TY - JOUR
T1 - DPK: Deep Neural Network Approximation of the First Piola-Kirchhoff Stress
AU - Hu , Tianyi
AU - Yang , Jerry Zhijian
AU - Yuan , Cheng
JO - Advances in Applied Mathematics and Mechanics
VL - 1
SP - 75
EP - 100
PY - 2023
DA - 2023/12
SN - 16
DO - http://doi.org/10.4208/aamm.OA-2022-0159
UR - https://global-sci.org/intro/article_detail/aamm/22290.html
KW - Piola-Kirchhoff stress, deep neural networks, Cauchy-Born rule.
AB - <p style="text-align: justify;">This paper presents a specific network architecture for approximation of the
first Piola-Kirchhoff stress. The neural network enables us to construct the constitutive
relation based on both macroscopic observations and atomistic simulation data. In
contrast to traditional deep learning models, this architecture is intrinsic symmetric,
guarantees the frame-indifference and material-symmetry of stress. Specifically, we
build the approximation network inspired by the Cauchy-Born rule and virial stress
formula. Several numerical results and theory analyses are presented to illustrate the
learnability and effectiveness of our network.</p>