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# Article

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Keywords:
hysteresis; elastoplasticity; fatigue; hyperbolic system
Summary:
The hypothesis that, on the macroscopic level, the accumulated fatigue of an elastoplastic material with kinematic hardening can be identified from the mathematical point of view with the dissipated energy, is used for the construction of a new constitutive elastoplastic fatigue model. Its analytical investigation characterizes conditions for the formation of singularities in a finite time. The corresponding constitutive law is then coupled with the dynamical equation of motion of a one-dimensional continuum and the resulting hyperbolic problem is solved via space-discretization method.
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