Variational asymptotic method for unit cell homogenization of thermomechanical behavior of composite materials

The properties of materials have been investigated throughout the twentieth century. However, with more and more knowledge in material science, it became extremely hard for individual materials to meet every specific requirements of engineering design in this modern world of high efficiency and performance. To fulfill the design needs of engineering structures, composite materials were widely developed in various ways since early 1990s. This leads to an enormous amount of research in the field of composites; moreover, researchers focused more and more on engineering microstructures in order to improve the performance of composite materials.;Problems of composite materials, which are often observed with complicated geometries, are very difficult to achieve analytical solutions. Therefore, the use of numerical methods such as finite element method (FEM) is required for solving such problems. With the fast development of FEM, this numerical method is well established and recognized by more and more analysts and scientists. This numerical analysis tool is very powerful to obtain behaviors of engineering structures under different boundary conditions and loads. However, for problems of composites featuring heterogeneity, the total degrees of freedom of the composite materials can be so large that even with the significant strides in computer hardware, the direct finite element analyses of such composites sometimes could be impossible. A microscopic building block (aka unit cell or representative volume element or representative structural element in literature) which stores the necessary local information of composites is used to carry out an analysis in microscopic level in order to obtain the effective material properties, and after that to recover the corresponding local stress and strain fields within the original heterogeneous material based on the global behavior of the macroscopic structural analysis.;The thermomechanical behavior of materials is always concerned in engineering because of the temperature dependent material performance in the nature. Almost all materials under their working conditions cannot be kept at unchanged temperature fields which makes the study of thermomechanical behavior of materials meaningful and important. In this dissertation, micromechanics modeling of such problems are developed based on variational asymptotic method which uses a variational statement to solve such problems. This methodology is more efficient as it only deals with one functional while the traditional asymptotic method deals with a group of differential equations. Variational Asymptotic Method for Unit Cell Homogenization (VAMUCH) has been developed recently and will be used to conduct the micromechanics modeling throughout this dissertation. The following problems will be addressed in this dissertation: (1) micromechanics modeling of composites with temperature dependent constituent properties; (2) micromechanics modeling of composites with finite temperature variations; (3) micromechanics modeling of composites under nonuniformly distributed temperature field; and (4) micromechanics modeling of composites under internal and external loads.