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Damage and fatigue described by a fractional derivative model. (English) Zbl 1349.74030
Summary: 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.

MSC:
74A45 Theories of fracture and damage
35R11 Fractional partial differential equations
35Q74 PDEs in connection with mechanics of deformable solids
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