Reliability-Oriented Analytical Framework for Fragment-Resistant Multilayer Protective Equipment Under Impulsive Loading

This paper presents a reliability-oriented analytical framework for the quantitative assessment of fragment-resistant multilayer protective equipment subjected to impulsive fragment loading. The study is motivated by the stochastic nature of fragment generation and impact conditions in industrial and occupational accident scenarios, where deterministic penetration criteria are insufficient to describe protective performance. Fragment interactions are modelled as stochastic spatial events, with impact locations and kinematic characteristics treated as random variables and mapped onto a predefined protected region. System failure is formulated using an energy-based limit-state criterion defined by comparison between the absorbed energy demand induced by fragment impact and a critical admissible energy threshold. The fragment–PPE interaction is described using a reduced-order dynamic formulation with concentrated parameters, capturing the dominant normal deformation response under short-duration impulsive loading. Closed-form analytical expressions are derived that relate fragment mass and velocity to impact impulse and absorbed energy. The resulting formulation establishes a direct link between impulse-driven dynamic response, progressive multilayer engagement, and failure probability under single and repeated impact events. Application of the proposed framework to a representative multilayer protective configuration demonstrates physically consistent reliability trends and confirms its computational efficiency. The framework provides a practical tool for reliability-informed assessment and preliminary design of fragment-resistant multilayer protective equipment.