A cycle jumping scheme for numerical integration of coupled damage and viscoplastic models for cyclic loading paths
Keywords:
viscoplasticity, damage, low cycle fatigue, asymptotic integration, cycle jump, finite elementsAbstract
A new practical methodology for the analysis of the damage to viscoplastic structures under low cycle fatigue loading paths is proposed The idea consists of carrying out a two time scale scheme an implicit algorithm for the numerical integration of the constitutive equations inside the loading cycles (small time scale), and an explicit scheme over the loading cycles (large time scale) For the small time integration, an implicit asymptotic algorithm based on the integral formulation of the constitutive equations, is used For the large time scale integration, an explicit algorithm, called "cycle jump technique" is used to integrate the model over all the loading cycles It can be shown that the combination of the two schemes is advantageous It allows to use and restore a limited number of variables, which are sufficient to estimate a cycle jump and give a measure of the way in which all the state variables are changing over the loading cycles Numerical results are presented and discussed at both Gauss point and structural levels in order to judge the applicability, efficiency and accuracy of the proposed method
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