Data-Driven Computational Homogenization Method Based on Euclidean Bipartite Matching

Abstract

Image processing methods combined with scanning techniques—for example, microscopy or microtomography—are now frequently being used for constructing realistic microstructure models that can be used as representative volume elements (RVEs) to better characterize heterogeneous material behavior. As a complement to those efforts, the present study introduces a computational homogenization method that bridges the RVE and material-scale properties in situ. To define the boundary conditions properly, an assignment problem is solved using Euclidean bipartite matching through which the boundary nodes of the RVE are matched with the control nodes of the rectangular prism bounding the RVE. The objective is to minimize the distances between the control and boundary nodes, which, when achieved, enables the bridging of scale-based features of both virtually generated and image-reconstructed domains. Following the minimization process, periodic boundary conditions can be enforced at the control nodes, and the resulting boundary value problem can be solved to determine the local constitutive material behavior. To verify the proposed method, virtually generated domains of closed-cell porous, spherical particle-reinforced, and fiber-reinforced composite materials are analyzed, and the results are compared with analytical Hashin-Shtrikman and Halpin-Tsai methods. The percent errors are within the ranges from 0.04% to 3.3%, from 2.7% to 14.9%, and from 0.5% to 13.2% for porous, particle-reinforced, and fiber-reinforced composite materials, respectively, indicating that the method has promising potential in the fields of image-based material characterization and computational homogenization.