A Locking-Free DP-Q2-P1 MFEM for Incompressible Nonlinear Elasticity Problems

Authors

  • Weijie Huang LMAM & School of Mathematical Sciences, Peking University, Beijing, China
  • Zhiping Li LMAM & School of Mathematical Sciences, Peking University, Beijing, China

DOI:

https://doi.org/10.4208/nmtma.OA-2018-0087

Keywords:

DP-Q2-P1 mixed finite element, damped Newton method, locking-free, incompressible nonlinear elasticity, large deformation gradient, cavitation.

Abstract

A mixed finite element method (MFEM), using dual-parametric piecewise biquadratic and affine (DP-Q2-P1) finite element approximations for the deformation and the pressure like Lagrange multiplier respectively, is developed and analyzed for the numerical computation of incompressible nonlinear elasticity problems with large deformation gradient, and a damped Newton method is applied to solve the resulted discrete problem. The method is proved to be locking free and stable. The accuracy and efficiency of the method are illustrated by numerical experiments on some typical cavitation problems.

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Published

2019-10-12

Issue

Vol. 12 No. 4 (2019)

Section

Articles