The study of bullet penetration into soil is critical for various fields such as forensic science, military applications, and geotechnical engineering. Understanding the mechanics of how a projectile interacts with granular media like soil enables accurate reconstruction of shooting incidents, design of protective barriers, and improvement of projectile performance.

In this example, the model is similar to this paper,” Calibration of empirical penetration models using large deformation explicit finite element simulations of rapid penetration in clay.” This example aims to determine the depth of the bullet penetration in the soil.

One powerful numerical method used to simulate such complex interactions is the Coupled Eulerian-Lagrangian (CEL) analysis. CEL combines the advantages of both Eulerian and Lagrangian formulations, allowing detailed modeling of large deformations and interactions between solids and fluids or granular materials.

• Lagrangian formulation tracks the mesh that moves and deforms with the material, ideal for solids.

• Eulerian formulation uses a fixed mesh through which materials can flow, making it suitable for fluids or granular soils that experience large deformation and displacement.

In CEL analysis of bullet penetration into soil, the bullet is typically modeled as a Lagrangian solid, while the soil is represented using an Eulerian mesh. This hybrid approach effectively captures the dynamic impact, penetration, and soil displacement without severe mesh distortion issues common in purely Lagrangian simulations.

Key aspects of CEL analysis in this context include:

• Material modeling: Accurate constitutive models for both the bullet material and soil are crucial, with soil often modeled as a granular material with compaction and shear failure behavior.

• Boundary conditions and initial velocity: The bullet’s velocity upon impact and boundary constraints on the soil domain must be carefully defined to replicate real-world conditions.

• Contact interactions: The interaction between the bullet and soil surfaces is simulated with friction and penetration criteria to capture realistic penetration mechanics.

By using CEL analysis, researchers can obtain detailed insights into the penetration depth, soil deformation patterns, stress distribution, and energy dissipation during the impact event. This contributes to better predictive capabilities and improved designs in applications involving projectile-soil interaction.