This section presents the findings obtained from both experimental and numerical analyses addressing rapid deformation phenomena in wound ballistics. In the experimental procedure, ballistic gelatin (BG) blocks were shot with two different bullets using a gas-operated firing mechanism positioned at a distance of 5 m. A high-speed camera capable of capturing up to 50,000 frames per second was employed to observe the bullet cores'trajectories within the BG and to analyze the formation and evolution of temporary and permanent cavities. A schematic representation of the experimental setup is provided in Fig. 3.

The movements of the bullets within the ballistic gelatin (BG) were recorded throughout the experiment using a high-speed camera. The finite element (FE) analysis results were subsequently compared with these experimental observations. Due to the inherently chaotic nature of wound ballistics, achieving exact correspondence between experimental and numerical results is extremely challenging. Nevertheless, a comparative assessment revealed strong similarities between the experimental and FE results in terms of both the trajectories of the bullet cores and the extent of tissue damage observed. The velocity and motion of the projectiles after exiting the BG were not examined, as they were beyond the scope of this study. Upon impact, a projectile in a statically balanced state encounters tissues of varying densities and elasticities. As the projectile transitions from air—a relatively low-density medium—into high-density tissue (simulated by BG), it undergoes a rapid decrease in linear velocity and kinetic energy. This abrupt deceleration, combined with the projectile’s initial angular velocity, causes it to revert toward its hyperstatic equilibrium state [27]. As a result of this sudden deceleration, a deflection of approximately 2° to 4° occurs along the projectile axis, which is sufficient to induce wobbling within the tissue [28]. Upon contact with tissue, the projectile generates pressure waves, resulting in the loss of approximately 99% of its initial kinetic energy. The increasing pressure forces surrounding tissues to displace outward from the center of the cavity. This displacement forms a temporary cavity, which persists during the penetration process. Within milliseconds, the surrounding tissues recoil toward the cavity center, ultimately forming a permanent cavity [29]. Notably, the temporary cavity formations observed in the experimental high-speed recordings exhibited strong agreement with the finite element (FE) simulation results.

Initially, the penetration behavior of each bullet type was simulated through numerical analyses, based on the characteristics of the bullet and the material properties of the target medium. The simulations produced time-dependent profiles of penetration depth for each bullet type, as well as visualizations of the temporary cavity formations surrounding the bullets.

Subsequently, these simulation results were validated through controlled experimental studies. Real-world firing tests were conducted to observe the ballistic behavior of the bullets under standardized conditions. The experimental data were then compared with the numerical analysis results, completing the validation process (Figs. 4 and 5).

Comparisons of the deformations from the experiment and the finite element simulation for 9 × 19 fmj

Comparisons of the deformations from the experiment and the finite element simulation for newly designed bullet

In line with the findings, graphs illustrating the variation of penetration depth over time for each bullet type are presented. By comparing the numerical and experimental results, these graphs clearly demonstrate the influence of bullet type on penetration behavior over time (Fig. 6).

Temporal cavity comparison of bullet cores. a 9 × 19 mm FMJ bullet FEA and experimental result b Newly designed bullet (NDB) FEA and experimental result

Through this integrated analysis, we aim to provide readers with a comprehensive theoretical and practical understanding of how bullet performance evolves over time (Fig. 7).

Temporal cavity comparison of bullet cores

A temporary cavity refers to a transient cavity that forms and subsequently expands when a bullet or other high-velocity object impacts a material. This phenomenon results from the rapid transfer of kinetic energy at the moment of impact, causing substantial damage to the surrounding medium.

The formation of temporary cavities is a critical area of research in wound ballistics and impact engineering, as it directly affects the durability and failure mechanisms of the impacted material. Understanding the effects of temporary cavity formation on biological tissues is essential for both injury analysis and the design of protective systems. These effects can be broadly summarized as follows:

Formation Mechanism: A temporary cavity forms when a bullet or projectile contacts body tissues. During this brief interaction, a portion of the projectile’s kinetic energy concentrates at the point of impact, resulting in a sudden increase in pressure and the formation of a transient cavity.

Expansion and Effects: The initial temporary cavity, formed at the moment of impact, expands outward from a localized region. This expansion process can deform surrounding tissues, particularly affecting soft tissues and bones by inducing plastic deformation or causing a transition from elastic to plastic behavior.

Destructive Potential: The expansion of the temporary cavity can result in significant damage to surrounding tissues. Under the influence of high-velocity projectiles, tissues subjected to the forces of the temporary cavity may experience cracking, fragmentation, or internal hemorrhaging. Understanding this destructive potential is crucial for a comprehensive assessment of ballistic injuries and post-traumatic effects.

Applications and Importance: Temporary cavity formation plays a critical role in the design of ballistic protection systems and the clinical management of ballistic injuries. Accurate characterization of this phenomenon is vital for military personnel, law enforcement agencies, and researchers in the field of ballistic protection dealing with projectile impacts.

The effects of temporary cavity formation contribute to advancements in medical treatment technologies, materials science, and impact engineering. An in-depth understanding of this phenomenon, coupled with the development of effective prevention and treatment strategies, enables the design of more effective future security and medical solutions. A comparison of the two bullet designs with respect to this critical parameter is presented in Fig. 6.