Continuum modeling and finite element simulation of incompressible dielectric viscoelastic actuators at finite strains

Dielectric elastomers, known for their ability to undergo large deformations exceeding
100%, are widely used as actuators in adaptive structures and soft robotics. Within the current
contribution, we present a continuum material model that captures the incompressibility and viscous
behavior of these polymers under finite s train and e lectric a ctuation. To address l arge deformations,
we use a multiplicative decomposition of the deformation gradient to separate elastic and viscous
effects. The elastic response is represented by a Yeoh potential, which is well suited to describe the
material behavior under large strains. The evolution of internal strains is modeled using a dissipation
function. Electric field a nd d ielectric d isplacement a re modeled i n s patial c onfiguration, le ading to
an electromechanically coupled problem. We propose a mixed finite e lement f ormulation w ithin a
variational framework based on the above thermodynamic principles. We introduce a novel approach
using volume-preserving tensor-valued elements for internal strains, where we make use of matrix
exponential functions to achieve incompressiblity exactly. As an example, we consider an experimental
setup of a three-dimensional circular actuator. We provide material parameters for VHB4910 for the
proposed model, and compare our results to experimental data from a different work.