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Bubble-Enriched Smoothed Finite Element Methods for Nearly-Incompressible Solids

Changkye Lee1, Sundararajan Natarajan2, Jack S. Hale3, Zeike A. Taylor4, Jurng-Jae Yee1,*, Stéphane P. A. Bordas3,*

1 University Core Research Center for Disaster-Free and Safe Ocean City Construction, Dong-A University, Busan, 49315, Korea
2 Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, 600036, India
3 Faculty of Science, Technology and Communication, University of Luxembourg, Esch-sur-Alzette, L-4364, Luxembourg
4 CISTIB-Center for Computational Imaging & Simulation Technologies in Biomedicine, School of Engineering, Leeds, LS2 9JT, UK

* Corresponding Authors: Jurng-Jae Yee. Email: email; Stéphane P. A. Bordas. Email: email

Computer Modeling in Engineering & Sciences 2021, 127(2), 411-436. https://doi.org/10.32604/cmes.2021.014947

Abstract

This work presents a locking-free smoothed finite element method (S-FEM) for the simulation of soft matter modelled by the equations of quasi-incompressible hyperelasticity. The proposed method overcomes well-known issues of standard finite element methods (FEM) in the incompressible limit: the over-estimation of stiffness and sensitivity to severely distorted meshes. The concepts of cell-based, edge-based and node-based S-FEMs are extended in this paper to three-dimensions. Additionally, a cubic bubble function is utilized to improve accuracy and stability. For the bubble function, an additional displacement degree of freedom is added at the centroid of the element. Several numerical studies are performed demonstrating the stability and validity of the proposed approach. The obtained results are compared with standard FEM and with analytical solutions to show the effectiveness of the method.

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APA Style
Lee, C., Natarajan, S., Hale, J.S., Taylor, Z.A., Yee, J. et al. (2021). Bubble-enriched smoothed finite element methods for nearly-incompressible solids. Computer Modeling in Engineering & Sciences, 127(2), 411-436. https://doi.org/10.32604/cmes.2021.014947
Vancouver Style
Lee C, Natarajan S, Hale JS, Taylor ZA, Yee J, Bordas SPA. Bubble-enriched smoothed finite element methods for nearly-incompressible solids. Comput Model Eng Sci. 2021;127(2):411-436 https://doi.org/10.32604/cmes.2021.014947
IEEE Style
C. Lee, S. Natarajan, J.S. Hale, Z.A. Taylor, J. Yee, and S.P.A. Bordas "Bubble-Enriched Smoothed Finite Element Methods for Nearly-Incompressible Solids," Comput. Model. Eng. Sci., vol. 127, no. 2, pp. 411-436. 2021. https://doi.org/10.32604/cmes.2021.014947



cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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