A Simplified ALE model for finite element simulation of ballistic impacts with bullet splash – development and experimental validation

Abstract

An original simplified finite element model is proposed to simulate the effects of non-penetrating ballistic impacts causing the so-called bullet splash phenomenon (complete bullet fragmentation), while no fragmentation is caused to the target. The model is based on the Arbitrary Lagrangian Eulerian formulation (ALE) and it simulates the impact as a fluid-structure interaction. The bullet splash phenomenon has been tested by experimental analyses of AISI 304L plates impacted by 9x21 FMJ (full metal jacket) bullets. The model has been developed with the aim of creating a simplified approach to be used in the industry and forensic sciences to simulate the non-penetrating interaction of soft impactors with hard targets. Comparisons between evidence and simulation results lead to the conclusion that the proposed approach can be used in a conservative way to estimate both local and global effects of bullet-splash phenomena.

A simplified formula to estimate the load history due to ballistic impacts with bullet splash. Development and validation for finite element simulation of 9x21mm full metal jacket bullets

“…ccording to Andreotti et al [9], bullet splash phenomena are mainly governed by the inertial, geometrical and compressibility properties of the impactor, while the deviatoric part of the constitutive law of the bullet's materials can be considered neglectable. The simplification effectively introduced to treat bullet splash as a fluid structure I A interaction, where the fluid represents the mass of the bullet's debris flowing against the target's surface, suggests therefore a further simplification, valid for splashing bullets hitting planar surfaces at 90° incidence angle, which is the worst impact angle a ballistic protection can face.…”

“…o validate the load history approach we simulated the same impact analyzed by Andreotti et al [9] to validate the FSI method. The simulated impact is therefore a 9x21mm full metal jacket (FMJ) bullet hitting a 250x250mm 4 mm thick AISI 304L plate at 322 m/s with an impact angle of 90degree.…”

“…Regarding the effects of the fragmentation of the bullet, Bresciani et al [8] in 2016 published a study about the use of adaptive remeshing and smooth particle hydrodynamics (SPH) methods to investigate the interactions between impactor and target when they both encounter fragmentation. In this context, Andreotti et al (2021) [9] proposed a simplified finite element approach to simulate the interaction between bullet fragments and target during bullet splash phenomena. The model then proposed was based on an arbitrary lagrangianeulerian (ALE) formulation to simulate the interaction between fragments and target as a fluid structure interaction (FSI), therefore avoiding the mechanical characterization of the deviatoric components of the constitutive law assigned to the bullet's material.…”

“…The formula is aimed to be useful to define load curves to be applied to simplified finite element models to conduct explicit dynamics analyses on any simulation platform featured with an explicit structural solver. The approach has been validated by comparing the results of the detailed fluid-structure interaction already experimentally validated by Andreotti et al [9] with the results of a simplified simulation in which the load history is estimated by means of an analytical-numerical approach based on the proposed theoretical formula. The comparisons between the history of global reaction forces and the stress waves being transferred through the plates during the simulations show a clear consistency of the method.…”

“…Moreover, the comparison between the FSI and non-FSI calculation times shows a clear advantage in terms of computational cost. Section 2 of the article illustrates the development of the load history formula and its practical application to the 9x21 FMJ bullet considered by Andreotti et al [9]. Section 3 explains how the finite element simulations were conducted.…”