Predicting the effective mechanical property of heterogeneous materials by image based modeling and deep learning

In contrast to the composition uniformity of homogeneous materials, heterogeneous materials are normally composed of two or more distinctive constituents. It is usually recognized that the effective material property of a heterogeneous material is related to the mechanical property and the distribution pattern of each forming constituent. However, to establish an explicit relationship between the macroscale mechanical property and the microstructure appears to be complicated. On the other hand, machine learning methods are broadly employed to excavate inherent rules and correlations based on a significant amount of data samples. Specifically, deep neural networks are established to deal with situations where input–output mappings are extensively complex. In this paper, a method is proposed to establish the implicit mapping between the effective mechanical property and the mesoscale structure of heterogeneous materials. Shale is employed in this paper as an example to illustrate the method. At the mesoscale, a shale sample is a complex heterogeneous composite that consists of multiple mineral constituents. The mechanical properties of each mineral constituent vary significantly, and mineral constituents are distributed in an utterly random manner within shale samples. Large quantities of shale samples are generated based on mesoscale scanning electron microscopy images using a stochastic reconstruction algorithm. Image processing techniques are employed to transform the shale sample images to finite element models. Finite element analysis is utilized to evaluate the effective mechanical properties of the shale samples. A convolutional neural network is trained based on the images of stochastic shale samples and their effective moduli. The trained network is validated to be able to predict the effective moduli of real shale samples accurately and efficiently. Not limited to shale, the proposed method can be further extended to predict effective mechanical properties of other heterogeneous materials.