Materials Behavior as Mechanism Ensembles: A Probabilistic Framework for Emergent Behaviors
arXiv:2607.27163
The paper proposes a probabilistic framework that treats material behavior as an ensemble of competing mechanisms, using fatigue crack propagation as an example to show how mechanism activation and interaction can be inferred to predict emergent outcomes.
Abstract
Materials behavior is often treated as a deterministic mapping from structure to properties, yet many important phenomena emerge from the conditional activation of multiple mechanisms across scales. This is especially evident in fatigue of metals, where crack growth is typically modeled as monotonic and irreversible process, despite evidence that local microstructure, loading history, and competing unit processes can shift the balance among propagation, arrest, and self-healing. Here we present a probabilistic framework that describes materials behavior as an ensemble of constituent mechanisms whose activation, interaction, and evolution determine emergent outcomes. The framework connects mechanism activation, state evolution, and macroscopic observables in a probabilistic way. In the case of fatigue crack propagation, it reframes damage tolerance as an inference problem over mechanism competition and provides a basis for integrating multiscale simulation, multimodal characterization, and machine learning. The same logic extends to other physical and chemical systems suggesting a portable framework for any system in which emergent behavior reflects mechanism competition under changing conditions. The broader ambition of this perspective review is a shift from correlating structure and performance after the fact to identifying, in advance, the conditions that make desired emergent behavior probable.