Geodesic
Modelling of singularities in elastoplastic materials with fatigue
Applications of Mathematics, Tome 39 (1994) no. 2, pp. 137-160

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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.
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.
DOI : 10.21136/AM.1994.134250
Classification : 35L67, 73M10, 74R99
Keywords: hysteresis; elastoplasticity; fatigue; hyperbolic system 
Krejčí, Pavel. Modelling of singularities in elastoplastic materials with fatigue. Applications of Mathematics, Tome 39 (1994) no. 2, pp. 137-160. doi: 10.21136/AM.1994.134250
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