On quantitative characterization of microstructures and effective properties

Proper quantitative characterization of microstructures, for the purpose of modeling the effective properties, is discussed. This is a broad subject that covers different physical properties (elastic, conductive, transport, etc.), as well as various types of microstructures. The present work focuses on microstructures that can be characterized as continuous matrices containing isolated inhomogeneities of diverse shapes, properties and orientations. We address their proper quantitative characterization in the context of elastic and conductive properties (transport and fracture-related properties are also briefly discussed).Proper microstructural parameters must correctly represent the individual inhomogeneity contributions to the considered property. They may differ for different physical properties. The key problem is to identify the mentioned individual contributions. For the elastic properties, we demonstrate, on a number of microstructures, how the proper parameters are implied by the elastic potential. Relative importance of various “irregularity factors” (shape irregularities, orientation scatter) is analyzed.We discuss similarities and differences between microstructural parameters intended for different physical properties. The possibility of explicit cross-property connections between two physical properties depends on whether the proper microstructural parameters for these two properties are sufficiently similar. We outline such explicit connections between the elastic and the conductive properties.The micromechanical approach is compared with the one based on an a priori introduced “fabric” tensors and general tensor representations that contain a number of uncertain factors. Various problems arising in this context are discussed.