Open Access

ARTICLE

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

by Changkye Lee¹, Sundararajan Natarajan², Jack S. Hale³, Zeike A. Taylor⁴, Jurng-Jae Yee^1,*, Stéphane P. A. Bordas^3,*

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: ; Stéphane P. A. Bordas. Email:

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

Received 10 November 2020; Accepted 04 January 2021; Issue published 19 April 2021

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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Keywords

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