Large deformation mixed finite elements for smart structures

Abstract

Recently, “Tangential Displacement Normal Normal Stress” elements were introduced for small-deformation piezoelectric structures. Benefits of these elements 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 deformation 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.

Keywords:

• Large deformation electro-elasticity
• updated Lagrangian
• mixed finite elements
• locking free
• smart materials