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Hyperelastic finite deformation analysis with the unsymmetric finite element method containing homogeneous solutions of linear elasticity

Zhi Li, Song Cen, Junbin Huang, Chenfeng Li Orcid Logo

International Journal for Numerical Methods in Engineering, Volume: 121, Issue: 16

Swansea University Author: Chenfeng Li Orcid Logo

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DOI (Published version): 10.1002/nme.6378

Abstract

A recent unsymmetric 4‐node, 8‐DOF plane finite element US‐ATFQ4 is generalized to hyperelastic finite deformation analysis. Since the trial functions of US‐ATFQ4 contain the homogenous closed analytical solutions of governing equations for linear elasticity, the key of the proposed strategy is how...

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Published in: International Journal for Numerical Methods in Engineering
ISSN: 0029-5981 1097-0207
Published: Wiley 2020
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa54435
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Abstract: A recent unsymmetric 4‐node, 8‐DOF plane finite element US‐ATFQ4 is generalized to hyperelastic finite deformation analysis. Since the trial functions of US‐ATFQ4 contain the homogenous closed analytical solutions of governing equations for linear elasticity, the key of the proposed strategy is how to deal with these linear analytical trial functions (ATFs) during the hyperelastic finite deformation analysis. Assuming that the ATFs can properly work in each increment, an algorithm for updating the deformation gradient interpolated by ATFs is designed. Furthermore, the update of the corresponding ATFs referred to current configuration is discussed with regard to the hyperelastic material model, and a specified model, neo‐Hookean model, is employed to verify the present formulation of US‐ATFQ4 for hyperelastic finite deformation analysis. Various examples show that the present formulation not only remain the high accuracy and mesh distortion tolerance in the geometrically nonlinear problems, but also possess excellent performance in the compressible or quasi‐incompressible hyperelastic finite deformation problems where the strain is large.
Issue: 16