Damage and fatigue described by a fractional derivative model

As in 1], damage is associated with fatigue that a material undergoes. In this paper, because we work with viscoelastic solids represented by a fractional model, damage is described by the order of the fractional derivative, which represents the phase field satisfying Ginzburg-Landau equation, which describes the evolution of damage.Finally, in our model, damage is caused, not only by fatigue, but also directly by a source related to environmental factors and described by a positive time function.

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