Modeling structure-property relationships with convolutional neural networks: Yield surface prediction based on microstructure images

The use of micromechanics in conjunction with homogenization theory allows for the prediction of the effective mechanical properties of materials based on microstructural information. The geometrical features of microstructures are often summarized in the form of a multi-dimensional image that may contain information such as grain morphology and grain orientations. Here, an attempt is made to encode microstructural information contained in images through convolutional neural networks (CNN). In particular, we pose the problem of predicting the yield surfaces of porous media based on images of their unit cell. It is shown that an encoder composed of two parallel CNN strands is able to reduce the geometrical information stored in 100 × 100 pixel images of perforated microstructures to ten characteristic features. Furthermore, a fully-connected neural network model with multiplicative layers is introduced to predict the effective yield surfaces based on the encoded geometrical information. The result is a computationally-efficient CNN-FCNN model that is able to replicate the effective yield surface predictions of a detailed FE-based unit cell model. Based on this successful proof of concept, it may be envisioned to train CNNs based on the results from crystal plasticity models as well as experimental data on real materials to obtain structure-property models for the design of optimization of polycrystalline materials.