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

TL;DR

This paper introduces a locking-free mixed finite element method using dual-parametric bi-quadratic and affine elements for solving incompressible nonlinear elasticity problems with large deformations, demonstrating stability and efficiency.

Contribution

The paper develops and analyzes a novel locking-free mixed finite element method (DP-Q2-P1 MFEM) for large deformation incompressible elasticity problems, with proven stability and demonstrated accuracy.

Findings

Method is locking free and stable.

Numerical experiments confirm accuracy and efficiency.

Effective for cavitation problems.

Abstract

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.