A Mixed Finite Element Method for Multi-Cavity Computation in Incompressible Nonlinear Elasticity

A Mixed Finite Element Method for Multi-Cavity Computation in Incompressible Nonlinear Elasticity

Year:    2019

Author:    Weijie Huang, Zhiping Li

Journal of Computational Mathematics, Vol. 37 (2019), Iss. 5 : pp. 609–628

Abstract

A mixed finite element method combining an iso-parametric $Q_2$-$P_1$ element and an iso-parametric $P^+_2$-$P_1$ element is developed for the computation of multiple cavities in incompressible nonlinear elasticity. The method is analytically proved to be locking-free and convergent, and it is also shown to be numerically accurate and efficient by numerical experiments. Furthermore, the newly developed accurate method enables us to find an interesting new bifurcation phenomenon in multi-cavity growth.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1807-m2018-0137

Journal of Computational Mathematics, Vol. 37 (2019), Iss. 5 : pp. 609–628

Published online:    2019-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    20

Keywords:    Multiple cavitation computation Incompressible nonlinear elasticity Mixed finite element method Locking-free Convergent.

Author Details

Weijie Huang

Zhiping Li