Data-Driven Methodology to Extract Stress Fields in Materials Subjected to Dynamic Loading

Full-field stress determination is critical for dynamic loading condition when the stress fields are non homogeneous. Recent advances in high-speed experimental mechanics have led to methods that estimate stress from full-field deformation measurements. However, these methods require multiple numerical differentiation of displacement data, making them less accurate due to noise content in experimental measurements. In order to efficiently tackle noisy displacement data and predict accurate stress fields, a methodology based on neural networks is developed. Specifically, physics-informed neural networks are employed so that the information embedded in physical laws is also utilized along with the experimental measurements. The proposed method to inversely estimate the stress is illustrated by applying it to the impact of rigid mass on an elastic rod that generates a sharp stress discontinuity. A multi-network model is developed where independent feedforward neural networks approximate the displacement and stress. Physical laws are incorporated through equilibrium equations that effectively guide the method toward the right solution. It is shown that the method provides reliable estimates of stress even if the stress field is discontinuous and noise present in the data.