Large deformation mixed finite elements for smart structures

TL;DR

This paper extends TDNNS finite elements to large deformations in electro-active polymers, demonstrating their effectiveness in avoiding locking issues and enabling accurate modeling of slender structures.

Contribution

It introduces large deformation TDNNS elements for electro-active polymers within an updated Lagrangian framework, maintaining convergence and avoiding locking.

Findings

Convergence remains stable with increasing Lamé parameter.

Flat volume elements effectively discretize slender structures.

Elements are implemented in open source software.

Abstract

Recently, "Tangential Displacement Normal Normal Stress" (TDNNS) elements were introduced for small-deformation piezoelectric structures. Benefits of these ele- ments are that they are free from shear locking in thin structures and volume locking for nearly incompressible materials. We extend these elements to the large defor- mation case for electro-active polymers in the framework of an updated Lagrangian method. We observe that convergence does not deteriorate as the material becomes nearly incompressible with growing Lam\'e parameter $\lambda$, and that the discretization of slender structures by flat volume elements is feasible. The elements are freely available in the open source software package Netgen/NGSolve.