&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; In the field of computational material science, Digital Image Processing and Big Data analysis play a crucial role in microstructure characterization and reconstruction (MCR), especially in the estimation of structure-property relationships. In this work, we are interested in the calculation of the effective transport properties of composite materials from digital images. Because most MCR techniques are heavily statistical, they are plagued by significant microstructural information loss as they are incapable of reproducing exact images of microstructures. Here, we take advantage of pattern recognition algorithms to extract exact morphological information pertaining to the interphase boundaries from digital microstructural images, thereby minimizing information loss. The data extracted then serves as the basis for a novel computational framework for the estimation of effective properties of image-based microstructure, in a way that is fully automated, fast, stable, memory efficient, and accurate.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; More specifically, our computational scheme is based on formulating transport problems in the form of boundary integral equations, which are endowed with following essential features and advantages:&nbsp; a reduction of the problem dimensionality as the computational domain is reduced to the phase boundaries, without the need to generate mesh over the entire material; significant gains in efficiency and memory by taking advantage of the Fast Multipole Method;&nbsp; representations of the effective properties in terms of power series expansions of phase-contrast parameters, which separate the analytic dependence on the material properties (i.e. conductivities) from the dependence on the microstructural geometric distribution of the material constituents. These expansions are transformed into rational functions,&nbsp;by expressing them as a ratio 
of two truncated series, known as Pade approximants, in order to accelerate their convergence.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Because accurate and reliable microstructure data extraction-a crucial step in the application of our boundary integral formulation of the effective property-is dependent on the pixel density of the processed image, we conducted preliminary tests on two-dimensional, two-phase microstructural images, by assessing the effect of the pixel density on the accuracy of the calculated effective properties. The tests yielded accurate results over a finite range of image pixel-densities, regardless of the phase-contrast parameter, from perfectly-insulating to perfectly-conducting circular inclusions. These tests validate the efficacy and robustness of the proposed scheme for the treatment of a variety of microstructures, from piecewise-circular or elliptical inclusions to inclusions of arbitrary shape. We will also compare our scheme with the more standard method based on Fast-Fourier Transforms.Keywords: Digital Image Processing; Heterogeneous Media; Homogenization; Fast Multipole Method; Pade Approximants.

A Novel Computational Framework for the Effective Transport Properties of Heterogeneous Materials Reconstructed From Digital Images

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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