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Stability Analysis on the Algorithm of Constitutive Relation in Viscoplastic Materials

Published online by Cambridge University Press:  03 June 2016

M.-T. Liu ,
Y.-C. Li ,
X.-Z. Hu ,
J. Zhang  and
T.-G. Tang
M.-T. Liu
Affiliation:
Institute of Fluid PhysicsChina Academy of Engineering PhysicsSichuan, China
Y.-C. Li
Affiliation:
Department of Modern MechanicsUniversity of Science and Technology of ChinaAnhui, China
X.-Z. Hu
Affiliation:
Department of Modern MechanicsUniversity of Science and Technology of ChinaAnhui, China
J. Zhang
Affiliation:
Department of Modern MechanicsUniversity of Science and Technology of ChinaAnhui, China
T.-G. Tang*
Affiliation:
Institute of Fluid PhysicsChina Academy of Engineering PhysicsSichuan, China
*
*Corresponding author ([email protected])
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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.

Keywords

Viscoplastic constitutive relationshipNumerical stabilityExplicit precise algorithmIterative algorithm
Type
Research Article
Information
Journal of Mechanics , Volume 33 , Issue 2 , April 2017 , pp. 173 - 181
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2017 

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