Two-Scale Asymptotic Analysis For Electro-Thermo-Mechanical Coupling Problem In Multiple Physical Fields

In recent years,with the wide application of thermo-piezo-electric materials in daily life,the research on the equivalent properties of thermo-piezo-electric materials has attracted great attention of scholars.In Mathematics,the behavior of thermo-piezo-electric materials under heat,mechanics and electricity can be described by coupling partial differential equations,it is difficult to obtain the analytical solutions of the equations because the corresponding equations coefficients have small periodic oscillation.Owing to the local multi-scale properties of thermo-piezo-electric materials,it has important theoretical significance and wide application prospect to study the asymptotic behavior of the solutions of this kind of problems by using the higher order two-scale method.In Chapter II by using the higher order two-scale method,the asymptotic expansions of the solutions for the thermo-electro-mechanical coupling problem in the periodic domain under the Dirichlet boundary condition are constructed firstly,then based on the general twoscale theory,the homogenization equations corresponding to coupling equations and the homogenization constants corresponding to coefficients are obtained,finally the asymptotic error estimates of the two-scale solutions are analyzed.In Chapter III by using similar method and matched boundary layer method,the asymptotic behavior of thermo-electro-mechanical coupling problem with mixed boundary conditions is studied for general oscillatory structures.