Bifurcation of a finitely deformed functionally graded dielectric elastomeric tube

• Published in: International journal of non-linear mechanics Vol. 127; p. 103593
• Main Authors: Zhou, Weijian, Chen, Yingjie, Su, Yipin
• Format: Journal Article
• Language: English
• Published: New York Elsevier Ltd 01.12.2020; Elsevier BV
• Subjects: Actuators; Bifurcation theory; Buckling; Computational fluid dynamics; Deformation; Dielectrics; Elastomers; Electric potential; Functionally graded dielectric tube; Functionally gradient materials; Impedance matrix; Inhomogeneity; Linearized buckling; Neo-Hookean material; Nonlinear response; Surface impedance matrix method; Voltage; Functionally graded dielectric tube; Surface impedance matrix method; Linearized buckling; Neo-Hookean material
• ISSN: 0020-7462; 1878-5638
• DOI: 10.1016/j.ijnonlinmec.2020.103593

Soft functionally graded materials have attracted intensive attention owing to their special material inhomogeneity and are realized as various applications. In this paper, we theoretically investigate the finite deformation and superimposed bifurcation behaviors of an incompressible functionally graded dielectric tube subject to a combination of axial stretch and radial voltage. The theoretical framework of nonlinear electroelasticity and the related linearized incremental version is employed. We assume that the modulus and permittivity of the elastomer vary linearly along the thickness of the tube. The surface impedance matrix method is adopted to obtain the bifurcation equation for buckling of the tube. We present numerical calculation for the ideal neo-Hookean dielectric elastomer to study the effects of the applied voltage, geometrical size and material grading parameters on the nonlinear response and the incremental buckling behavior of the tube. We validate our results through comparison with those of the elastic problem. The results can provide solid guidance for the design and realization of dielectric actuators. •We theoretically investigate the finite response and the associated 3D incremental wrinkling behavior of a functionally graded dielectric elastomer (FGDE) tube.•We study the effects of the applied voltage, geometrical size and material gradients on the deformation and incremental buckling behavior of the FGDE tube.•We find that the electric breakdown failure of the material can be designed to occur first at the inner or outer face of the tube by properly choosing the material gradient.•We find that the application of the voltage stabilizes the tube and this stabilization can be enhanced by tuning the material gradients.