Large deformation mixed finite elements for smart structures

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 Lamé parameter $λ$, 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.