Thermomechanics of damage and fatigue by a phase field model
  In the paper we present an isothermal model for describing damage and fatigue by the use of the Ginzburg-Landau (G-L) equation.   Fatigue produces progressive damage, which is related with a variation of the internal structure of the material. The G-L equation studies the evolution of the order parameter, which describes the constitutive arrangement of the system and, in this framework, the evolution of damage. The thermodynamic coherence of the model is proved.   In the last part of the work, we extend the results of the paper to a non-isothermal system, where fatigue contains thermal effects, which increase the damage of materials. 
Giovambattista Amendola and Mauro Fabrizio
math-ph math.MP