Coupled electro-elastic deformation and instabilities of a toroidal membrane

TL;DR

This paper investigates large deformations and instabilities in dielectric toroidal membranes under coupled electrical and mechanical loads, revealing how load ratios influence reversible buckling and wrinkling phenomena.

Contribution

It introduces a variational approach and a modified shooting method to analyze highly nonlinear coupled electro-mechanical deformations and instabilities in toroidal membranes.

Findings

Identification of limit point, wrinkling, and buckling instabilities.

Instability onset depends on the ratio of mechanical to electrical load.

Control of state switching through load ratio manipulation.

Abstract

We analyse here the problem of large deformation of dielectric elastomeric membranes under coupled electromechanical loading. Extremely large deformations (enclosed volume changes of 100 times and greater) of a toroidal membrane are studied by the use of a variational formulation that accounts for the total energy due to mechanical and electrical fields. A modified shooting method is adopted to solve the resulting system of coupled and highly nonlinear ordinary differential equations. We demonstrate the occurrence of limit point, wrinkling, and symmetry-breaking buckling instabilities in the solution of this problem. Onset of each of these "reversible" instabilities depends significantly on the ratio of the mechanical load to the electric load, thereby providing a control mechanism for state switching.