Assessment of confinement’s influence on a concrete target’s ability to approximate semi-infinite perforation performance

Abstract

The ability to accurately evaluate impact penetration resistance of a structural element in an experimental setting often requires the experimental impact specimen configuration to be as close as possible to a structural element in a fielded protective design scheme. This includes the target’s capability to estimate the semi-infinite response of a structural element such as a wall where inertial confinement is provided by undamaged material surrounding the area damaged by impact. Artificially simulating this confinement in an experimental target can take several forms, including use of a circumferential steel ring as a confining medium. Experimental data gathered from impact tests were utilized to create a representative numerical simulation of a confined target design. This simulation evaluated artificial and inertial confinement on concrete perforation by varying target to projectile diameters with and without artificial confinement. Perforation performance was found to be unaffected by confinement type when the target diameter to projectile diameter ratio was 16. Semi-infinite surface approximation was found to occur when the target diameter to projectile diameter ratio was 64 despite the confinement type at higher impact velocities; however, this ratio could be reduced while maintaining semi-infinite performance for lower velocity impacts.

Keywords

Impact confined concrete target semi-infinite target edge effects

Introduction

Semi-infinite behavior in a full-scale wall element can be attributed to the large difference between the area of the fragment or projectile and the area of the wall itself. A full-scale concrete wall is typically much larger than the area damaged upon impact or the impacting fragment. The undamaged concrete surrounding the damaged impact zone provides inertial confinement to the damaged concrete during an impact event. Confinement of concrete subjected to impact loads has been found to affect the mechanical properties of concrete, with ultimate strength and the associated strain capacity of the material increasing as confinement is increased (Sukontasukkul et al., 2005). This is somewhat intuitive given that confinement during dynamic events, such as impact, reduces tensile strain and subsequent tensile failure at the target’s free edges.

The diameter of an experimental concrete target (D) is typically a function of the diameter of the impacting fragment or projectile (d), where larger impactors often necessitate larger targets (Frew et al., 2006). However, efficient experimentation often requires that the target specimen be small enough to ensure portability. Depending on the diameter of the fragment or projectile to be evaluated, this may prove difficult to achieve given the high unit weight of concrete and the large surface area required to provide enough inertial confinement adjacent to impact damaged areas to approximate a semi-infinite response. Subsequently, this inertial confinement provided by undamaged concrete in a full-scale wall element is commonly approximated, often through the use of a target with artificial radial confinement.

Artificially confined targets have been evaluated as one piece of a cellular array system that, when combined with other confined concrete cells, make up a protective wall (Song et al., 2019; Wan et al., 2016). The performance of this type of target has also been evaluated against multiple hits from a projectile (Gomez and Shukla, 2001). In addition, the effect of a target’s diameter on penetration depth has been evaluated (Frew et al., 2006). However, the ability of artificial confinement to approximate the perforation response of a full-scale monolithic wall subjected to a fragment or projectile impact and the influence of confined target size on impact performance has not been extensively studied.

Therefore, data gathered from impact experiments using unreinforced concrete cylinders artificially confined using a steel ring was used to conduct a numerical analysis of target performance. The steel ring in the experimental targets was intended to reduce radial tensile strain and provide a rough approximation of the inertial confinement provided by undamaged concrete in a wall element. These impact tests are detailed in Brown (forthcoming). The artificial confinement provided by the steel ring results in reflections of shockwaves induced by impact that are not likely to be present in an actual wall element depending on the proximity of the impact location relative to a reflection plane (i.e. free wall edge).

These reflections cannot attenuate as they travel through the target before reflection as they would in an actual semi-infinite surface. Therefore, this type of target design can only be considered to estimate the performance of an inertially confined semi-infinite element by artificially confining the radial tensile strains at the edges of the finite surface. The velocity of the impactor after perforating the confined targets was the experimental metric utilized to ensure that the numerical simulation produced similar perforation data compared to the experimental target response. A series of simulations were then used to evaluate performance of targets with different diameters. The data and results from the simulations were utilized to evaluate how edge effects and artificial confinement can influence a target’s ability to approximate the perforation performance of an inertially confined semi-infinite surface during impact.

Experimental reference data for simulation development

The data associated with the artificially confined concrete targets used to create the numerical simulation utilized herein was gathered from impact tests detailed in Brown (forthcoming). This study evaluated the effect of fragment aspect ratio on impact response, along with the influence of compressive strength and fiber reinforcement. A 12.7-mm-diameter ball bearing (BB) was the fragment analyzed herein. The two concretes evaluated herein were a normal strength concrete (NSC) and a high-strength concrete (HSC-A). These materials were cast into cylindrical specimens where the outer edge was artificially radially confined with a commercially available steel pipe having a wall thickness of approximately 0.64 cm. The pipe served as the formwork into which the concrete was cast.

The target geometry varied depending on the parameter of interest and the size of the impacting fragment. The target diameter (D) was approximately 32 times the projectile diameter (d). A 32:1 D/d aspect ratio was selected based on prior experimentation that found penetration depth was unaffected by D/d ratios greater than 24 (Frew et al., 2006). Thinner targets (5.1 cm) were utilized to evaluate perforation response, where the impact velocity (V_s) was compared to the residual velocity (V_r) after the fragment had passed through the specimen. These thinner specimens, and the measured V_s and V_r values associated with the BB impact, were utilized to inform the computational simulation created and analyzed herein. The BB data gathered from this experimental series on the concrete materials that were utilized to conduct the numerical analysis herein is provided in Table 1.

Table 1.

Experimental striking velocity (V_s) versus residual velocity (V_r) for BB.

Material	f_c (MPa)	Diameter (cm)	Thickness (cm)	V_s (m/s)	V_r (m/s)
NSC	28.7	40.6	5.1	548	0
				596	0
				617	0
				829	106
				873	160
				1007	302
				1167	468
				1420	657
				1642	771
				1842	816
				2086*	800
HSC-A	100	40.6	5.1	697	0
				717	0
				746	4
				752	27
				873	55
				1042	223
				1199	376
				1376	504
				1553	605
				1847	805

Indicates a transition from nearly rigid-body projectile penetration to large deformation of projectile.

Numerical simulation of confined experimental target impact by BB projectile

A numerical simulation of the BB experimental target specimen described in the prior section was created using the Elastic-Plastic Impact Computation (EPIC) hydrocode. EPIC is an explicit (wave propagation) code based on finite elements and meshless particles used primarily by the Department of Defense (DoD) for intense impulsive loading due to high-velocity impact and explosive detonation. The code includes a range of element types, several meshless-particle options, numerous material models, a large library of material parameters, and a wide range of preprocessing and postprocessing options (Johnson et al., 2020). When EPIC is used in conjunction with the High-Rate-Brittle (HRB) concrete model (Frank, 2012; Frank et al., 2020a), it has been shown to accurately simulate impact events similar to those evaluated experimentally (Frank et al., 2017; Sherburn et al., 2017).

Model calibration methodology

The NSC and HSC-A materials utilized in the numerical simulations were modeled with the aforementioned HRB concrete constitutive model. This model is a three-invariant rate-dependent elastic-plastic model that utilizes a complex scalar material damage law with a distinct fracture algorithm. The hydrostatic response is non-linear and decoupled from the deviatoric response. Complex logic is included to provide hysteresis during hydrostatic loading and unloading cycles. The deviatoric response (shear modulus) is prescribed by a non-linear loading function with unloading constrained by a constant Poison’s ratio (Frank, 2012; Frank et al., 2020a).

A three-invariant non-linear failure surface is prescribed with independent cohesive and frictional parts, that is, the third invariant effects are only applied to the cohesive strength. The rate-dependent strength laws provide both cohesive strengthening and frictional weakening, resulting in a dynamic strength envelope that evolves based on the local strain rates. The scalar damage law is non-linear and composed of three distinct damage modes that are rate dependent and can produce both brittle and ductile behaviors; hydrostatic crushing, shear cracking, and tensile cracking. A distinct fracture algorithm has also been included and is dependent on the maximum principal tensile stress and strain values. Material fracture is thereby inherently included a priori in the material response and does not need to be arbitrarily derived posteriori (Frank, 2012; Frank et al., 2020a).

The material parameters (i.e. material model fitting) for HSC-A have been extensively simulated in EPIC and are well-developed (Frank et al., 2020b). However, a material model fit for the exact mixture constituents of the NSC was not available, although a similar NSC material fit has also been extensively used (Frank et al., 2020b). Therefore, the NSC material fit used in these simulations was adjusted to match the compressive strength from the NSC experiments described herein (28.7 MPa). Is noteworthy that the material model fitting parameters for NSC and HSC-A materials were predefined and not modified in any way to fit the simulation results to the experimental data evaluated in this paper. Parameter values for the NSC and HSC-A materials are detailed in several prior works (Frank et al., 2020a, 2020b; Johnson et al., 2020).

The Johnson-Cook (JC) material model was utilized to simulate the steel ring providing artificial confinement in the target specimens and the BB projectile. The steel confining ring utilized an EPIC library material model fit for mild steel with a yield strength of 430 MPa. Parameter values for the JC material model utilized can be found in several other works (Frank et al., 2020a; Johnson et al., 2020). A pipe with a relatively thin wall was utilized for confinement experimentally and in the simulations, with thickness varying depending on what was commercially available for each diameter. The diameters that were used to provide artificial confinement in the simulations are provided for each D/d value in Table 2.

Table 2.

Pipe wall thicknesses utilized as simulated artificial confinement.

D/d	Wall thickness (cm)
8	0.31
16	0.38
24	0.46
32	0.64
40	0.64
48	0.64
64	0.79
80	0.95

The BB was simulated using an EPIC library material fit for S7 tool steel for initial comparison to the experimental data. Based on those simulation results, the material fit for the S2 tool steel was derived herein. The S2 material fit was derived from the S7 material fit by modifying both the yield strength (1517 MPa for S7 and 2000 MPa for S2) and the fracture parameters. These modifications were made so that the condition of the BB fragmentation in the simulation was similar to that which was experimentally observed after impact. The S2 material fit resulted in a better correlation between the experimental and simulated perforation velocity data, as well as BB fragmentation.

The models evaluated herein were conducted in 3D and the effects of mesh size on the half-symmetry BB simulation behavior were evaluated using several different simulations with varying element geometry. The size of the mesh is critical to simulation performance. As the element size decreases the simulation requires additional computational time and resources. However, smaller mesh sizes may also provide more accurate and detailed results. The optimal element size was evaluated using iterative simulations by quantitatively comparing residual velocity and qualitatively comparing material damage. The simulation with the coarsest target mesh evaluated had approximately one million elements while the model with the finest mesh had approximately 10 million elements. The optimal mesh size that provided the necessary amount of detail while requiring a reasonable amount of computational resources had approximately seven million elements total between the target and projectile. This resolution resulted in the size of the target elements being approximately 0.78 mm and the elements in the BB projectile being approximately 0.15 mm. This was the element size that was maintained for each simulation evaluated herein. Uniform element sizes were utilized throughout the target and projectile.

Numerical model results

The striking velocity (V_s) values included in the model represented the experimental data. These velocities were selected in increments of approximately 152 m/s that began just beyond the perforation limit determined experimentally and continued to where the BB projectile began to transition from nearly rigid-body penetration of the projectile to large deformation or shattering of the projectile at higher impact velocities. The residual velocity (V_r) values determined from the numerical simulations are provided in Table 3 along with the experimental data that was gathered within the same range of impact velocities.

Table 3.

BB striking (V_s) versus residual velocity (V_r) of a target with D/d = 32.

Material	Target	V_s (m/s)	V_r (m/s)	Material	Target	V_s (m/s)	V_r (m/s)
NSC	Experimental	548	0	HSC-A	Experimental	697	0
		596	0			717	0
		617	0			746	4
		829	106			752	27
		873	160			873	55
		1007	302			1042	223
		1167	468			1199	376
		1420	657			1376	504
	Numerical	762	44		Numerical	762	21
		914	201			914	103
		1067	367			1067	255
		1219	504			1219	420
		1372	634			1372	550
		1524	729			1524	646

Impact simulation visualizations where the V_s was 1067 m/s are provided in Figure 1 for the NSC and HSC-A materials. The gray colored area indicates areas of no damage, red indicates fully damaged material, and blue indicates lower levels of damage. The most severe damage was noted nearest the BB impact location. As the distance from the point of impact increases, material damage decreases. Radial cracking is also visible in both material types. This type of damage is representative of the other simulations as well as the experimental target condition post-impact.

Figure 1.

Rear face damage contour for target with D/d = 32 at 1067 m/s: (a) NSC, and (b) HSC-A.

The V_s and V_r data for each concrete material and target type provided in Table 3 are illustrated graphically in Figure 2. The data is fit with a trend line created using a Lambert relationship, which is commonly utilized for this type of perforation analysis (Zukas et al., 1982). The Lambert fit relationship is shown in equation (1),

V_{r} = {\begin{matrix} 0, 0 \leq V_{s} \leq V_{l} \\ α {(V_{s}^{ρ} - V_{l}^{ρ})}^{\frac{1}{ρ}}, V_{s} > V_{l} \end{matrix}}

(1)

where α and ρ are calibrated parameters and V_l is the perforation limit velocity. This velocity is nominally the minimum velocity to attain a V_r greater than 0. Only the data points with V_s less than 1524 m/s were included in the analysis due to a transition observed from nearly rigid-body penetration of the projectile to large deformation or shattering of the projectile at higher impact velocities.

Figure 2.

Experimental and simulation results comparison: (a) NSC and (b) HSC-A.

The simulation data for the BB with an S2 material fit compared with the experimental data much better than the simulation data for the BB with an S7 material fit. This was observed for the NSC and HSC-A target materials. Therefore, the S2 material fit, which was a suitable correlation, was used to evaluate the effects of confinement and diameter on simulated target perforation performance.

Data analysis

The influence of confinement method on the simulated target’s perforation response was evaluated by removing the artificial confinement provided by the steel ring from the model while varying the D/d of the targets. As D/d increased, the inertial confinement (i.e. confinement from concrete) also increased. These scenarios were evaluated through approximately 220 different simulations that are summarized in Table 4. A summary of the V_s and V_r data obtained from the numerical simulations for the two target types (artificially confined and inertially confined) at each D/d that was evaluated is provided. The data from the numerical simulations shown in Table 3 is are also shown in Table 4 for completeness (D/d = 32). Similar to the calibration simulations, the confinement provided was that of a commercially available thin-walled pipe for each target diameter.

Table 4.

Striking (V_s) versus residual velocity (V_r) at varying D/d ratios.

V_s (m/s)	V_r (m/s)
	NSC
	Inertially confined (i.e. concrete confined) D/d								Artificially confined (i.e. steel ring confined) D/d
	8	16	24	32	40	48	64	80	8	16	24	32	40	48	64	80
457	27	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–
533	65	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–
610	115	23	2	–	–	–	–	–	20	11	–	–	–	–	–	–
686	172	53	29	–	–	–	–	–	70	45	8	–	–	–	–	–
762	237	117	89	67	49	33	40	25	153	107	83	44	52	31	43	48
914	384	272	243	199	180	134	137	153	309	265	239	201	180	136	135	129
1067	491	426	391	357	338	292	257	229	452	429	389	367	333	297	255	226
1219	623	577	544	507	481	446	388	359	597	577	544	504	476	441	376	346
1372	756	721	677	632	596	563	476	451	747	723	675	634	600	539	488	446
1524	882	847	794	725	678	657	546	523	878	843	788	729	686	620	560	542
HSC-A
457	5	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–
533	25	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–
610	64	2	–	–	–	–	–	–	–	–	–	–	–	–	–	–
686	102	34	6	–	–	–	–	–	17	20	31	–	–	–	–	–
762	145	93	51	14	23	23	30	15	47	58	70	21	21	29	24	13
914	278	198	162	114	98	100	128	123	195	199	159	103	106	129	134	114
1067	399	325	312	266	233	226	230	208	452	326	301	255	237	229	228	201
1219	546	486	451	412	383	345	325	298	598	483	448	420	383	343	324	295
1372	674	634	592	541	503	425	401	379	747	632	588	550	497	422	376	352
1524	784	747	705	661	605	551	463	441	842	756	700	646	600	546	431	418

Effect of artificial versus inertial confinement on perforation performance and damage

The influence of artificial confinement from a steel ring on perforation response was evaluated by comparing the Table 4 data from inertial confined (IC) versus artificial confined (AC) targets of the same D/d ratio. The data for each D/d ratio is shown for the NSC and HSC-A materials in Figures 3 and 4, respectively. Simulation trends were very similar for both materials. When the D/d value was 16 or larger, the artificially and inertially confined targets of the same diameter performed nearly the same. However, when the D/d of the simulated specimen was reduced to eight, the specimens of each material type displayed a divergence in perforation performance regardless of the confinement utilized, especially at lower impact velocities. These trends indicate that the perforation performance of a specimen with the same diameter are unaffected by the presence of artificial radial confinement when the D/d is greater than or equal to 16.

Figure 3.

NSC perforation performance with and without artificial confinement (m/s): (a) D/d = 8, (b) D/d = 16, (c) D/d = 24, (d) D/d = 32, (e) D/d = 40, (f) D/d = 48, (g) D/d = 64, and (h) D/d = 80.

Figure 4.

HSC-A perforation performance with and without artificial confinement (m/s): (a) D/d = 8, (b) D/d = 16, (c) D/d = 24, (d) D/d = 32, (e) D/d = 40, (f) D/d = 48, (g) D/d = 64, and (h) D/d = 80.

However, as D/d is increased, the V_r values decrease incrementally as demonstrated by the comparison of the targets with a D/d of 16 versus the larger targets. This indicates that inertial confinement continues to influence a target’s perforation performance with or without artificial confinement in both material types. This is further illustrated in Figure 5 where the Lambert function discussed in the section “Numerical model results” has been fit to the simulation data for the artificially and inertially confined normal and high-strength concrete simulations

Figure 5.

Effect of D/d on V_r (m/s): (a) NSC artificially confined, (b) NSC inertially confined, (c) HSC-A artificially confined, and (d) HSC-A inertially confined.

As illustrated in Figure 5, until the D/d value reaches 64, V_r values continue to decrease as D/d, and subsequently, inertial confinement increase. However, upon reaching a D/d of 64, V_r values begin to converge with those of a target with a D/d of 80, with and without artificial confinement. This indicates that edge effects influence V_r values until D/d exceeds 64 and that the simulated target does not approximate the performance of an inertially confined semi-infinite surface, similar to that of a wall until that D/d threshold is met or exceeded. This is likely due to many factors including increased wave attenuation and decreased reflection times as the shock propagates through the additional inertial confinement provided by the increased D/d target.

The disparity between V_r values for different D/d ratios was more apparent at higher V_s levels. This indicates that as the magnitude of the impact velocity increases, the inertial confinement must also be increased to provide a more accurate approximation of a semi-infinite response. Subsequently, a target with a smaller D/d value and less inertial confinement could be utilized to provide a semi-infinite response at lower impact velocities. The data analyzed herein indicates that at impact velocities less than approximately 1000 m/s, a D/d could be as small as 48 in the HSC-A material and still provide a near semi-infinite response. This indicates that different concrete mixture types may display slightly different performance characteristics. As the impact velocity increases to 1500 m/s, the minimum D/d for a near semi-infinite response is approximately 64 for either material. This is illustrated in Figure 6 where the V_r values for each D/d and confinement condition are graphed for V_s values of 1000 m/s along with the V_r values for a V_s of 1500 m/s for comparison. Polynomial trend lines for each data set are provided in Table 5.

Figure 6.

D/d versus V_r at V_s of 1000 m/s and 1500 m/s: (a) NSC, (b) NSC, (c) HSC-A, and (d) HSC-A.

Table 5.

Trend line equations.

Material	V _s	IC	AC
NSC	1000	V_r = –0.0004(D/d)³ + 0.1028(D/d)² – 8.7652(D/d) + 485.01	V_r = 8E-06(D/d)³ + 0.0335(D/d)² – 5.2552(D/d) + 416.62
NSC	1500	V_r = 0.0012(D/d)³ – 0.1348(D/d)² – 1.1556(D/d) + 887.45	V_r = 0.0008(D/d)³ – 0.0763(D/d)² – 4.2034(D/d) + 905.02
HSC-A	1000	V_r = –0.0004(D/d)³ + 0.1086(D/d)² – 9.9007(D/d) + 433.07	V_r = –6E-05(D/d)³ + 0.0497(D/d)² – 6.2299(D/d) + 356.81
HSC-A	1500	V_r = 0.001(D/d)³ – 0.0914(D/d)² – 4.1785(D/d) + 825.87	V_r = 0.0004(D/d)³ + 0.0097(D/d)² – 9.2635(D/d) + 881.7

Regression coefficient (R²) values for these equations were on the order of 0.98, indicating a relatively good fit to the data. These equations can be utilized to determine expected V_r values for varying D/d ratios at V_s values of 1000 m/s and 1500 m/s. Given the constraints associated with large targets, laboratory limitations, etc., a D/d of 64 may be difficult to achieve. Therefore, these relationships provide the ability (for similar materials) to estimate the potential change in perforation performance with smaller target geometries that may be required in many situations.

The effect of artificial and inertial confinement on damage in the target during an impact event was also evaluated. This was accomplished by comparing a visualization of the simulation results from the two types of confinement at 1 milli-second post-impact. A representative sample of these comparative visualizations for a V_s of 1067 m/s at different D/d values is provided in Figures 7 and 8 for the NSC and HSC-A materials, respectively.

Figure 7.

Effect of confinement on NSC target damage.

Figure 8.

Effect of confinement type on HSC-A target damage.

The damage response illustrated in Figures 7 and 8 demonstrates damage magnitude decreases as inertial confinement increases. Furthermore, the influence of artificial confinement also decreases with increasing D/d ratios. This trend can largely be attributed to the magnitude of radial strain at the outside edge of the target increasing as the inertial confinement decreases. Given that concrete is particularly weak in tension, reducing tensile strains likely reduces target damage due to impact. Similar to the V_s versus V_r analysis results, this is likely due to many factors such as increased wave attenuation and decreased reflection times as the D/d, and subsequently the inertial confinement is increased. The difference in compressive strength between the NSC and HSC-A did not appear to have a noticeable influence on this relationship.

Summary and conclusion

The perforation resistance and impact performance of concrete targets of varying target diameter (D) to projectile diameter (d) ratio (D/d) with and without artificial confinement were evaluated numerically using a material model that was shown to have a suitable correlation with available experimental results. The two primary findings of this research initiative are included below.

- Artificial radial confinement by way of a steel ring has a relatively small influence on perforation performance when the D/d is greater than or equal to 16. This is likely due to inertial confinement dominating the perforation response as D/d increases.

- Inertial confinement from concrete influences perforation performance with or without artificial confinement up to a D/d of approximately 64. Therefore, the D/d of an experimental target should be greater than or equal to 64 if a semi-infinite perforation response is desired at elevated impact velocities. However, the D/d can be reduced to as low as 48 at lower impact velocities while still providing a semi-infinite response.

Footnotes

Appendix

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study was supported by the U.S. Army Engineer Research and Development Center and would not have been possible without the valuable contributions of Mr. Andrew Barnes and Mr. Ricky Magee of ERDC. Permission to publish was granted by the Director, ERDC Geotechnical & Structures Laboratory.

ORCID iDs

Jared L. Brown

Isaac L. Howard

References

Brown

(Forthcoming) Response of concrete elements with varying compressive strength to impact by fragments with different aspect ratios. Doctoral Dissertation, Mississippi State University.

Frank

(2012) An elastic-plastic material model for concrete under high rate impulsive loads: Modeling, implementation, and testing of the High Rate Brittle (HRB) concrete model. Technical report ERDC/GSL TR-12-10, Vicksburg MS, US Army ERDC, March.

Frank

Brown

Jordan

, et al. (2020a) Hardened installation protection for persistent operations (HIPPO) II: Protective design for oblique penetration: Modeling, simulation, and experimental validation. Technical report ERDC/GSL, Vicksburg MS, US Army ERDC, May.

Frank

Roth

Heard

(2020b) Residual penetration resistance from multi-hit events: Multi-hit experiments with modeling and simulation. Technical report ERDC/GSL, Vicksburg MS, US Army ERDC, June.

Frank

Vankirk

Roth

, et al. (2017) Hardened installation protection for persistent operations (HIPPO) II. Calibration of the high-rate-brittle (HRB) model for penetration into generic ultra-high- performance concrete (GUHPC). Technical report ERDC/GSL TR-17-7, Vicksburg MS, US Army ERDC, April.

Frew

Forrestal

Cargile

(2006) The effect of concrete target diameter on projectile deceleration and penetration depth. International Journal of Impact Engineering 32: 1584–1594.

Gomez

Shukla

(2001) Multiple impact penetration of semi-infinite concrete. International Journal of Impact Engineering 25: 965–979.

Johnson

Beissel

Gerlach

, et al. (2020) User Instructions for the 2016 Version of the EPIC Code. San Antonio, TX: Southwest Research Institute.

Sherburn

Frank

Burroughs

, et al. (2020) Hardened installation protection for persistent operations (HIPPO) II. Advanced computational mechanics: Prediction calculations and experiments. Technical report ERDC/GSL TR-20-16, Vicksburg MS, US Army ERDC, March.

10.

Song

Tan

Zhan

, et al. (2019) Experimental investigation on the cellular steel-tube-confined concrete targets against projectile impact. International Journal of Impact Engineering 131: 94–110

11.

Sukontasukkul

Mindess

Banthia

(2005) Properties of confined fibre-reinforced concrete under uniaxial compressive impact. Cement and Concrete Research 35: 11–18.

12.

Wan

Zhigang

Tan

, et al. (2016) Response of steel-tube-confined concrete targets to projectile impact. International Journal of Impact Engineering 94: 50–59.

13.

Zukas

Nicholas

Swift

, et al. (1982) Impact Dynamics. Hoboken, NJ: John Wiley & Sons.