Applied Mathematics and Mechanics >
Study on indentation formation mechanism and mass loss under impact loading in concrete penetration
Received date: 2025-11-11
Revised date: 2026-01-28
Online published: 2026-03-31
Copyright
Current erosion models for penetrating projectiles are almost exclusively developed for either rigid-body assumptions or hyper-velocity impacts. At such velocities, projectile deformation is primarily rheologically dominated. These models rarely capture the medium-velocity regime, where the impact speed drives plastic deformation, and the surface indentation governs progressive wear. The gap is addressed in this study by presenting a multi-scale framework that couples indentation mechanics, cavity-expansion theory, and impact-wave dynamics, and quantitatively correlates the indentation depth with the material properties and impact speed for the first time. Dimensional analysis identifies the dimensionless governing group, i.e., the dimensionless projectile elastic-inertial ratio Tp, dimensionless penetration resistance-inertia ratio Tt, dimensionless projectile ductility parameter λ1, and dimensionless target strength parameter λ2 as the trigger for erosion initiation. Then, a physically based wear model is derived analytically and calibrated against high-resolution simulations using adaptive mesh refinement to capture the projectile indentation. The resulting empirical formula is validated against independent experimental data, yielding errors of less than 7%. The proposed model provides armor-piercing projectile designers with an accurate and ready-to-use predictive tool for erosion in the medium-velocity regime.
Yulong ZHENG , Yao TANG , Duo ZHANG , Xianwen RAN . Study on indentation formation mechanism and mass loss under impact loading in concrete penetration[J]. Applied Mathematics and Mechanics, 2026 , 47(4) : 791 -814 . DOI: 10.1007/s10483-026-3367-9
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