Abstract
This paper is concerned with the bifurcation analysis of a pressurized electroelastic circular cylindrical tube with closed ends and compliant electrodes on its curved boundaries. The theory of small incremental electroelastic deformations superimposed on a finitely deformed electroelastic tube is used to determine those underlying configurations for which the superimposed deformations do not maintain the perfect cylindrical shape of the tube. First, prismatic bifurcations are examined and solutions are obtained which show that for a neo-Hookean electroelastic material prismatic modes of bifurcation become possible under inflation. This result contrasts with that for the purely elastic case for which prismatic bifurcation modes were found only for an externally pressurized tube. Second, axisymmetric bifurcations are analyzed, and results for both neo-Hookean and Mooney–Rivlin electroelastic energy functions are obtained. The solutions show that in the presence of a moderate electric field the electroelastic tube becomes more susceptible to bifurcation, i.e., for fixed values of the axial stretch axisymmetric bifurcations become possible at lower values of the circumferential stretches than in the corresponding problems in the absence of an electric field. As the magnitude of the electric field increases, however, the possibility of bifurcation under internal pressure becomes restricted to a limited range of values of the axial stretch and is phased out completely for sufficiently large electric fields. Then, axisymmetric bifurcation is only possible under external pressure.
Highlights
Electroactive elastomeric materials have attracted much interest in the literature in recent years because their properties are suitable for many potential applications in engineering science, such as in the production of actuators, sensors and other devices
One of the geometries of relevance in this context is that of a circular cylindrical tube actuator made of a dielectric elastomer with flexible electrodes on its curved boundaries
For thin- and thick-walled cylindrical shells of elastic material under internal and external pressure, extensive bifurcation analyses have been provided in the papers [7,8] by Haughton and Ogden on the basis of the theory of small deformations superimposed on a finite deformation
Summary
Electroactive elastomeric materials have attracted much interest in the literature in recent years because their properties are suitable for many potential applications in engineering science, such as in the production of actuators, sensors and other devices. For thin- and thick-walled cylindrical shells of elastic material under internal and external pressure, extensive bifurcation analyses have been provided in the papers [7,8] by Haughton and Ogden on the basis of the theory of small deformations superimposed on a finite deformation. For a specific model of a neo-Hookean electroelastic material we find that prismatic modes of bifurcation are possible under inflation in the presence of an electric field, which is in contrast to the result for the purely mechanical situation obtained in [8]. The results are compared with those in the purely elastic case: depending on the magnitude of the electric field its presence may make the electroelastic tube more susceptible to bifurcation for each of the two energy functions adopted (neo-Hookean and Mooney–Rivlin-based electroelastic models), i.e., bifurcation becomes possible at lower circumferential stretches than is the case for purely elastic materials without electromechanical interactions. Some important aspects of the code, which employs a numerical scheme used in [8], are discussed and explained briefly in [13]
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