Abstract Based on the recently discovered mechanics of structure genome, a micromechanics theory is developed for computing the effective properties and local fields of aperiodic heterogeneous materials . This theory starts with expressing the displacements of the heterogeneous material in terms of those of the corresponding homogeneous material and fluctuating functions. Integral constraints are introduced so that the kinematics including both displacements and strains of the homogeneous material can be defined as the average of those of the heterogeneous material. The principle of minimum information loss is used along with the variational asymptotic method to formulate the governing variational statement for the micromechanics theory. As this theory does not require conditions applied on the boundaries, it can handle microstructures of arbitrary shapes. This theory can also straightforwardly model periodic materials by enforcing the equality of the fluctuating functions on periodic edges. This theory provides a rational approach for avoiding the difficulty of creating periodic meshes and automatically captures finite dimension effects. Furthermore, this theory can model heterogeneous materials with partial periodicity. We have used several examples to verify and demonstrate the capability of this theory.