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Modelling and Simulation in Engineering
Volume 2017, Article ID 6132106, 10 pages
Research Article

Autotuning of Isotropic Hardening Constitutive Models on Real Steel Buckling Data with Finite Element Based Multistart Global Optimisation on Parallel Computers

1Faculty of Engineering, The University of Bristol, Bristol BS8 1TR, UK
2Advanced Computing Research Centre, The University of Bristol, Bristol BS8 1QU, UK

Correspondence should be addressed to Anton Shterenlikht;

Received 9 August 2016; Revised 18 October 2016; Accepted 6 December 2016; Published 16 January 2017

Academic Editor: Jean-Michel Bergheau

Copyright © 2017 Anton Shterenlikht et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An automatic framework for tuning plastic constitutive models is proposed. It is based on multistart global optimisation method, where the objective function is provided by the results of multiple elastoplastic finite element analyses, executed concurrently. Wrapper scripts were developed for fully automatic preprocessing, including model and mesh generation, analysis, and postprocessing. The framework is applied to an isotropic power hardening plasticity using real load/displacement data from multiple steel buckling tests. M. J. D. Powell’s BOBYQA constrained optimisation package was used for local optimisation. It is shown that using the real data presents multiple problems to the optimisation process because the objective function can be discontinuous, yet relatively flat around multiple local minima, with similar values of the objective function for different local minima. As a consequence the estimate of the global minimum is sensitive to the amount of experimental data and experimental noise. The framework includes the verification step, where the estimate of the global minimum is verified on a different geometry and loading. A tensile test was used for verification in this work. The speed of the method critically depends on the ability to effectively parallelise the finite element solver. Three levels of parallelisation were exploited in this work. The ultimate limitation was the availability of the finite element commercial solver license tokens.