A Mixed Finite Element Method for Multi-Cavity Computation in Incompressible Nonlinear Elasticity
For researchers in computational nonlinear elasticity, this provides an accurate and efficient numerical method for multi-cavity problems, with the discovery of a new bifurcation phenomenon.
The paper develops a mixed finite element method for computing multiple cavities in incompressible nonlinear elasticity, proving it locking-free and convergent, and demonstrating numerical accuracy and efficiency. The method reveals a new bifurcation phenomenon in multi-cavity growth.
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.