On improving the numerical convergence of highly nonlinear elasticity problems

Mei, Y., Hurtado, D. E., Pant, S. and Aggarwal, A. (2018) On improving the numerical convergence of highly nonlinear elasticity problems. Computer Methods in Applied Mechanics and Engineering, 337, pp. 110-127. (doi:10.1016/j.cma.2018.03.033)

Mei, Y., Hurtado, D. E., Pant, S. and Aggarwal, A. (2018) On improving the numerical convergence of highly nonlinear elasticity problems. Computer Methods in Applied Mechanics and Engineering, 337, pp. 110-127. (doi:10.1016/j.cma.2018.03.033)

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Abstract

Finite elasticity problems commonly include material and geometric nonlinearities and are solved using various numerical methods. However, for highly nonlinear problems, achieving convergence is relatively difficult and requires small load step sizes. In this work, we present a new method to transform the discretized governing equations so that the transformed problem has significantly reduced nonlinearity and, therefore, Newton solvers exhibit improved convergence properties. We study exponential-type nonlinearity in soft tissues and geometric nonlinearity in compression, and propose novel formulations for the two problems. We test the new formulations in several numerical examples and show significant reduction in iterations required for convergence, especially at large load steps. Notably, the proposed formulation is capable of yielding convergent solution even when 10–100 times larger load steps are applied. The proposed framework is generic and can be applied to other types of nonlinearities as well.

Item Type:Articles
Additional Information:This work was supported by Welsh Government and Higher Education Funding Council for Wales through theSˆer Cymru National Research Network in Advanced Engineering and Materials (Grant No. F28), and the Engineeringand Physical Sciences Research Council of the UK (Grant No. EP/P018912/1).
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Aggarwal, Dr Ankush
Authors: Mei, Y., Hurtado, D. E., Pant, S., and Aggarwal, A.
College/School:College of Science and Engineering > School of Engineering > Infrastructure and Environment
Journal Name:Computer Methods in Applied Mechanics and Engineering
Publisher:Elsevier
ISSN:0045-7825
ISSN (Online):1879-2138
Published Online:30 March 2018
Copyright Holders:Copyright © 2018 Elsevier
First Published:First published in Computer Methods in Applied Mechanics and Engineering 337:110-127
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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