrete targets subjected to long projectile impact. Thin-Walled Structures, 126:171-181.

[30]RosenbergZ, DekelE, 2010. The deep penetration of concrete targets by rigid rods-revisited. International Journal of Protective Structures, 1(1):125-144.

[31]RosenbergZ, KositskiR, 2016. Modeling the penetration and perforation of concrete targets by rigid projectiles. International Journal of Protective Structures, 7(2):157-178.

[32]RossiP, 1991. A physical phenomenon which can explain the mechanical behaviour of concrete under high strain rates. Materials and Structures, 24(6):422-424.

[33]TaylorLM, ChenEP, KuszmaulJS, 1986. Microcrack-induced damage accumulation in brittle rock under dynamic loading. Computer Methods in Applied Mechanics and Engineering, 55(3):301-320.

[34]WangZL, LiYC, ShenRF, et al., 2007. Numerical study on craters and penetration of concrete slab by ogive-nose steel projectile. Computers and Geotechnics, 34(1):1-9.

[35]XieHP, DongYL, LiSP, 1996. Study of a constitutive model of elasto plastic damage of concrete in axial compression test under different pressures. Journal of China Coal Society, 21(3):265-270 (in Chinese).

[36]XingHZ, ZhaoJ, WuG, et al., 2020. Perforation model of thin rock slab subjected to rigid projectile impact at an intermediate velocity. International Journal of Impact Engineering, 139:103536.

[37]XiongYB, 2009. Research on Constitutive Parameters of Concrete Based on the Johnson-Holmquist Concrete Model. MS Thesis, Northwest Institute of Nuclear Technology, Xi’an, China(in Chinese).

[38]XuLZ, RenWK, WangXD, et al., 2021. Analytical investigation on deformation of PELE projectile and opening damage to concrete target. Thin-Walled Structures, 161:107408.

[39]YankelevskyDZ, 1997. Local response of concrete slabs to low velocity missile impact. International Journal of Impact Engineering, 19(4):331-343.

[40]YankelevskyDZ, 2017. Resistance of a concrete target to penetration of a rigid projectile-revisited. International Journal of Impact Engineering, 106:30-43.

[41]ZhaoFQ, WenHM, 2018. Effect of free water content on the penetration of concrete. International Journal of Impact Engineering, 121:180-190.

[42]ZhuC, ArsonC, 2014. A thermo-mechanical damage model for rock stiffness during anisotropic crack opening and closure. Acta Geotechnica, 9(5):847-867.