Micromechanical Modelling For Electro-Magneto(-Thermo)-Elastic Coupling Behavior Of Smart Materials

Smart material is a kind of new materials with special functions. Compared with traditional materials, it can receive from the external influence, judge according to their own material properties, and finally get response corresponding to its own material. In short, smart material has the characteristics of perception, feedback and response. Smart material has a wide range of applications in the modern information technology, new material technology, aerospace and other high-tech fields, and increasingly show its great superiority.In view of the material characteristics in single field cannot meet the needs of the development of science and technology applications, the material characteristics in multi-coupling field become the focus of mechanics and materials science. But the existing research results show that the predictions of effective multi-fields material properties and the local field distribution are often difficult to give accurate results, and the approximate prediction of local field distribution in most models depends on the established assumptions including unit cell shape, size and periodic boundary conditions, etc. When the established assumptions are not same, the results are always different. Furthermore, the application of the methods are not generality and universality.Based on the variational asymptotic homogenization theory, the electro-magneto(-thermo)-elastic coupling behavior of smart materials is investigated in this graduation thesis. The variational asymptotic method is very effective in solving the stationary point of functional with single or multiple small parameters. Especially, it is a good tool to construct the micromechanics model of smart materials with identifiable unit cells.In the actual theoretical derivation, only the basic assumptions in traditional continuum mechanics are introduced and the total energy functional is obtained based on the electro-magneto-elastic coupled unified constitutive equation. Then, the energy functional is asymptotic extended to a series of approximate functionals by taking the ratio of microscopic scale to macro scale as small parameter. Based on the continuity conditions between adjacent unit cell and the characteristics of fluctuation functions, we use the Lagrange multiplier method to enforce the constraints into the energy functional. The analytical solution of the unknown fluctuation functions of field variables are obtained by minimizing the approximate functional, which establish a micromechanical model that as closer as possible to the physical and engineering authenticity. The finite element method is used to numerical solve the discrete energy functional. Finally, the local fields are recovered according to the global response and the fluctuation function, which can result in a complete local field distribution.As we know, if the thermal field analysis is added into the constructed micromechanical model for electro-magneto-elastic coupling behavior of smart materials, many excellent characteristics of original electro-magneto-elastic coupled equations would be damaged. Hence, we use the variational asymptotic homogenization method again to establish the micromechanical model to predict the fully coupled electro-magneto-thermo-elastic behavior of smart materials. The numerical examples shows that the constructed micromechanical model can accurately predict the fully coupled electro-magneto(-thermo)-elastic behavior and recover the local fields distribution. The constructed micromechanics model provides a general method and tools for the design and analysis the micromechanical structure of the smart material, and provides basis and convenience for achieving the ideal material properties.There are three innovations in this graduation thesis:(1) The micromechanics model and total energy functional are established based on the variational asymptotic method. The definite solution of electro-magneto(-thermo)-elastic coupling behavior is converted into a functional extremum problem, which avoids the defects of traditional micromechanics model that based on specific assumptions.(2) The combination of the variational asymptotic method and the finite element method gives full play to the advantages of two methods, which can accurately predict the effective material properties, and effectively simulate the effective behavior of smart materials in multi-physical fields.(3) By using the fluctuation function and the global response, the local field distribution is recovered by simple algebraic operations, which makes up the deficiency that the prediction method in traditional equivalent performance theory cannot obtain the internal microstructure situation of the complex material.