A mathematical model for cylindrical, fiber reinforced electro-pneumatic actuators

Abstract

a b s t r a c tIn recent years, dielectric elastomers have received increasing attention due to their unparalleled large strain actuation response (>100%). The force output, however, has remained a major limiting factor for many applications. To address this limitation, a model for a fiber reinforced dielectric elastomer actuator based on the deformation mechanism of McKibben actuators is presented. In this novel configuration, the outer cylindrical surface of a dielectric elastomer is enclosed by a network of helical fibers that are thin, flexible and inextensible. This configuration yields an axially contractile actuator, in contrast to unreinforced actuators which extend. The role of the fiber network is twofold: (i) to serve as reinforcement to improve the load-bearing capability of dielectric elastomers, and (ii) to render the actuator inextensible in the axial direction such that the only free deformation path is simultaneous radial expansion and axial contraction. In this paper, a mathematical model of the electromechanical response of fiber reinforced dielectric elastomers is derived. The model is developed within a continuum mechanics framework for large deformations. The cylindrical electro-pneumatic actuator is modeled by adapting Green and Adkins' theory of reinforced cylinders to account for the applied electric field. Using this approach, numerical solutions are obtained assuming a Mooney-Rivlin material model. The results indicate that the relationship between the contractile force and axial shortening is bilinear within the voltage range considered. The characteristic response as a function of various system parameters such as the fiber angle, inflation pressure, and the applied voltage are reported. In this paper, the elastic portion of the modeling approach is validated using experimental data for McKibben actuators.

Finite deformations of an electroelastic circular cylindrical tube

“…Otherwise the equations are unchanged. To include inextensible fibres, as in [13], an additional constraint is required.…”

“…The actuating (axial) force can be generated by inflation and/or an electric field, and is more versatile than if the actuation is purely from an electric field since it can take advantage of both actuation mechanisms. For example, actuation by inflation can be used for the delicate handling of fragile objects where a soft touch is needed [12], while actuation by an electric field can be advantageous for some applications where rapid and accurate deformation is required [13]. The collection of papers in the volume by Carpi et al [14] provides a source of information about the technology of dielectric actuators and their applications.…”

“…Their mechanical analysis, however, was based on the linear theory of elasticity. In the nonlinear elasticity context a mathematical model for a thinwalled cylindrical fibre-reinforced pneumatic actuator was introduced in [13] in which a purely elastic incompressible strain-energy function was adopted, the effect of electric field being incorporated through the Maxwell stress. The fibres were taken to be inextensible and symmetrically and helically wound and the mode of actuation consisted of an inflation pressure followed by an applied voltage (potential difference), leading to radial expansion and, because of the fibre inextensibility, to axial shortening.…”

“…Zhu et al [16] also examined the electromechanical stability of the tube by considering the relationship between the applied voltage and the resulting (axial) actuation strain. To the authors' knowledge the two papers [13] and [16] constitute the main literature concerned with analysing tubular dielectric actuators in the nonlinear context.…”

Analysis of multilayer electro-active tubes under different constraints

“…Singh and Pipkin (1966) and Carpi and De Rossi (2004) analyzed the electromechanical behavior of soft dielectric tubes for finite and small strains, respectively. Goulbourne (2009) developed and validated through comparison with experimental data a numerical model to describe axisymmetric deflections of a tubular DE sensor attached to a McKibben actuator. Zhu et al (2010) analyzed the electromechanical instability of a neo-Hookean soft dielectric tube prestretched by a load and actuated by a radial electric field.…”