Procedures to build trust in nonlinear elastoplastic integration algorithm: solution and code verification
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ORIGINAL ARTICLE
Procedures to build trust in nonlinear elastoplastic integration algorithm: solution and code verification Yuan Feng1 · Kaveh Zamani2 · Han Yang1 · Hexiang Wang1 · Fangbo Wang1 · Boris Jeremić1,3 Received: 18 December 2018 / Accepted: 23 May 2019 © Springer-Verlag London Ltd., part of Springer Nature 2019
Abstract In the last decades, with the development of a number of nonlinear elastic–plastic integration algorithms, the correctness or accuracy of the underlying solution becomes the main concern, in both academia and industry. Correctness or accuracy can be estimated (and improved) using verification. Verification is one of the main procedures to build trust in the numerical modeling of any phenomena. A full verification process comprises (a) solution verification (calculation verification) and (b) code verification. Presented in this paper are verification procedures for constitutive, elastic–plastic integration algorithms, as used in computational nonlinear solid mechanics. Both explicit and implicit integration algorithms for elastic–plastic constitutive equations are verified using existing and new developed verification technique. Verification techniques used include prescribed solution forcing and Richardson extrapolation. In addition, grid convergence index is applied to estimate the algorithmic uncertainty during the integration process. Verification of elastic–plastic integration algorithms is applied to a number of material models: from simple von Mises perfectly plastic to sophisticated hyperbolic Drucker–Prager with nonlinear Armstrong–Frederick rotational kinematic hardening. Besides, algorithmic uncertainty is estimated with both associative and non-associative material model. In addition, caveats and pitfalls to consider in the code/solution verification processes are deeply discussed. Keywords Elastoplastic algorithms · Prescribed solution forcing · Richardson extrapolation · Grid convergence index (GCI)
1 Introduction Modern computational modeling systems are very often used in engineering community for design and assessment. Given all the positive aspects of using computational modeling systems, a fundamental question is this: to what extent can we trust model results [29, 40]. There are a number of engineering failures that can be tied to problems in the numerical codes [12, 16] or to misuse of models. The set of activities and procedures that can be used to build trust in numerical modeling results are called verification and validation [40, 51]. According to Roache’s definition [37]
* Boris Jeremić [email protected] 1
Department of Civil and Environmental Engineering, University of California, Davis, CA, USA
2
Wood Rodgers, Sacramento, CA, USA
3
Earth and Environmental Sciences Area, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
verification is the response to the following question: “Is the model solving mathematical equations correctly?”. On the other hand, validation can be defined through this question: “Is the model solving the correct e
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