In this paper, a numerical model for the calculation of the drawbead restraining force is described. The model is formulated using an elastoplastic finite deformation, finite element method. Because of the bending, unbending and reverse bending deformation which occurs as the sheet metal passes through the drawbead, a kinematic hardening constitutive law associated with a description of the cyclic property and the Bauschinger effect is considered. In comparison with experiments, the results based on the kinematic hardening material model proved to be better than those based on the usual isotropic hardening material model.
The creep problems are often involved in soil under cyclic loading, and its behaviors of soil under cyclic loading sparks many arguments in current research field. To propose one new model to demonstrate these creep behaviors of soil under cyclic loading, the cyclic loading was simplified equivalently, and the elastic-viscoplastic model (EVPM) for soil under cyclic loading was established based on the Bingham model. The yield criterion for soil under cyclic loading with constant amplitude was proposed following the simplified load. A constitutive equation based on the EVPM was constructed by using the flow criterion related to the yield criterion. Meanwhile, the parameters of EVPM were identified and discussed. In addition, the case analysis of the EVPM was also performed. The results indicate that the stable and destructive creep behaviors of soil under cyclic loading could be well described by the recommended EVPM, and the obtained parameters in the model exhibited a clear regularity with the increase of dynamic stress amplitude. Besides, the established model could be selected to predict the stable and destructive creep behavior of soil under cyclic loading.
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