Liu Mingtao, Li Yongchi, Hu Xiuzhang, Zhang Jie. The numerical stability of the constitutive calculation on viscoplastic materials[J]. Explosion And Shock Waves, 2017, 37(5): 969-975. doi: 10.11883/1001-1455(2017)05-0969-07
Citation:
Liu Mingtao, Li Yongchi, Hu Xiuzhang, Zhang Jie. The numerical stability of the constitutive calculation on viscoplastic materials[J]. Explosion And Shock Waves, 2017, 37(5): 969-975. doi: 10.11883/1001-1455(2017)05-0969-07
Liu Mingtao, Li Yongchi, Hu Xiuzhang, Zhang Jie. The numerical stability of the constitutive calculation on viscoplastic materials[J]. Explosion And Shock Waves, 2017, 37(5): 969-975. doi: 10.11883/1001-1455(2017)05-0969-07
Citation:
Liu Mingtao, Li Yongchi, Hu Xiuzhang, Zhang Jie. The numerical stability of the constitutive calculation on viscoplastic materials[J]. Explosion And Shock Waves, 2017, 37(5): 969-975. doi: 10.11883/1001-1455(2017)05-0969-07
At first, we analyzed the numerical stability of the explicit exact algorithm developed for the viscoplastic material, and then found that the explicit exact algorithm is not absolutely stable, deduced a necessary criterion that the time step should be kept below a certain value to guarantee the constitutive calculation stability. A series of numerical examples were presented to validate the reliability of the present stability analysis on the explicit exact algorithm. The results of the numerical examples show that the effective stress is unstable while the stability criterion for the constitutive calculation is not satisfied, but a complex deformation process including the elastic load, the plastic load, the elastic unload, the reverse elastic load and the reverse plastic load is accurately described while the stability criterion is satisfied. Further numerical results indicate that the stability criterion can accurately predict the relationships between the maximum time step and each parameter.
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