This thesis consists of two closely related parts: Microstructure characterization and homogenization. Homogenization is a procedure to determine the effective properties of a material on macroscopic scale based on its heterogeneity on microscopic scale. The effective properties of a material are dependent on the spacial distribution of heterogeneity such as the distributions of material phases, the shapes of the continents, the distribution of microcracks, etc. The determination of the distribution of this geometrical heterogeneity is the task of microstructure characterization. The originality of the following work is claimed by the author: (1) Microstructure characterization: (a) Revealed a simple and useful relationship between volume fraction and mean chord-length. Volume fraction is the most important statistical property in homogenization and many other fields. Mean chord-length of a phase is mean size of the continents of that phase, which is easy to measure from the profile of material cross-sections. (b) Developed a method to obtain the two-point probability function for general anisotropic random material based on chord-length distribution and chord-center distribution. The two-point probability is the probability of finding the g-th phase at point P and finding the h-th phase at point Q simultaneously. Two-point probability has been identified as the basic function for characterizing the microstructures of random materials for the purpose of homogenization. (c) Introduced the concept of subphase which enables us to characterize the microstructure as detailed as one wishes without lazy higher order probabilities but more and more subphases. Materials are conventionally considered as multi-phase in terms of the difference of the mechanical properties of the continents such as elastic moduli and permeabilities. These multi-phase materials can be subdivided into more phases in terms of the geometrical differences (size, orientation of continents neighbor continents). Generally, to characterize the microstructure with n-point probabilities, higher-point probabilities are necessary in order to determine the microstructures in detailed. However, this will cause difficulties in two aspects. Firstly, for n $>$ 3, the n-point probabilities are usually very complex and difficult to obtain. Secondly, the complexity of the n-point probabilities will further cause difficulties in homogenization. These difficulties are overcome at a large degree by making subphases and combining the linear model of two-point probability. (2) Homogenization: (a) Developed a homogenization method for general anisotropic random materials with a probability approach. With this method, the effective moduli of n-phase anisotropic random elastic materials can be found. (b) Developed a homogenization method for conductivity problems for general anisotropic random materials with approach. The method can be used to calculate the effective permeabilities of n-phase anisotropic random materials. (c) Developed a homogenization method for randomly microcracking materials. With this method, the effective moduli of randomly cracking materials can found. The cracks under consideration can be any shape, any orientation distribution and dry or fluid-filled. It should be emphasized that the interaction between phases or cracks is fully considered in all these three methods. The effects of microstructures on effective properties are brought to the lights. In particular, the following effects are demonstrated: effects of microstructures on effective Young's moduli, effects of microcrack distributions on effective Young moduli, and effects of microstructures on effective permeabilities.
| Identifer | oai:union.ndltd.org:UMASS/oai:scholarworks.umass.edu:dissertations-8952 |
| Date | 01 January 1994 |
| Creators | Chang, Yang |
| Publisher | ScholarWorks@UMass Amherst |
| Source Sets | University of Massachusetts, Amherst |
| Language | English |
| Detected Language | English |
| Type | text |
| Source | Doctoral Dissertations Available from Proquest |
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