A Locking-free DP-Q2-P1 MFEM for Incompressible Nonlinear Elasticity Problems
For computational mechanics researchers, this provides a stable and locking-free numerical method for incompressible nonlinear elasticity, though it is an incremental improvement over existing MFEM approaches.
The paper develops a locking-free mixed finite element method (DP-Q2-P1) for incompressible nonlinear elasticity with large deformations, proving stability and demonstrating accuracy on cavitation problems.
A mixed finite element method (MFEM), using dual-parametric piecewise bi-quadratic 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.