2-dimensional Problems Of Electrostrictive Materials With Multi-holes Or Inclusions

With smaller hysteresis and lower aging effect than those of piezoelectric materials,electrostrictive materials (EMs) have found wide application in engineering, and thus mechanics ofEMs has been received more and more interest. Under the condition of small strain, in thisdissertation the two-dimensional problems of Ems containing holes or inclusions are studied based onthe assumption that the electric fields are uncoupled with strain. The main works of this dissertationare outlined as follows:In Chapter1mainly introduces the effects of electrostriction, applications of electrostrictivematerials, and related research background of mechanics problems.In Chapter2outlines the basic equations, such as equilibrium equations, constitutive equations,boundary conditions, etc. Then some equations for the complex variable method are presented.In Chapter3studied is the case of an infinite electrostrictive plate with two elliptical holessubjected to electric loads at infinity only based on the assumption that the elliptical holes areelectrically impermeable. By using the conformal transformation and expanding the complexpotentials into Faber series on the boundary, the potentials of electric field and stress fields arederived, respectively. Then, the stress concentrations around the hole and the interaction between twoelliptical holes are discussed.In Chapter4considered is the case where the elliptical holes are assumed to be electricallypermeable, and the results are given by using similar approach to that in Chapter3.In Chapter5presented are the solutions for the case of an infinite electrostrictive plate containingtwo elliptical inclusions under pure electric load. On the interface, the complex potentials of the plateand inclusions can be expanded into series, and then by using the continuous conditions, all the fieldsin the plate and inside the inclusions can be obtained, and then the influence of mechanical-electricconstants of both the plate and inclusions on stress concentrations is discussed by numericalexamples.In Chapter6, the work is summarized and some future works is proposed.