  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.
