The phenomenon of the fatigue in elastic materials is represented by introducing a derivative of real order in the stress–strain relation. It is found that this phenomenon occurs when aγ/ηD (Q is the specific dissipation, η the elastic parameter, ? the yield stress, D the maximum amplitude of the cyclic strain applied with period 4a) is near the critical value 1+0.113/Q. This model allows also to estimate the number of cycles which would give the fatique as function of the maximum strain applied and of its frequency.
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Michèle Caputo (1979) studied this question.
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