Strain smoothing for compressible and nearly-incompressible finite elasticity

Lee, Chang-Kye, Mihai, L. Angela ORCID: https://orcid.org/0000-0003-0863-3729, Hale, Jack S., Kerfriden, Pierre ORCID: https://orcid.org/0000-0002-7749-3996 and Bordas, Stephane Pierre Alain ORCID: https://orcid.org/0000-0001-8634-7002 2017. Strain smoothing for compressible and nearly-incompressible finite elasticity. Computers & Structures 182 , pp. 540-555. 10.1016/j.compstruc.2016.05.004

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Abstract

We present a robust and efficient form of the smoothed finite element method (S-FEM) to simulate hyperelastic bodies with compressible and nearly-incompressible neo-Hookean behaviour. The resulting method is stable, free from volumetric locking and robust on highly distorted meshes. To ensure inf-sup stability of our method we add a cubic bubble function to each element. The weak form for the smoothed hyperelastic problem is derived analogously to that of smoothed linear elastic problem. Smoothed strains and smoothed deformation gradients are evaluated on sub-domains selected by either edge information (edge-based S-FEM, ES-FEM) or nodal information (node-based S-FEM, NS-FEM). Numerical examples are shown that demonstrate the efficiency and reliability of the proposed approach in the nearly-incompressible limit and on highly distorted meshes. We conclude that, strain smoothing is at least as accurate and stable, as the MINI element, for an equivalent problem size.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics Engineering Advanced Research Computing @ Cardiff (ARCCA)
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Strain smoothing; Smoothed finite element method (S-FEM); Near-incompressibility; Large deformation; Volumetric locking; Mesh distortion sensitivity
Publisher:	Elsevier
Date of First Compliant Deposit:	5 May 2016
Date of Acceptance:	5 May 2016
Last Modified:	06 Nov 2024 11:30
URI:	https://orca.cardiff.ac.uk/id/eprint/90588

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