DPK: Deep Neural Network Approximation of the First Piola-Kirchhoff Stress (Advances in Applied Mathematics and Mechanics, 2023)
This paper presents a specific network architecture for approximation of thefirst Piola-Kirchhoff stress. The neural network enables us to construct the constitutiverelation based on both macroscopic observations and atomistic simulation data. Incontrast to traditional deep learning models, this architecture is intrinsic symmetric,guarantees the frame-indifference and material-symmetry of stress. Specifically, webuild the approximation network inspired by the Cauchy-Born rule and virial stressformula. Several numerical results and theory analyses are presented to illustrate thelearnability and effectiveness of our network.