A Deterministic Limit for Structural Failures: Deriving Critical Thresholds and Real-Time Monitoring of Catastrophic Events in Engineering Systems

This paper introduces a deterministic framework for predicting catastrophic structural failure in load-bearing materials and rotating systems. Unlike traditional probabilistic models, this approach derives exact spatial thresholds—critical crack tip radii, whirl radii, and phase transition thresholds—based on material toughness, membrane stiffness, and localized defect dynamics. The paper also proposes a novel real-time monitoring system using distributed acoustic emission sensors, fiber optic strain sensors, and eddy current probes to calculate and predict critical failure thresholds dynamically, enabling proactive structural integrity measures in aerospace, marine, and industrial applications.