Modeling and simulation have become essential tools for analyzing the fast dynamic phenomena encountered in many defense related scenarios1. These phenomena are characterized by extremely high strain rates within short time scales and complex interactions between materials and dynamic loads. Traditional experimental campaigns remain a reference for model validation and material characterization, but they are costly and limited in scope. In this context, 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.
For military applications, these simulations make it possible in particular to analyze the effects of mechanical loading, induced by projectiles or explosions, on protective structures. (e.g., armor piercing, grenade detonation)3. Numerical models provide access to quantities such as stress states after impact, the localization of deformations, the initiation of structural damage, and energy absorption. These quantities are all difficult to measure experimentally due to the high velocities involved.
This article explores the capabilities of the FORGE® software for defense applications characterized by high strain rates.
Unlike many computational codes dedicated to fast dynamics, which rely on explicit time integration schemes, FORGE® is based on an implicit formulation that is particularly suited to certain computational regimes. Explicit approaches are widely used for fast transient phenomena due to their robustness with respect to nonlinearities. However, they require very small time steps, governed by stability criteria, which can lead to high computational cost when the characteristic times are not exclusively controlled by very fast dynamics. Moreover, the frequent use of mass scaling techniques to accelerate computations can alter the physical fidelity of the results, notably by affecting stress levels and energy distribution.
In contrast, the implicit formulation adopted in FORGE® allows the use of significantly larger time increments, independent of conditional stability constraints. It is therefore particularly effective for problems involving strong material and geometric nonlinearities, while maintaining good accuracy in equilibrium states. Combined with an ALE formulation, a robust contact algorithm, as well as advanced remeshing strategies and high parallel efficiency, it provides a powerful framework for handling large deformations and rapidly evolving geometries, which are characteristic of ballistic computations and high-velocity impact phenomena.
Dynamic phenomena encountered 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. In this context, the quality of the simulation largely depends on the material’s constitutive 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 evaluated FORGE® for dynamic analysis using its standard implicit scheme, which includes acceleration effects in the equilibrium equations, together with a time-step adaptation derived from conventional metal forming approaches. The validation was based on reference configurations at high strain rates. The Taylor impact test was modelled as the high-velocity impact, 227 m/s, of a copper bar against a rigid wall, assuming sliding friction at the interface. Both unilateral and bilateral contact conditions were 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 longitudinal axis (X) 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 by Alexis Rusinek,LEM3, Université de Lorraine, in a collaboration with Transvalor. An experimental setup was designed to study the capacity of metallic armor to absorb the energy of a projectile (see Figure 3(a)). Due to the very high velocities involved, conventional sensors and experimental devices are unable to capture the event with sufficient accuracy and temporal resolution. Finite element modelling therefore becomes particularly valuable.
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 high strain rates, such as Johnson-Cook6 or Rusinek-Klepaczko7 formulations. Material failure was described using established damage 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 very 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.
The detonation of a grenade projects high-velocity fragments while generating shock waves and extremely rapid pressure loadings. Due to these extreme conditions, conventional experimental setups struggle to capture these phenomena with sufficient accuracy and temporal resolution.
Although dedicated hydrocodes are traditionally used to model such phenomena, finite element codes with dynamic capabilities, generally explicit, provide a relevant alternative. In particular, they make it possible to analyze the structural response of armor subjected to explosive loading in terms of deformation, shock wave propagation, and fragmentation.
FORGE® is based on a robust finite element environment that can be extended to non-conventional applications such as explosive loading. By defining appropriate boundary conditions, pressure-time loading curves, and constitutive laws incorporating damage and failure criteria, it becomes possible to model the mechanical response of armor subjected to a grenade detonation (see Figure 5).
A major advantage of FORGE® lies in the continuity it ensures with manufacturing process simulations. FORGE® enables the modelling of a wide range of metal forming processes such as forging, rolling, and heat treatment, making it possible to simulate the entire manufacturing chain of a component. The final state of the component can then be directly transferred into the detonation simulation, ensuring full digital continuity. This approach allows the behavior of the finished product under explosive loading to be evaluated while preserving the complete thermo-mechanical and microstructural history resulting from its manufacturing process.
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.
In this article, we have shown that the FORGE® software is a relevant tool for investigating phenomena involving very high strain rates encountered in defense applications. Through the simulation of Taylor impact tests and Hopkinson bar experiments, it demonstrates its ability to consistently reproduce the known dynamic behavior of materials.
When applied to impact and blast configurations, it provides valuable insights into the structural response in situations where experimental data remain difficult to obtain. One of the major numerical strengths of FORGE® lies in its automatic remeshing capabilities, which ensure the preservation of mesh quality during large deformations and naturally adapt to the significant geometric changes characteristic of high strain rate regimes.
A key advantage is the ability to continuously simulate the entire manufacturing process, and then directly evaluate the impact and high strain rate behavior of the resulting component. This continuity establishes a direct link between manufacturing processes and in-service performance within an integrated numerical framework.