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Volume 37, Issue 5
A Mixed Finite Element Method for Multi-Cavity Computation in Incompressible Nonlinear Elasticity

Weijie Huang & Zhiping Li

DOI: 10.4208/jcm.1807-m2018-0137

J. Comp. Math., 37 (2019), pp. 609-628.

Published online: 2019-03

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  • 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.

  • Keywords

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

  • AMS Subject Headings

65N12, 65N30, 74B20, 74G15, 74M99

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

huangwj@pku.edu.cn (Weijie Huang)

lizp@math.pku.edu.cn (Zhiping Li)

  • BibTex
  • RIS
  • TXT
@Article{JCM-37-609, author = {Huang , Weijie and Li , Zhiping}, title = {A Mixed Finite Element Method for Multi-Cavity Computation in Incompressible Nonlinear Elasticity}, journal = {Journal of Computational Mathematics}, year = {2019}, volume = {37}, number = {5}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1807-m2018-0137}, url = {http://global-sci.org/intro/article_detail/jcm/13037.html} }
TY - JOUR T1 - A Mixed Finite Element Method for Multi-Cavity Computation in Incompressible Nonlinear Elasticity AU - Huang , Weijie AU - Li , Zhiping JO - Journal of Computational Mathematics VL - 5 SP - 609 EP - 628 PY - 2019 DA - 2019/03 SN - 37 DO - http://doi.org/10.4208/jcm.1807-m2018-0137 UR - https://global-sci.org/intro/article_detail/jcm/13037.html KW - Multiple cavitation computation, Incompressible nonlinear elasticity, Mixed finite element method, Locking-free, Convergent. AB -

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.

Huang , Weijie and Li , Zhiping. (2019). A Mixed Finite Element Method for Multi-Cavity Computation in Incompressible Nonlinear Elasticity. Journal of Computational Mathematics. 37 (5). 609-628. doi:10.4208/jcm.1807-m2018-0137
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