Bifurcation analysis of residually stressed neo-Hookean and Ogden electroelastic tubes
Melnikov A. Merodio J. Bustamante R. Dorfmann L.
17 October 2022Royal Society Publishing
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
2022#380Issue 2234
The conditions for bifurcation of a circular cylindrical tube of elastic material subjected to combined axial loading and internal pressure are well known and are frequently used as a reference in related works. The present paper takes the theory further by considering a residually stressed circular cylindrical dielectric tube subjected to a combination of internal or external pressure, axial load and radial electric field. We examine axisymmetric incremental deformations and increments in the electric displacement superimposed on a known finitely deformed and residually stressed configuration in the presence of an electric field. The governing equations and boundary conditions are first obtained in general form and then specialized for the neo-Hookean and Ogden electroelastic models. The system of equations is solved numerically for different values of charge density and radial and circumferential residual stresses, and the results are compared with the purely elastic case. The bifurcation curves are presented as the azimuthal stretch on the inner surface versus the axial stretch together with the corresponding zero pressure curves. This article is part of the theme issue The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity.
dielectric elastomers , electroelastic instabilities , nonlinear electroelasticity
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Department of Mathematics, Nazarbayev University, Kabanbay Batyr Ave. 53, Nur-Sultan, 010000, Kazakhstan
Departamento de Matemática Aplicada A Las TIC, ETS de Ingeniería de Sistemas Informáticos, Universidad Politécnica de Madrid, Madrid, 28031, Spain
Departamento de Ingeniería Mecánica, Universidad de Chile, Santiago Centro, Santiago, Chile
Department of Civil and Environmental Engineering, Tufts University, Medford, 02155, MA, United States
Department of Mathematics
Departamento de Matemática Aplicada A Las TIC
Departamento de Ingeniería Mecánica
Department of Civil and Environmental Engineering
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