Nonlinear Electromechanical Behavior Of Dielectric Elastomer Structures

In recent years,the study of soft active material(SAM),which can produce large deformation under external stimulations to achieve certain functions,is rising gradually.The study of SAM from the perspective of mechanics is of great significant since it is helpful to understand the behavior and mechanism of materials and guide the applications.Dielectric elastomer(DE)is a typical SAM,which can obtain large deformation under electric field,and possesses the advantages of high energy density,fast response,light weight and easy processing and manufacturing.Dielectric elastomer has shown great potential in the field of intelligent bionics,biomedicine and others,and has been widely used in actuators,soft robots,braille displays,generators and sensors with various functions.In this dissertation,the nonlinear electromechanical behaviors of dielectric elastomer are studied.The nonlinear behaviors,such as instability,snap-through and phase transition,in various dielectric elastomer structures,including membrane,inflated membrane,inflated tube and balloon,are investigated,and the influence of viscoelasticity,stress softening and inertia and damping effect on the nonlinear behaviors are studied.The nonequilibrium behavior of dielectric elastomer membrane caused by viscoelasticity is studied.The dissipative dielectric elastomer theory based on the nonequilibrium thermodynamic framework and the continuum mechanics model is introduced,the constitutive relation of viscoelastic dielectric elastomer membrane is established by combining the rheological model,and the nonequilibrium evolution processes,such as creep,relaxation,instability and hysteresis,are studied.The stress softening of dielectric elastomer membrane is studied.The dielectric elastomer composite is prepared by filling silicone matrix with carbon nanotube,the stress softening of the composite under cyclic load is tested,the constitutive relation to describe idealized stress softening is established based on the pseudo-elastic theory.Considering the nonlinear relation between electric field and electric displacement,the constitutive relation is extended to electromechanical situation to investigate the electromechanical behavior of dielectric elastomer composite with stress softening effect.The rate-dependent stress softening and viscoelasticity of VHB dielectric elastomer are studied,the constitutive relation is established by combining the pseudo-elastic theory and rheological model,which explains stress softening and residual strain simultaneously.The snap-through deformation and shape evolution of an inflated dielectric elastomer membrane are studied.Considering the viscoelasticity of the material,the governing equations of the inflated dielectric elastomer membrane are derived,the deformation is solved by shooting method and the influence of loading method on deformation is discussed,the deformation of the membrane with fixed amount of air under ramping voltage is computed.The shape evolution of the dielectric elastomer membrane with fixed amount of air and fixed voltage is simulated,the top of the membrane bulges out after snap-through,accompanying by large deformation in central membrane and negative hoop stress,which may lead electrical breakdown and wrinkles,these theoretical computations capture the dynamic process of bulging-out deformation,as well as the electrical breakdown and wrinkles observed in the experiment.The co-existent state and electromechanical phase transition of a dielectric elastomer tube are studied.Considering the viscoelasticity of the material,the governing equations of the dielectric elastomer tube with internal air are derived,the co-existent condition of bulged and unbulged sections is presented,the electromechanical phase transition under ramping voltage is computed,and the influence of chamber size and loading rate on the phase transition voltage is discussed.Fixing the voltage at the initial phase transition voltage,the electromechanical phase transition of the dielectric elastomer tube induced by viscoelastic relaxation is simulated: with a large air chamber,the tube with small deformation experiences complete bulging propagation and steadily transits to large deformation;while a small air chamber will lead to incomplete bulging propagation and the tube eventually stabilizes at a state with bulged and unbulged sections coexisting in the tube,the computational results are consistent with the complete and incomplete electromechanical phase transition in the experiment.The nonlinear dynamic behaviors of a dielectric elastomer balloon are studied.With the consideration of damping effect,the dynamic governing equation of the dielectric elastomer balloon is established,the equilibrium state and natural frequency are computed,the dynamic snap-through processes in response to instantaneous and ramping voltage are simulated.The forced vibration of the dielectric elastomer balloon under perturbation by high-frequency AC voltage is analyzed,the mechanism of steady and chaotic vibration is explained from the perspective of potential energy.With small perturbation energy,the balloon presents ‘beat' vibration,while damping transforms the vibration to periodic vibration;with large perturbation energy,the balloon may undergo chaotic vibration accompanying by snap-through and snap-back,large damping force restrains snap-through and makes the balloon vibrate around the equilibrium state at small stretch,while small damping force makes the balloon vibrate around the equilibrium state at large stretch after snap-through.