Stress field prediction for composite materials using deep learning

Stress field prediction in the field of computational solid mechanics using deep learning is an ongoing topic of research. We consider a 2-d fiber-reinforced matrix composite plate where the constituent materials (fiber and matrix) are linear and elastic. When the plate is subjected to different loading and boundary conditions, local stress and strain fields are generated throughout the domain of the plate. Apart from the loading and boundary conditions, this stress field depends on the mechanical properties of the matrix and the individual fibers as well as the geometrical features of the model. The geometrical properties include the spatial distribution of the fibers, the shape of the fibers and the volume fraction of the fiber material in the plate. The output of interest here is the stress and strain field while the spatial distribution and the elastic properties of the fibers are the input variables.
The goal of this work is to use deep learning based tools to generalize our problem of stress prediction in composite material, from small number of fibers to large number of fibers under different spatial distributions. Due to the lack of analytical approaches we need to rely on finite element method (FEM) to solve this problem. However, such approaches discretize the whole 2-d model and solve for each element, which is computationally very expensive. In this problem we want to rely on the generalization capability of convolutional neural networks and its ability to capture intricate relationships between different parameters. We want to use the CNNs to map the spatial distribution of the fibers in the composite material to its stress field contours under application of some load. The advantage of using CNN is its ability to capture location invariant attributes from the input feature maps that will help predict the stress field under different spatial orientation of the fibers. In this work, we utilize a U-Net type network.