#### Event Title

#### Description

This study presents a model of a curved cantilever dielectric elastomer actuator (DEA) containing liquid-phase metal electrodes utilizing universal solutions from finite nonlinear elasticity. The DEA comprises a compliant capacitor which has been prestrained some prescribed amount, affixed to a substrate, and bonded to a secondary layer of unstrained bulk elastomer. Upon release of the cured layers, internal stresses cause a bending moment and force the final configuration into a beam with some initial curvature. Application of a voltage across the electrodes creates an electrostatic pressure, inducing compressive Maxwell stresses across the dielectric layer. This relieves some of the internal moment and forces actuation of the device in the form of beam straightening. We assume incompressibility and isotropic, neo-Hookean behavior of our bulk elastomeric material. Employing simplifying assumptions such as constant curvature across the length of the beam (i.e., a perfectly circular arc) and plane strain in the plane of actuation, we utilize the Universal Solution in finite bending to represent the kinematics and implement Maxwell’s equations to describe beam deflection as a function of applied voltage. We use the principal of minimum potential energy to solve for beam deflection (represented by curvature of the device) as a function of electric potential across the electrodes after considering energy contributions due to elasticity, electrostatics and expended electric work. This model is then compared to experimental data obtained from testing multiple fabricated devices. The emerging fields of soft robotics and wearable computing require new classes of soft and elastically deformable electronics, which unlike traditional electronic components, must be flexible and/or stretchable. Thus it is important to develop predictive and comprehensive models describing their behavior.

#### Recommended Citation

Finkenauer, L.,
Wissman, J.,
Majidi, C.,
&
Deseri, L.
(2014).
Modeling of curved cantilever dielectric elastomer actuator using universal solution in finite bending.
In A. Bajaj, P. Zavattieri, M. Koslowski, & T. Siegmund (Eds.).
*
Proceedings of the Society of Engineering Science 51st Annual Technical Meeting, October 1-3, 2014
*,
West Lafayette: Purdue University Libraries Scholarly Publishing Services, 2014.
http://docs.lib.purdue.edu/ses2014/mss/ssm/30

Modeling of curved cantilever dielectric elastomer actuator using universal solution in finite bending

This study presents a model of a curved cantilever dielectric elastomer actuator (DEA) containing liquid-phase metal electrodes utilizing universal solutions from finite nonlinear elasticity. The DEA comprises a compliant capacitor which has been prestrained some prescribed amount, affixed to a substrate, and bonded to a secondary layer of unstrained bulk elastomer. Upon release of the cured layers, internal stresses cause a bending moment and force the final configuration into a beam with some initial curvature. Application of a voltage across the electrodes creates an electrostatic pressure, inducing compressive Maxwell stresses across the dielectric layer. This relieves some of the internal moment and forces actuation of the device in the form of beam straightening. We assume incompressibility and isotropic, neo-Hookean behavior of our bulk elastomeric material. Employing simplifying assumptions such as constant curvature across the length of the beam (i.e., a perfectly circular arc) and plane strain in the plane of actuation, we utilize the Universal Solution in finite bending to represent the kinematics and implement Maxwell’s equations to describe beam deflection as a function of applied voltage. We use the principal of minimum potential energy to solve for beam deflection (represented by curvature of the device) as a function of electric potential across the electrodes after considering energy contributions due to elasticity, electrostatics and expended electric work. This model is then compared to experimental data obtained from testing multiple fabricated devices. The emerging fields of soft robotics and wearable computing require new classes of soft and elastically deformable electronics, which unlike traditional electronic components, must be flexible and/or stretchable. Thus it is important to develop predictive and comprehensive models describing their behavior.