Studies On Electro-elastic Coupled Problems Of Electrostrictive Dielectrics With Holes

Due to lower aging effect, smaller hysteresis and faster response than piezoelectric materials, electrostrictive materials are widely used in intellectual instruments, such as mechanical micropositioner, ultrasonic motor, and energy harvesting. Since defects, such as cracks, holes, and inclusions, are easy to occur during manufacturing; therefore failure mechanisms of electrostrictive dielectrics have been attracting considerable rsearch interest. This thesis systematically studies the electro-mechanical coupling theory and related problems with defects using analytical and numerical methos. The whole work of this dissertation is outlined below:(1) Chapter 1 mainly introduces the electrostrictive effect and electrictive materials, and current research state of electro-mechanical coupling behavior, and the problems needed to be further studied.(2) Although there are several electro-mechanical coupling theories of dielectrics, especially isotropic electrostrictive dielectrics, however, some key points still haven’t reached an agreement yet. Therefore, Chapter 2 first studies the electro-mechanical coupling theory of anisotropic dielectrics, trying to provide a self-consistent presentation. Based on Minkowski’s four-dimensional tensor description of electromagnetism and Lorentz transformation, the electromagnetic body force, body couple moment, and electromagnetic field energy in the dielectric are given. Then the obtained results are degenerated to the classical Newton mechanics, and the equilibrium equations, deformation equations, energy conservation equations, constitutive equations are discussed by following the traditional construction of theory of elasticity. Furthermore, the objectiveness of constitutive equations and effects of material symmetry on constitutive equations are also taken into consideration.(3) Based on the modified theory, the two-dimensional generalized plane stress problem of an infinite isotropic electrostrictive plate with an elliptical hole is revisited in Chapter 3, trying to(a) compare the results obtained by the modified and traditional constitutive equations,(b) discuss the two different definitions of generalized plane stress problem,(c) study the two different definitions of zero stress state in experiments and recalculate the electrostrictive coefficients,(d) analyze two different electric boundary conditions, where the electric filed is applied on the dielectric directly or on the environment at infinity, and(e) evaluating polarization induced by the strain-stress field, and the error of traditional uncoupled treatment.(4) Then the two-dimensional generalized plane stress problem of an infinite anisotropic electrostrictive plate with an elliptical hole is studied in Chapter 4, using the traditional uncoupled treatment and complex variable method. One shall see that even by uncoupling the electric field from the strain-stress filed, the Cauchy stress tensor and Minkowski stress tensor are both asymmetric, which adds great difficulty to the problem solving. Besides, different cases of complex parameters of the electric field and stress field should be discussed, since they will influence the general solution of the stress function.(5) Since little work has been done on the coupled solution of the electro-mechanical coupling problem of isotropic electrostrictive dielectrics, no matter to the anisotropic case, therefore in Chapter 5 the focus of this dissertation is then turned to finding the coupled solution. By using the principle of virtual work, a general finite element method of the electro-mechanical coupling problem of anisotropic dielectrics is presented. Subsequently, a 3D 8-node isoparametric electrostrictive solid element and 20-node solid element are defined in ABAQUS user subroutine UEL. While, post-processing of the results is achieved by dummy element method and ABAQUS user subroutine UVARM. Numerical examples are then given, analyzing the electro-mechanical problems of a finite isotropic electrostrictive plate with an elliptical hole and two elliptical holes respectively. By comparing the uncoupled theoretical and uncoupled FEM results, the reliability of the FEM program is tested. And by comparing the uncoupled and coupled FEM results, it is found that the traditional uncoupled treatment may cause a large error, and the coupled treatment is therefore quite necessary in general.There are three main achievements of this dissertation:(1) The electro-mechanical coupling theory of anisotropic dielectrics is studied systematically. And a detailed derivation of equilibrium equations and constitutive equations are for the first time given by taking the electric body force and electric body couple moment into consideration. Besides, the effect of different material sysmetry on electrostrictive coefficients and elastic coefficients are discussed.(2) The stress concentration problems of isotropic and anisotropic electrostrictive plates with holes subjected to electric and mechanical loads are studied, based on the modified constitutive equations and different boundary conditions.(3) The three-dimensional finite element method of anisotropic electrostrictive diecelctrics under electric and mechanical loads are presented. Based on ABAQUS user subroutines UEL and UVARM, a complete electrostrictive element is then programed, and the numerical calclations are performend successfully, obtaing both coupled and uncoupled solutions.