A stochastic gradient estimate-based formulation for capturing the high strain-rate behaviour of a ductile target subjected to ballistic impact

Abstract

Investigating high strain-rate phenomena characterized by high-velocity impact is crucial for designing protective structures. Such impacts cause rapid microstructural changes, nonlinear deformations, plasticity, fractures, fragmentation, and thermal softening due to the generation of heat in ductile materials. Modelling these phenomena is often a challenging task, since the existing models rely on artificial parameters lacking a solid foundation, leading to unphysical behaviour at different load cases and posing scalability issues. In this regard, we develop a continuum theory based on the rigorously developed and versatile classical continuum mechanics. However, to circumvent the bottleneck in the form of the requirement of sufficient differentiability of the field variables in the classical theory, here, the derivatives are interpreted based on a stochastic gradient estimator (SGE). It considers the nonlocality and microstructural effect in thermo-visco-plastic deformations under high strain-rate impacts and interestingly remains well-posed even in the context of discontinuity of the field variables without requiring any additional restrictive prescriptions. The failure criteria are obtained using the Johnson-Cook model, and based on this, the interaction of material points ceases when the damage factor reaches a critical threshold. The proposed model accurately predicts the failure of a Weldox 460E target and projectile velocities, aligning well with the experimental data. This demonstrates that the method pushes the boundaries of existing numerical techniques and enables robust analysis of complex impact mechanics problems.