Modeling and simulation have become essential tools for analyzing the fast dynamic phenomena encountered in many defense related scenarios1. These events are characterized by extremely high strain rates within short time scales and complex interactions between materials and energetic loads. Traditional experimental campaigns remain essential but are costly and limited in scope.
Finite element modeling offers an alternative to studying transient dynamic problems involving large deformations, nonlinear material behavior and strong coupling between mechanical, thermal and damage mechanisms2. In a military environment, such simulations can be used to analyze projectile or explosive loading impacts on protective structures (e.g., armor piercing, grenade detonation)3. Numerical models provide access to quantities such as stress states, strain localization, damage initiation and energy absorption, which are difficult to measure experimentally during very rapid events.
This article examines how FORGE® can support high strain rate defense applications. Its 3D FEM framework, ALE formulation and advanced remeshing strategies are designed to handle large deformations and rapidly evolving geometries typical of high-velocity and ballistic calculations.
Dynamic events in defense applications are inherently nonlinear, coupling plasticity, damage, thermal softening and wave propagation1. When strain rates exceed 10³ s⁻¹, numerical stability, time integration, and mesh sensitivity all become pressing concerns, and the quality of the simulation is ultimately only as good as the underlying material description. The Hopkinson Pressure Bar test and Taylor impact test are the go-to experiments for this regime4,5. Their results feed directly into the calibration and validation of constitutive models before these are trusted in more demanding scenarios.
We have evaluated FORGE® for dynamic analysis using its standard implicit scheme, with acceleration effects included in the equilibrium equations and a time step adapted from conventional metal forming approaches. Validation was carried out through classical high strain rate configurations. The Taylor impact test was modeled as the high velocity (227 m/s) impact of a copper bar against a rigid wall, with sliding friction assumed at the interface and both unilateral and bilateral contact formulations examined (see Figure 1).
Figure 1: (a) Pressure and (b) Von Mises Stress results of the Taylor bar test simulated using FORGE®.
In parallel, FORGE® was used to simulate the split Hopkinson pressure bar test, in which a thin specimen disc is sandwiched between two elastic bars subjected to dynamic compression. The simulation calculated the velocity along the specimen’s longitudinal axis, providing a benchmark to assess the model’s ability to accurately reproduce the material’s high strain rate stress-strain response.
Figure 2: Velocity calculated along the X axis during the Hopkins bar test simulation with FORGE®.
With a validated numerical setup, the software can then be applied to simulate defense-relevant scenarios such as armor penetration.
The simulation of armor piercing by a high-speed projectile provides critical insights into the complex interaction between projectiles and armor materials. FORGE® enables detailed analysis of stress, deformation, and failure mechanisms during impact events, capturing phenomena like plugging, cracking, and localized plastic deformation.
As an illustrative example, an armor-piercing event was investigated in collaboration with Alexis Rusinek from LEM3, Université de Lorraine. An experimental setup was designed to study the capacity of a metallic armor to absorb the energy of a projectile (see Figure 3(a)). Due to the extremely high-speed nature of the event, experimental sensors are unable to capture the full response with sufficient accuracy and temporal resolution, hence the importance of finite element modeling.
Figure 3: (a) Configuration of the armor-piercing experimental setup. (b) Von Mises Stress results of the simulated armor-piercing event using FORGE®.
The configuration was then modeled with FORGE®, as shown in Figure 3(b), employing elastoplastic constitutive laws suited for large deformations, such as Johnson-Cook6 or Rusinek-Klepaczko7 formulations. Material failure was described using established fracture criteria, including Johnson-Cook and Wierzbicki8 models, to capture the onset of rupture during impact.
To assess the reliability of the simulations, predicted failure outcomes were compared with experimental results as a function of the initial impact velocity (see Figure 4). The agreement between simulation and experiment is consistent across the investigated range, indicating that the model captures the observed failure behavior with good accuracy. This confirms the capability of FORGE® to provide reliable predictions for high strain rate impact events.
Figure 4: (a) Experimental failure observed during experiments for different initial impact velocities. Experiments were conducted in collaboration with Alexis Rusinek at the LEM3 laboratory. (b) Comparison with FORGE® failure simulations for the same parameters.
Grenade detonations involve shock waves, rapid pressure loading, and high-velocity fragments. While these effects are usually modeled with dedicated hydrocodes, finite element tools with explicit dynamics can provide useful insight into how structures respond to blast loading, especially in terms of deformation, stress wave propagation, and fragmentation risk.
FORGE® offers a robust finite element framework that can be extended to non-conventional applications such as blast. By defining appropriate boundary conditions, pressure-time loading curves and suitable material constitutive laws (i.e. damage and failure criteria), FORGE® can be used to model the mechanical response of structures subjected to grenade explosive loads (see Figure 5). A key advantage of this approach lies in the continuity it provides with fabrication process simulations. Since FORGE® models manufacturing operations such as forging, rolling, or heat treatment, the resulting material state of the component, as it comes out of the production process, can be directly carried over into the blast simulation.
Figure 5: FORGE® simulation of grenade detonation and fragmentation in a dual-armor configuration, illustrating the spatial distribution of pressure generated by the explosive event and its interaction with the protective structures.
FORGE® proves to be a relevant tool for exploring high strain rate phenomena in defense contexts. Through simulations of Taylor impact and Hopkinson bar test configurations, it demonstrates its ability to produce results consistent with known dynamic material behavior. Applied to impact and blast-related configurations, it provides useful insight into structural response where experimental data remain difficult to obtain. A notable numerical strength of FORGE® lies in its automatic remeshing capability, which ensures mesh quality throughout large deformation processes and adapts naturally to the severe geometry changes encountered in high strain rate applications. Another distinctive advantage lies in the seamless ability to simulate the full manufacturing process and directly assess the high strain rate and impact behavior of the resulting component, bridging the gap between fabrication and performance in a single integrated framework.
References
1. Jonas Zukas. "Introduction to hydrocodes". Vol. 49. Elsevier (2004).
2. Ted Belytschko et al. "Nonlinear finite elements for continua and structures". John wiley & sons (2014).
3. T. Børvik et al. "Perforation of 12 mm thick steel plates by 20 mm diameter projectiles with flat, hemispherical and conical noses: Part I: Experimental study." International journal of impact engineering 27.1 (2002): 19-35.
4. Yuchen Yang et al. "Review of SHPB Dynamic Load Impact Test Characteristics and Energy Analysis Methods." Processes (2023). https://doi.org/10.3390/pr11103029.
5. Chong Gao et al. "Finite Element Analysis on a Newly-Modified Method for the Taylor Impact Test to Measure the Stress-Strain Curve by the Only Single Test Using Pure Aluminum.", Metals (2018), 8, 642. https://doi.org/10.3390/met8080642.
6. C. Mareau et al. "A thermodynamically consistent formulation of the Johnson–Cook model." Mechanics of Materials, 143 (2020): 103340. https://doi.org/10.1016/j.mechmat.2020.103340.
7. A. Rusinek, & J. R. Klepaczko. "Shear testing of a sheet steel at wide range of strain rates and a constitutive relation with strain-rate and temperature dependence of the flow stress". International Journal of Plasticity, (2001),17(1), 87-115.
8. Tomasz Wierzbicki et al. "Calibration and evaluation of seven fracture models." International Journal of Mechanical Sciences 47.4-5 (2005): 719-743.