Numerical computation of the effective thermal conductivity of two-phase composite materials by digital image analysis

We consider the numerical determination of the effective thermal conductivity of 2D, two-phase com-posite materials, whose microstructural geometries are described by digital images. More specifically, key microstructural data pertaining to the spatial distribution and volume fractions of the constituent phases in the material are extracted, along with the shapes of the interphase boundaries, using computer vision techniques. For inclusions of simple shapes (polygons, circles, ellipses), the extracted interphase boundary data is easily obtained and can be exploited immediately (e.g. polygonal vertices) or can be fitted with smooth curves, using least square error minimization techniques in order to reconstruct parametric rep-resentations in the case of circular or elliptical boundaries. For more intricate microstructure geometries characterized by clustered or agglomerated intersecting inclusions, piecewise cubic spline functions are adopted to obtain a least-square fitting of the interphase boundaries. The effective thermal conductivities are then calculated based on a boundary integral formulation defined over the reconstructed inclusion boundaries. They are expressed in terms of power series expansions of a conductivity contrast parameter of the constituent phases in the material. To accelerate the convergence of these expansions, nonlinear transformations (known as Pad?? Approximants) are used to yield rational approximations of the effective thermal conductivity tensor. Tests conducted on a variety of 2D, two-phase microstructures yielded accu-rate results over a wide range of microstructure image resolution, regardless of the contrast parameters of the constituent phases, thus, validating the efficacy and robustness of the proposed scheme. ?? 2022 Elsevier Ltd. All rights reserved.

Automated summary

This paper discusses the numerical determination of the effective thermal conductivity of 2D, two-phase composite materials using digital images and computer vision techniques. Key microstructural data, such as spatial distribution and volume fractions, are extracted and used to calculate the effective thermal conductivities. Different fitting methods are applied based on the shapes and complexities of the inclusions. The proposed scheme is validated through accurate results obtained under various conditions.