Acoustic Emission as a Stochastic Microfailure Process: Unified Quantitative Laws

The prediction of fracture and progressive damage in solid materials can be assessed with acoustic emission (AE) monitoring, yet most quantitative AE-stress/strain relationships remain largely empirical. In this work, we present a unified stochastic framework that derives and generalizes these relationships from a microfailure distribution. By modeling the temporal occurrence of microfailures as a stochastic Poisson process, we establish direct statistical connections between AE activity and macroscopic mechanical variables such as stress and strain. This perspective allows us to reinterpret proposed empirical AE laws as particular statistical regimes, while also advancing a generalized formulation capable of capturing more complex behaviors often observed under dynamic loading. Extensive stochastic simulations further reveal that simple assumptions about internal deterioration rates naturally lead to heuristic quantitative laws for the number of AE events, thereby grounding empirical observations in probabilistic reasoning. The framework is validated against experimental datasets from cortical bone and collagenous soft tissue, confirming its robustness and predictive capacity. Beyond providing a rigorous theoretical foundation for empirical AE laws, our results demonstrate how microlevel statistical assumptions can explain macroscopic fracture signatures, offering new tools for structural health monitoring and prediction of fractures.