Modares Mechanical Engineering

Modares Mechanical Engineering

Scaling the Penetration of Rigid Projectiles in Concrete Targets Using the Finite similitude Method

Document Type : Original Article

Authors
Davood Lotfi 1
Hossein Khodarahmi 1
Alireza Nadaf Oskooei 1
Seyed Mohammad Vahab Mousavi 1
Tohid Mirzababaie Mostofi 2
1 Mechanical Engineering Department, Imam Hossein University, Tehran, Iran
2 Mechanical Engineering Department, Ivankey University, Tehran, Iran
10.48311/mme.2026.118063.82905
Abstract
Scaling high strain-rate phenomena in concrete structures remains challenging due to the nonlinear and strain-rate-dependent behavior of concrete, which prevents full similitude between scaled models and prototypes. This study proposes an analytical framework termed the Finite similitude Method for scaling concrete structures subjected to high-rate impact loading. The formulation is derived from the integral forms of the conservation laws of mass, momentum, and energy, while explicitly incorporating strain-rate-dependent material behavior. Scaling factors are established for both purely dimensional and combined dimensional–material scaling, enabling extrapolation from scaled models to full-scale structures. To assess the method’s accuracy, numerical simulations were conducted for rigid spherical projectile penetration at one-fifth and one-tenth scales, and rigid ogive-nosed projectile penetration at 1.15 and 1.67 scales, impacting concrete targets with varying compressive strengths. Simulations were performed using Autodyn, and concrete behavior was modeled with the RHT constitutive model. Results show that increasing the scaling factor leads to larger deviations in peak force, absorbed energy, crater diameter and depth, and residual velocity. Maximum deviations reached 8% in dimensional scaling and 24% in dimensional–material scaling for spherical projectiles, and 13.2% and 21.1%, respectively, for ogive-nosed projectiles. The findings confirm that the proposed method provides reliable accuracy within limited scaling ranges and offers a practical tool for designing scaled impact experiments in concrete structures.
Keywords
Projectile penetration
Finite similitude
Scaling Concrete structures
RHT behavioral model, High-rate loading
Subjects

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Modares Mechanical Engineering
Volume 27, Issue 1
January 2027
Pages 79-91