Article

Stability Analysis on the Algorithm of Constitutive Relation in Viscoplastic Materials

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  • Institute of Fluid Physics
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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.

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a b s t r a c t This paper investigates the computational performance of S-CLAY1S constitutive model by varying its yield function equation. S-CLAY1S is an advanced anisotropic elasto-plastic model that has been developed based on the extension of conventional critical state theory. In addition to modified Cam-Clay's hardening law, S-CLAY1S also accounts for inherent and evolving plastic anisotropy, interparticle bonding and degradation of bonds during plastic straining. A modified Newton–Raphson stress update algorithm has been adopted for the implementation of the model and it was found that the algorithm's convergence performance is sensitive to the expression of the yield function. It is shown that for an elasto-plastic model which is developed based on the critical state theory, it is possible to improve the performance of the numerical implementation by changing the form of the yield function. The results of this work can provide a new perspective for computationally cost-effective implementation of complex constitutive models in finite element analysis that can yield in more efficient boundary value level simulations. & 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/).
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