Analysis Of Waves And Instabilities In Soft Electroactive Structures Under Biasing Fields

Soft electrroactive materials are a novel type of smart materials that respond to electrical stimuli with a significant and rapid size or shape change.They have stirred up tremendous interests from academic and industrial communities due to their great application prospects in developing high-performance mechanical devices such as soft robots,artificial muscles,actuators,etc.Accurate and reliable analyses may render references for guiding the design,fabrication and operation of electroactive elastomer actuators.Hence,this thesis focuses on theoretical investigation on waves and instabilities in soft electroactive structures base on Dorfinann and Ogden’s nonlinear theory of electroelasticity and the associated linear incremental theory.An analytical method is developed to investigate the effect of biasing fields on the propagation and reflection of homogeneous plane waves in an incompressible soft electroactive half-space.According to the incremental forms of the incompressibility constraint and Maxwell equations,the displacement and electric potentials are introduced to simplify the incremental governing equations.The speed of plane waves propagating in a specific direction in the half-space under a specific bias is obtained.The constraints on the bias which guarantee the existence of harmonic surface waves in the deformed half-space are derived based on the strong ellipticity inequalities.The reflection of plane waves in the deformed half-space is systematically studied,which is further illustrated and verified along with the slowness curves.The explicit frequency equations and bifurcation equations expressed in terms of Bessel functions are derived for a soft incompressible electroactive hollow cylinder subjected to an axial pre-stretch and an axial biasing electric displacement.Numerical results with respect to an incompressible neo-Hookean electroactive model are presented to illustrate the influences of the initial biasing fields,the geometrical parameters,the electroelastic coupling parameters as well as the exterior electric field on the wave propagation characteristics and instabilities of the cylinder.The so-called Stroh formula in linear anisotropic elasticity is extended to the case with electromechanical coupling effect,based on which the problem to solve the incremental equations for the material under uniform biasing fields is transposed to an eigenvalue problem.Combined with the boundary conditions,the wrinkling of soft electroactive half-spaces and plates as well as the interfacial wrinkling of electroactive film-substrate,substrate-substrate and laminated systems are investigated using the Surface Impedance Matrix Method.The plane-strain bending deformation of an incompressible soft electroactive block and/or a bimorph actuator made of ideal neo-Hookean material subjected to mechanical loading and electric displacement is analytically analysed.By rearranging the incremental governing equations,the Stroh formula in the polar coordinates is derived.Numerical examples are presented to illustrate the influence of the biasing fields as well as the geometrical parameters on the bending instabilities.The electromechanical instability of a thin electroactive elastomer disk subjected to the combination of an applied voltage and a prestress is studied based on the so-called Hessian approach.Numerical calculations for materials of Gent model are conducted to investigate the influence of the prestress,the coefficient of electrostriction,and the strain-stiffening effect on the electromechanical instability.The criterion that the electromechanical instability is suppressed is also obtained.