A New Statistical Descriptor for the Physical Characterization and 3D Reconstruction of Heterogeneous Materials

Abstract

3D reconstruction of heterogeneous materials from 2D images is essential for a precise characterization of their physical properties (mechanical, thermal, electrical, and so on). For this, statistical descriptors such as two-point correlation function (TPCF), lineal path function (LPF), or two-point correlation cluster function (TPCCF) are frequently used. But the effective properties of the reconstructed microstructures are not always corresponding to the real ones as the statistical distribution functions may distribute the material microstructure in a different way from the original one. This is more pronounced for cellular and porous materials such as trabecular bone, fuel cell, and rocks where the connectivity between clusters is not well correlated with the one of real material and degrades the materials physical behavior predictions. This paper proposes a new statistical descriptor, called quality of connection function (QCF), able to determine the quality of connections between clusters and has detailed statistical information about the microstructure distribution. The proposed descriptor is tested on trabecular bone obtained from X-ray micro-computed tomography and used as an example of heterogeneous material having a complex microstructure. Effective properties such as Young’s modulus were calculated for these microstructures and compared with real ones. The new descriptor shows improved capacity to describe the material microstructure distribution and prediction of its physical properties.