عنوان مقاله [English]
Three-dimensional reconstruction of microstructure and evaluation of the various properties (such as mechanical, thermal, etc.) using limited two-dimensional cut-sections are intriguing subjects in microstructure optimal design. There are many practical cases, including material science, biology and medicine, and petroleum engineering for which only 2D images are available for analysis instead of 3D media. Furthermore, direct reconstruction of heterogeneous microstructures using stitching digitized serial section images is not well-suited to routine engineering applications, because providing the acquired images by FIB-SEM, X-ray computed tomography (micro CT), scanning laser confocal microscopy, and other imaging methods are expensive due to their complicated technology, lack of skilled operators and many other technical issues. Thus, three-dimensional reconstruction of such a heterogeneous microstructure is highly useful in performing homogenization, characterization, and finding correlations between microstructural attributions and effective properties of a material. In this paper, a new and powerful method is presented that reconstructs the microstructure using only one cut-section. The method is based upon correlation functions and phase recovery algorithm. The effective properties of a random heterogeneous material are strongly correlated with a particular formalism called n-point statistics. At first, using the available cut-section, two-dimensional two-point correlation functions are determined.
Then, three-dimensional, two-point correlation functions are approximated using 2D ones. Indeed, using the phase recovery algorithm, based on the approximated correlation functions, the three-dimensional microstructure is reconstructed. Besides the isotropic microstructures, this procedure can be used for reconstruction of transversely isotropic microstructures using only one cut-section. Thermal conductivity for the original and reconstructed microstructures is calculated and compared with each other; it is shown that the proposed method reconstructs the original microstructure with a small error rate. An effective reconstruction procedure enables one to generate close to target structures at will, and a subsequent analysis can be performed on the reconstructed microstructure to obtain approximate macroscopic properties (e.g., mechanical, transport, and electromagnetic properties) of the heterogeneous media.