Teaching solid mechanics to artificial intelligence—a fast solver for heterogeneous materials

We propose a deep neural network (DNN) as a fast surrogate model for local stress calculations in inhomogeneous non-linear materials. We show that the DNN predicts the local stresses with 3.8% mean absolute percentage error (MAPE) for heterogeneous elastic media with mechanical contrast up to 1.5 between neighboring domains, while running 103 times faster than spectral solvers. The DNN reproduces stress distributions in geometries different from those used in training. For elasto-plastic materials with up to fourfold contrast in yield stress among adjacent regions, the trained model achieves 6.4% MAPE in a single forward pass without iterations, yielding accelerations up to 8300× over typical solvers. These results indicate an efficient approach to solve non-linear mechanical problems.