The Energy-Efficiency Dynamics of Materials: Strength, Toughness, and Fatigue — An EET Framework for Mechanical Performance

Materials are the physical embodiment of constrained-state energy. Their mechanical properties—strength, toughness, fatigue life—reflect the ability to store, dissipate, and reorganize energy under external loads. Yet current theories describe these properties through separate empirical frameworks (Griffith theory, Paris law, S-N curves) without a unifying first-principles foundation. This paper develops a framework within Energy-Efficiency Theory (EET). Starting from Yang's three causal-functional postulates, we propose that materials are constrained-state energy structures, and mechanical performance is governed by the competition between energy storage and energy release. The Energy-Efficiency Regulator (EER) operates at the microstructural level: stress concentration stores energy at crack tips; plastic deformation and crack propagation release it. Yang's Ben-Shi sliding describes the transition between brittle (Ben) and ductile (Shi) behavior. We derive quantitative relations: strength (Griffith) from energy balance, toughness as critical energy release rate at the Ben-Shi transition, and fatigue life from cumulative damage with Paris law exponent linked to damage sensitivity. The framework unifies static and cyclic failure, resolves the brittle-ductile transition, and provides testable predictions linking microstructural parameters (grain size, dislocation density) to macroscopic properties. Three falsifiable predictions with statistical power validation are proposed. This work establishes a first-principles energy ontology for materials science, bridging atomic-scale constraints to engineering performance.