Angle-of-Attack, Induced Attitude Evolution in a Coupled Crater, and Plugging Penetration of Thin Concrete Targets
Abstract
1. Introduction
2. Theoretical Model
2.1. Theoretical Foundations and Model Inheritance
- (1)
- Chen et al. [27] developed the classical three-stage model describing rigid projectile penetration into concrete—comprising crater formation, tunnel extension, and shear plugging. Grounded in momentum and energy conservation, this model captures trajectory deflection and angular response caused by asymmetric loading and remains widely used.
- (2)
- Duan et al. [28,29] introduced a theoretical model for attitude deviation in oblique penetration, focusing on torque caused by eccentricity between the projectile’s center of mass and the pressure center on the nose. Their formulation established differential equations for angular velocity evolution, revealing how asymmetric pressure fields destabilize projectile orientation. However, it did not account for feedback from the shear plugging region.
- (3)
- Liu et al. [30] extended the model to include angle-of-attack effects, showing how asymmetric nose-surface velocities induce contact force imbalances. By considering free-surface effects and using the differential surface force method, they improved the accuracy in modeling projectile behavior during the crater phase.
- (1)
- Projectile is rigid, with no deformation or damage;
- (2)
- Resistance acts only on the nose of the projectile;
- (3)
- No rotation occurs about the projectile’s longitudinal axis during motion; only planar motion is considered;
- (4)
- Coarse aggregates are neglected, and the concrete is assumed to be a homogeneous and isotropic material.
2.2. Dynamic Shear_Plugging Model
- (1)
- Based on the findings of Peng et al. [44], the thickness of the shear plug formed during the penetration of thin concrete targets is approximately half the target thickness. When the projectile nose reaches mid-thickness, an initial conical shear plug is generated behind the projectile (see red region in Figure 7).
- (2)
- The axis of the shear plug is colinear with the projectile axis. The half-cone angle of the subsequent shear plug remains consistent with that of the initial plug, and their central axes are parallel.
- (3)
- During penetration, the initial shear plug remains relatively intact and continues to exert resistance on the projectile. However, newly generated shear zones (see blue region in Figure 7), which peel off in layers, no longer resist the projectile. Once the projectile nose reaches the rear surface of the target, the plug is fully fractured and ceases to offer resistance.
- (4)
- The failure surface during the shear-plugging process originates at the intersection between the projectile nose surface and the mid-plane of the target. It propagates toward the rear surface while maintaining a constant half-cone angle.
2.3. Model Implementation and Numerical Solution
3. Experimental Study and Model Validation
3.1. Experimental Design
3.2. Measurement System
3.3. Results and Model Validation
4. Parametric Analysis of the Evolution of Projectile Attitude Angle and Angle of Attack During Penetration
4.1. Influence of the Initial Attitude Angle
4.2. Influence of Impact Velocity
4.3. Influence of Target Thickness
4.4. Combined Influence of Multiple Parameters
5. Conclusions
- (1)
- For rigid projectiles penetrating thin concrete targets—especially when the target thickness is less than twice the projectile nose length—the shear plugging stage initiates before the cavity formation phase is fully completed. Treating cavity formation and shear plugging as isolated processes can lead to significant errors in predicting projectile deflection trends. By introducing a dynamic shear plugging stage, the proposed model accurately captures the evolution of projectile attitude angle during penetration.
- (2)
- Application of the proposed theoretical model to the penetration of a 30 mm projectile with an angle of attack into concrete with a uniaxial compressive strength of 27 MPa yielded a maximum error of 15% in post-impact velocity and 19.7% in post-impact attitude angle relative to the experimental results. These accuracies demonstrate a higher consistency with experimental observations than those obtained from existing theoretical models.
- (3)
- When the projectile’s velocity vector lies between the projectile axis and the normal vector of the target’s front face, the angle of attack tends to decrease during the early phase of penetration. This decreasing trend becomes more pronounced as the initial attitude angle increases. However, both the final attitude angle and angle of attack upon target exit increase with higher initial attitude angles.
- (4)
- The impact velocity of the projectile influences the evolution of its attitude and angle of attack during concrete target penetration. Although a lower impact velocity reduces the normal velocity component and thus the local stress on the projectile nose surface, it also increases the time required to reach a given penetration depth. As a result, both the final attitude angle and angle of attack at exit decrease as impact velocity increases.
- (5)
- During the early stage of penetration into concrete targets of varying thicknesses, the effect of the rear free surface is negligible, and the initial resistance remains consistent across cases. Consequently, the evolution of the projectile attitude and angle of attack is initially similar. Once shear plugging begins, the angle of attack increases more rapidly, followed by a decrease in the rate of growth. Eventually, the projectile is no longer subjected to resistance from the target and rotates at a constant angular velocity, resulting in a constant rate of increase in the angle of attack per unit time. Both the final attitude angle and angle of attack increase with target thickness.
- (1)
- Conduct meso-scale numerical simulations of oblique projectile penetration into concrete to investigate the influence of aggregate on projectile attitude evolution.
- (2)
- Develop a theoretical study on the shear-plugging mechanism of concrete, aiming to explore the dynamic process of plug formation and improve the description of dynamic plugging behavior.
- (3)
- Carry out additional experimental studies on projectile penetration with an angle of attack into thin concrete targets of different strengths, in order to verify the universality of the proposed theoretical model.
- (4)
- Perform projectile penetration experiments equipped with onboard sensors to record acceleration histories during the penetration process, thereby enabling continuous refinement of the theoretical model.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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NO. | Impact Velocity (m/s) | Initial Angle of Attack (°) | Target Thickness (mm) |
---|---|---|---|
1# | 600 | 12 | 90 |
2# | 600 | 6 | 75 |
3# | 900 | 6 | 90 |
4# | 900 | 12 | 105 |
5# | 1200 | 6 | 90 |
6# | 900 | 6 | 105 |
7# | 900 | 6 | 75 |
Mass (kg) | Centroid (mm) | Moment of Inertia (kg·m2) | ||||
---|---|---|---|---|---|---|
X | Y | Z | X-axis | Y-axis | Z-axis | |
0.59 | 67.99 | 0.01 | −0.02 | 9.76 × 10−5 | 9.03 × 10−4 | 9.14 × 10−4 |
NO. | Pre-Impact Horizontal Velocity, vx0 (m/s) | Pre-Impact Attitude Angle, Ψ0 (°) | Post-Impact Horizontal Velocity, vx1 (m/s) | Post-Impact Attitude Angle, Ψ1 (°) | Target Plate Thickness, (mm) | Nose–Rear Surface Distance, (mm) |
---|---|---|---|---|---|---|
#1* | 610.4 | 14.9 | 496.2 | 47.9 | 90 | 505.4 |
#2 | 617.1 | 8.7 | 559.9 | 24.4 | 79 | 683.7 |
#3 | 871.5 | 7.1 | 803.2 | 15.5 | 94 | 738.6 |
#4 | 933.1 | 14.2 | 780.4 | 51.3 | 98 | 729.8 |
#5 | 1147.4 | 6.9 | 1080.5 | 25.3 | 94 | 474.5 |
#6* | 903.9 | 6.6 | 803.3 | 23.8 | 105 | 503.6 |
#7 | 899.4 | 8.5 | 820.9 | 27.5 | 79 | 701.6 |
NO. | Experimental Result | Theoretical Result | Error | |||
---|---|---|---|---|---|---|
Post-Impact Attitude Angle, Ψ1e (°) | Post-Impact Horizontal Velocity, vx1e (m/s) | Post-Impact Attitude Angle Ψ1t (°) | Post-Impact Horizontal Velocity, vx1t (m/s) | ΔΨ/Ψ1e | Δvx/vx1e | |
#1* | 47.9 | 496.2 | 56.6 | 570.5 | 18.0% | 15.0% |
#2 | 24.4 | 559.9 | 26.6 | 588.5 | 8.9% | 5.1% |
#3 | 15.5 | 803.2 | 18.5 | 839.7 | 19.7% | 4.5% |
#4 | 51.3 | 780.4 | 60.5 | 832.2 | 17.8% | 6.6% |
#5 | 25.3 | 1080.5 | 21.6 | 1115.4 | −14.5% | 3.2% |
#6* | 23.8 | 803.3 | 25.4 | 865.8 | 6.7% | 7.8% |
#7 | 27.5 | 820.9 | 27.8 | 873.8 | 1.1% | 6.4% |
NO. | Duan’s Theoretical Result | Liu’s Theoretical Result | ||
---|---|---|---|---|
Post-Impact Attitude Angle, Ψ1D (°) | Post-Impact Horizontal Velocity, Vx1D (m/s) | Post-Impact Attitude Angle, Ψ1L (°) | Post-Impact Horizontal Velocity, Vx1L (m/s) | |
#1* | 2.4 | 559.5 | 0.2 | 539.4 |
#2 | 3.6 | 594.6 | 2.1 | 581.0 |
#3 | 3.4 | 848.5 | 2.7 | 833.4 |
#4 | 6.2 | 867.2 | 4.3 | 848.6 |
#5 | 5.3 | 1121.9 | 4.5 | 1109.0 |
#6* | 3.0 | 880.1 | 2.4 | 862.4 |
#7 | 5.6 | 872.9 | 4.5 | 862.5 |
Theoretical Model | Mean Absolute Error (MAE) | Root Mean Square Error (RMSE) | Mean Absolute Percentage Error (MAPE) |
---|---|---|---|
the present model | 4.1 | 5.2 | 12.4% |
Duan’s model | 26.6 | 29.3 | 84.6% |
Liu’s model | 27.9 | 30.6 | 88.7% |
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Tao, Z.; Li, W.; Zhu, W.; Xu, J.; Yan, J. Angle-of-Attack, Induced Attitude Evolution in a Coupled Crater, and Plugging Penetration of Thin Concrete Targets. Symmetry 2025, 17, 1572. https://doi.org/10.3390/sym17091572
Tao Z, Li W, Zhu W, Xu J, Yan J. Angle-of-Attack, Induced Attitude Evolution in a Coupled Crater, and Plugging Penetration of Thin Concrete Targets. Symmetry. 2025; 17(9):1572. https://doi.org/10.3390/sym17091572
Chicago/Turabian StyleTao, Zheng, Wenbin Li, Wei Zhu, Junjie Xu, and Jihua Yan. 2025. "Angle-of-Attack, Induced Attitude Evolution in a Coupled Crater, and Plugging Penetration of Thin Concrete Targets" Symmetry 17, no. 9: 1572. https://doi.org/10.3390/sym17091572
APA StyleTao, Z., Li, W., Zhu, W., Xu, J., & Yan, J. (2025). Angle-of-Attack, Induced Attitude Evolution in a Coupled Crater, and Plugging Penetration of Thin Concrete Targets. Symmetry, 17(9), 1572. https://doi.org/10.3390/sym17091572