Stability Analysis on the Algorithm of Constitutive Relation in Viscoplastic Materials. (3rd June 2016)

• Record Type: Journal Article
• Authors: Liu, M.-T.; Li, Y.-C.; Hu, X.-Z.; Zhang, J.; Tang, T.-G.
• Is Part Of: Journal of mechanics. Volume 33:Number 2(2017)
• Page Start: 173
• Page End: 181
• Publication Date: 2016-06-03
• Subjects: Viscoplastic constitutive relationship -- Numerical stability -- Explicit precise algorithm -- Iterative algorithm; Mechanics, Analytic -- Periodicals; Mechanics -- Periodicals; 620.1005
• DOI: 10.1017/jmech.2016.49
• Languages: English
• ISSNs: 1727-7191

Abstract

Abstract : The numerical stability of the explicit precise algorithm, which was developed for the viscoplastic materials, was analyzed. It was found that this algorithm is not absolutely stable. A necessary but not sufficient condition for the numerical stability was deduced. It showed that the time step in numerical calculation should be less than a certain value to guarantee the stability of explicit precise algorithm. Through a series of numerical examples, the stability analysis on the explicit precise algorithm was proved to be reliable. At last, an iterative algorithm was presented for viscoplastic materials. Both of the theoretical and numerical results showed that the iterative algorithm is unconditionally stable and its convergence rate is rapid. In practice, the explicit precise algorithm and iterative algorithm can be combined to obtain reliable results with the minimum computing costs.