2018/10/03 by Yipin Su, Bin Wu, Su, Yipin +5 · 1 citation
Engineering · #Advanced Sensor and Energy Harvesting Materials #Dielectric materials and actuators #FOS: Physical sciences #Soft Condensed Matter (cond-mat.soft) #Vibration Control and Rheological Fluids
paper · pdf · doi:10.48550/arxiv.1810.01653
openalex publication_date 2018/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the finite bending and the associated bending instability of an incompressible dielectric slab subject to a combination of applied voltage and axial compression, using nonlinear electro-elasticity theory and its incremental version. We first study the static finite bending deformation of the slab. We then derive the three-dimensional equations for the onset of small-amplitude wrinkles superimposed upon the finite bending. We use the surface impedance matrix method to build a robust numerical procedure for solving the resulting dispersion equations and determining the wrinkled shape of the slab at the onset of buckling. Our analysis is valid for dielectrics modeled by a general free energy function. We then present illustrative numerical calculations for ideal neo-Hookean dielectrics. In that case, we provide an explicit treatment of the boundary value problem of the finite bending and derive closed-form expressions for the stresses and electric field in the body. For the incremental deformations, we validate our analysis by recovering existing results in more specialized contexts. We show that the applied voltage has a destabilizing effect on the bending instability of the slab, while the effect of the axial load is more complex: when the voltage is applied, changing the axial loading will influence the true electric field in the body, and induce competitive effects between the circumferential instability due to the voltage and the axial instability due to the axial compression. We even find circumstances where both instabilities cohabit to create two-dimensional patterns on the inner face of the bent sector.