Guided Waves In Soft Electroelastic Circular Cylinders Under Biasing Fields

Owing to the advantages such as low cost,light weight,low actuation voltage,rapid response and large deformation under electric stimuli,high fracture toughness and energy density,soft electroelastic materials as a novel type of smart materials have received considerable attention recently from academic and industrial communities,finding broad application prospects in bio-engineering,medical devices,display technology,sensors,mechanical control,etc.However,the strong nonlinearity and notable electromechanical coupling characteristics of soft electroelastic materials have brought great challenge to the research and application.Therefore,establishing accurate and reliable theoretical and numerical analysis methods may provide effective guidance for the design,fabrication and operation of soft electroelastic devices.Hence,this thesis will focus on the problems of guided elastic waves propagating in homogeneous or functionally graded(FG)soft electroelastic circular cylinder(including tube and phononic crystal(PC)cylinder)under different electromechanical biasing fields.The present work not only is of significant theoretical interest but also is of specific practical importance.Many new and seemingly different versions of the nonlinear theory of solids with electromechanical coupling have appeared.Based on the general framework of the nonlinear continuum theory,the theory of nonlinear electroelasticity that accounts for biasing fields by adopting both Lagrangian description and the updated Lagrangian description based on three configurations is reviewed and compared in detail.The similarities and differences between different versions of the theory are identified in order to clear the confusions in the current literature and provide a theoretical guidance for the related research in the future.Based on Dorfmann and Ogden's theory of nonlinear electroelasticity and the associated linear theory for small incremental motion,the propagation characteristics of guided circumferential elastic waves in homogeneous incompressible soft electroelastic tube actuators under biasing fields are investigated.The biasing fields,induced by the application of an electric voltage difference to the electrodes on the inner and outer cylindrical surfaces of the tube in addition to an axial pre-stretch,are inhomogeneous in the radial direction.The nonlinear governing equations for axisymmetric(or cylindrically symmetric)deformations are derived for an arbitrary energy density function.An accurate and efficient numerical method(abbreviated as SSM)combining the state-space formalism for the incremental wave motion along with the approximate laminate technique is proposed for alleviating the difficulty associated with inhomogeneous biasing fields.The dispersion relations for circumferential waves are derived in a particularly efficient way.For a neo-Hookean ideal dielectric model,the proposed SSM is first validated numerically.Numerical examples are then given to show the static axisymmetric deformations and the inhomogeneous biasing fields.Our numerical findings demonstrate that it is feasible to use guided circumferential waves for the ultrasonic non-destructive online structural health monitoring to detect interior structural defects or fatigue cracks and for the self-sensing of the actual state of the soft electroelastic tube actuator.For the purpose of characterizing the material properties,the biasing field state,the structural defects or cracks of FG soft electroelastic tube,and designing tunable waveguides via material tailoring along with an adjustment of the electromechanical biasing fields,the guided axisymmetric wave propagations in FG soft electroelastic tube under inhomogeneous biasing fields induced by the combination of an axial stretch,a pressure difference,and a radial electric voltage are analyzed based on Dorfmann and Ogden's theory of biasing fields.The isotropic FG soft tube is characterized by the incompressible Mooney-Rivlin energy density function but with the material parameters varying with the radial coordinate in an affine way.The axisymmetric deformations of the FG tube under the above-mentioned biasing fields are first considered.The proposed SSM is used to obtain the dispersion relations for the axisymmetric waves,and numerical examples are then displayed to illustrate the effects of some involved parameters.Finally,this thesis proposes a simple one-dimensional soft PC cylinder made of dielectric elastomer(DE)to show how large deformation and electromechanical coupling can be used jointly to tune the longitudinal waves propagating in the PC.A series of soft electrodes,which are mechanically negligible,are placed periodically along the DE cylinder,and hence the material can be regarded as uniform in the undeformed state.This is also the case for the uniformly pre-stretched state induced by a static axial force only.The effective periodicity of the structure is then achieved through two loading paths,i.e.by maintaining the longitudinal stretch and applying an electric voltage over any two neighbouring electrodes,or by holding the axial force and applying the voltage.All physical field variables for both configurations can be determined exactly based on the nonlinear theory of electroelasticity.An infinitesimal wave motion is further superimposed on the pre-deformed configurations and the corresponding dispersion equations are derived analytically by invoking the linearized theory for incremental motions.The outstanding performance of the proposed tunable soft electroelastic PC is clearly demonstrated by comparing with the conventional design adopting the hard piezoelectric material.In particular,the snap-through instability of the axially free PC cylinder made of a generalized Gent material may be used to efficiently trigger a sharp transition in the band gaps.Numerical discussions indicate that both large deformation and electromechanical coupling play an important role in the longitudinal wave propagation in the DE PC cylinder and can be efficient means to engineer the band structure.