Year: 2024
Author: Tianyi Hu, Jerry Zhijian Yang, Cheng Yuan
Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 1 : pp. 75–100
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2022-0159
Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 1 : pp. 75–100
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Piola-Kirchhoff stress deep neural networks Cauchy-Born rule.