Modern technologies require the materials with combinations of properties that can not be met by conventional single phase materials. This requirement leads to the development of composite materials or other materials with engineered microstructures, such as polymer composites and nanotube. Though the well-established finite element analysis (FEA) has the ability to analyze a small portion of such material, for the whole structure, the total degrees of freedom of a finite element model can easily exceed the bearable time in analysis or the capability of the best mainstream computers. To reduce the total degrees of freedom and save the computational efforts, an efficient way is to use a simpler and coarser mesh at the structure level with the micro level complexities captured by a homogenization method. Throughout the dissertation, the homogenization is carried on by variational asymptotic method which has been developed recently as the Variational Asymptotic Method for Unit Cell Homogenization (VAMUCH). This methodology is also expandable to the structure analysis as long as a representative structural element (RSE) can be obtained from structure. In the present research, the following problems are handled: (1) Maximizing the flexibility of choosing a RSE; (2) Bounding the effective properties of a random RSE; (3) Obtaining the equivalent plate stiffnesses for a corrugated plate from a RSE; (4) Extending the shell element of relative degree of freedom to analyze thin-walled RSE. These problems covered some important topics in homogenization theory. Firstly, the rules need to be followed when choosing a unit cell from a structure that can be homogenized. Secondly, for a randomly packed structure, the efficient way to predict effective material properties is to predict their bounds. Then, the composite material homogenization and the structural homogenization can be unied from a mathematical point of view, thus the repeating structure can be always simplified by the homogenization method. Lastly, the efficiency of analyzing thin-walled structures has been enhanced by the new type of shell element. In this research, the first two topics have been solved numerically through the finite element method under the framework of VAMUCH. The third one has been solved both analytically and numerically, and in the last, a new type of element has been implemented in VAMUCH to adapt the characteristics of a thin-walled problem. Numerous examples have demonstrated VAMUCH application and accuracy as a general-purpose analysis tool.

To seek better material behaviors, the research of material properties has been mas- sively carried out in both industrial and academic fields throughout the twentieth century. Composite materials are known for their abilities of combining constituent materials in or- der to fulfill the desirable overall material performance. One of the advantages of composite materials is the adjustment between stiffness and lightness of materials in order to meet the needs of various engineering designs. Even though the finite element analysis is mature, composites are heterogeneous in nature and can present difficulties at the structural level with the acceptable computational time. A way of simplifying such problems is to find a way to connect structural analysis with corresponding analysis of representative microstructure of the material, which is normally called micromechanics modeling or homogenization.Generally speaking, the goal of homogenization is to predict a precise material behavior by taking into account the information stored in both microscopic and macroscopic levels of the composites. Of special concern to researchers and engineers is the thermomechanical behavior of composite materials since thermal effect is almost everywhere in real practical cases of engineering. In aerospace engineering, the thermomechanical behaviors of compos- ites are even more important since flight under high speed usually produces a large amount of heat which will cause very high thermal-related deformation and stress.In this dissertation, the thermomechanical behavior of composites will be studied based on the variational asymptotic method for unit cell homogenization (VAMUCH) which was recently developed as an efficient and accurate micromechanics modeling tool. The theories and equations within the code are based on the variational asymptotic method invented by Prof. Berdichevsky. For problems involving small parameters, the traditional asymptotic method is often applied by solving a system of differential equations while the variational asymptotic method is using a variational statement that only solves one functional of such problems where the traditional asymptotic method may apply.First, we relax the assumption made by traditional linear thermoelasticity that not only a small overall strain is assumed to be small but also the temperature variation. Of course, in this case we need to add temperature dependent material properties to VAMUCH so that the secant material properties can be calculated. Then, we consider the temperature field to be point-wise different within the microstructure; a micromechanics model with nonuniformly distributed temperature field will be addressed. Finally, the internal and external loads induced energies are considered in order to handle real engineering structures under their working conditions.