Characterization of local response of random heterogeneous materials using moving-window GMC and finite element analysis

The study of the response of composite materials under various loading conditions is often based on characterization of the material at the macroscopic level only, through the use of effective properties. However, when the information about local response is required, this characterization becomes more difficult, since many composite materials exhibit significant randomness in the microstructural configuration. A significant source of this randomness can be the random variations in the shape, size and/or spatial distribution of the inclusions within the matrix material that arise in many composites. In this case, characterization of the heterogeneous continuum requires description of local elastic properties in order to model critical behavior such as the local stresses.; In this research, the moving-window generalized method of cells (moving-window GMC) technique is used to estimate local fields of effective elastic material properties associated with a given material microstructural image. The moving-window technique is used to divide the heterogeneous image into small windows, and the GMC method is performed to homogenize each window and therefore to produce a field of effective elastic properties. These fields are subsequently applied in finite element analyses, which are used to predict the local stresses associated with a given microstructure under prescribed loading and boundary conditions.; Moving-window GMC is performed under the assumptions that each moving window that is extracted from the digital image is subjected to periodic boundary conditions and that each window represents a repeating unit cell that can be used as a building block to construct the entire composite. The severity of these assumptions is studied through comparison to estimates of the constitutive properties obtained from a full brute-force finite element model of a 2-D microstructure. Furthermore, the results of this work show that the window size has a strong influence on the resulting fields of local elastic properties, an issue that is addressed in some detail in this work.