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On improving the numerical convergence of highly nonlinear elasticity problems

Yue Mei, Daniel E. Hurtado, Sanjay Pant Orcid Logo, Ankush Aggarwal Orcid Logo

Computer Methods in Applied Mechanics and Engineering, Volume: 337, Pages: 110 - 127

Swansea University Authors: Sanjay Pant Orcid Logo, Ankush Aggarwal Orcid Logo

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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 transfo...

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Published in: Computer Methods in Applied Mechanics and Engineering
ISSN: 0045-7825
Published: 2018
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa39195
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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.
Keywords: Nonlinear elasticity, Newton’s method, Nonlinear preconditioning, Compression, Soft tissues, Solver convergence
Start Page: 110
End Page: 127