The unified mechanics theory (UMT) is ab-initio unification of the second law of thermodynamics and Newton's universal laws of motion, in which Boltzmann's second law of entropy formulation governs dissipation & degradation. Hence, the unified mechanics theory does not require any empirical dissipation & degradation potential function or an empirical void evolution function. Material degradation is quantified on the Thermodynamic state index (TSI) axis based on the specific entropy production, which starts at zero and asymptotically approaches one at failure. However, to calculate the TSI coordinate, the thermodynamic fundamental equation of the material must be derived analytically.

The unified mechanics theory (UMT) was used to predic the high cycle fatigue and ultrasonic vibration fatigue life of low-carbon steel in these two studies, respectively. Thermal conduction due to thermo-mechanical coupling, microplastic energy dissipation at defect sites, and internal friction scattering due to rate-dependent dislocation motion, during the elastic fatigue loading are discussed in detail.

https://doi.org/10.1016/j.mechmat.2021.104116

https://doi.org/10.1016/j.ijsolstr.2021.111313