A New Micromechanics Theory for Homogenization and Dehomogenization of Heterogeneous Materials

Abstract

To avoid the difficulty of applying periodic boundary conditions and deal with aperiodic heterogeneous materials, a new micromechanics theory is developed based on the mechanics of structure genome. This new theory starts with expressing the kinematics including both displacements and strains of the original heterogeneous material in terms of those of the equivalent homogeneous material and fluctuating functions with the kinematic equivalency enforced through integral constraints of the fluctuating functions. Then the principle of minimum total potential energy can be used along with the variational asymptotic method to formulate the variational statement for the micromechanics theory. As this theory does not require boundary conditions, one is free to choose the analysis domain of arbitrary shape and they need not be volumes with periodic boundaries. This theory can also handle periodic materials by enforcing the periodicity of the fluctuating functions. To demonstrate the application of this new theory, we will compare the results of different micromechanics approaches for both periodic and aperiodic materials.