Abstract
For problems involving rate constitutive equations, such as rate-independent elasto-plasticity, consistent or algorithmic tangent moduli (operators) play an important role in preserving the asymptotic quadratic rate of convergence of incremental-iterative solution schemes based on Newton’s method. Furthermore, consistent (algorithmic) tangent moduli are required in structural response sensitivity analysis based on the direct differentiation method. This paper focuses on the derivation of the consistent tangent moduli for a pressure independent multi-yield-surface J2 (Von Mises) plasticity model that has been used extensively in nonlinear constitutive modeling of soil materials, but can be used for other materials as well. Application examples are provided to validate the consistent tangent moduli derived herein, and to compare the rate of convergence and computational time of nonlinear incremental-iterative analyses performed using the consistent and continuum tangent moduli, respectively.
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Acknowledgments
This research was partially funded by the Pacific Earthquake Engineering Research (PEER) Center through the Earthquake Engineering Research Center Program of the National Science Foundation under Award No. EEC-9701568 and a grant from Lawrence Livermore National Laboratory with Dr. David McCallen as Program Leader. This support is gratefully acknowledged. The authors would like to thank Dr. Jinchi Lu for providing invaluable help for the use of the OpenSeesPL software to create the mesh for third application example. Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the sponsor.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Gu, Q., Conte, J.P., Yang, Z. et al. Consistent tangent moduli for multi-yield-surface J2 plasticity model. Comput Mech 48, 97–120 (2011). https://doi.org/10.1007/s00466-011-0576-7
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DOI: https://doi.org/10.1007/s00466-011-0576-7