An Introduction to Programming Physics-Informed Neural Network-Based Computational Solid Mechanics

Article

Bai, Jinshuai, Jeong, Hyogu, Batuwatta-Gamage, C. P., Xiao, Shusheng, Wang, Qingxia, Rathnayaka, C.M., Alzubaidi, Laith, Liu, Gui-Rong and Gu, Yuantong. 2023. "An Introduction to Programming Physics-Informed Neural Network-Based Computational Solid Mechanics." International Journal of Computational Methods. 20 (10). https://doi.org/10.1142/S0219876223500135
Article Title

An Introduction to Programming Physics-Informed Neural Network-Based Computational Solid Mechanics

ERA Journal ID36477
Article CategoryArticle
AuthorsBai, Jinshuai, Jeong, Hyogu, Batuwatta-Gamage, C. P., Xiao, Shusheng, Wang, Qingxia, Rathnayaka, C.M., Alzubaidi, Laith, Liu, Gui-Rong and Gu, Yuantong
Journal TitleInternational Journal of Computational Methods
Journal Citation20 (10)
Article Number2350013
Number of Pages29
Year2023
PublisherWorld Scientific Publishing
Place of PublicationSingapore
ISSN0219-8762
1793-6969
Digital Object Identifier (DOI)https://doi.org/10.1142/S0219876223500135
Web Address (URL)https://www.worldscientific.com/doi/10.1142/S0219876223500135
Abstract

Physics-informed neural network (PINN) has recently gained increasing interest in computational mechanics. This work extends the PINN to computational solid mechanics problems. Our focus will be on the investigation of various formulation and programming techniques, when governing equations of solid mechanics are implemented. Two prevailingly used physics-informed loss functions for PINN-based computational solid mechanics are implemented and examined. Numerical examples ranging from 1D to 3D solid problems are presented to show the performance of PINN-based computational solid mechanics. The programs are built via Python with TensorFlow library with step-by-step explanations and can be extended for more challenging applications. This work aims to help the researchers who are interested in the PINN-based solid mechanics solver to have a clear insight into this emerging area. The programs for all the numerical examples presented in this work are available at https://github.com/JinshuaiBai/PINN_Comp_Mech.

KeywordsPhysics-informed neural network; computational mechanics; deep learning
ANZSRC Field of Research 20204602. Artificial intelligence
Public Notes

File reproduced in accordance with the copyright policy of the publisher/author.

Byline AffiliationsQueensland University of Technology
University of Queensland
Centre for Applied Climate Sciences
University of the Sunshine Coast
University of Cincinnati, United States
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Thibbotuwawa, Namal, Oloyede, Adekunle, Senadeera, Wijitha, Li, Tong and Gu, YuanTong. 2015. "Investigation of the mechanical behavior of kangaroo humeral head cartilage tissue by a porohyperelastic model based on the strain-rate-dependent permeability." Journal of The Mechanical Behavior of Biomedical Materials. 51, pp. 248-259. https://doi.org/10.1016/j.jmbbm.2015.07.018
Analysis of strain-rate dependent mechanical behavior of single chondrocyte: a finite element study
Gu, YuanTong, Nguyen, Trung Dung, Oloyede, Adekunle and Senadeera, Wijitha. 2014. "Analysis of strain-rate dependent mechanical behavior of single chondrocyte: a finite element study." International Journal of Computational Methods. 11 (1 (Supplement)), pp. 1344005-1. https://doi.org/10.1142/S0219876213440052
A particle based model to simulate microscale morphological changes of plant tissues during drying
Karunasena, H. C. P., Senadeera, W., Brown, R. J. and Gu, Y. T.. 2014. "A particle based model to simulate microscale morphological changes of plant tissues during drying." Soft Matter. 10 (29), pp. 5249-5268. https://doi.org/10.1039/c4sm00526k
A mesh free model for plant tissue deformations during drying
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Numerical investigation of plant tissue porosity and its influence on cellular level shrinkage during drying
Karunasena, H. C. P., Gu, Y. T., Brown, R. J. and Senadeera, W.. 2015. "Numerical investigation of plant tissue porosity and its influence on cellular level shrinkage during drying." Biosystems Engineering. 132, pp. 71-87. https://doi.org/10.1016/j.biosystemseng.2015.02.002
Application of meshfree methods to numerically simulate microscale deformations of different plant food materials during drying
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Scanning electron microscopic study of microstructure of gala apples during hot air drying
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Numerical investigation of case hardening of plant tissue during drying and its influence on the cellular-level shrinkage
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A constitutive model for mechanical response characterization of pumpkin peel and flesh tissues under tensile and compressive loadings
Shirmohammadi, Maryam, Yarlagadda, Prasad K. D. V. and Gu, YuanTong. 2015. "A constitutive model for mechanical response characterization of pumpkin peel and flesh tissues under tensile and compressive loadings ." Journal of Food Science and Technology. 52 (8), pp. 4874-4884. https://doi.org/10.1007/s13197-014-1605-2
Comprehensive Contribution of Filament Thickness and Crosslinker Failure to the Rheological Property of F-actin Cytoskeleton
Li, Tong, Liu, Ling, Hu, Dean, Oloyede, Adekunle, Xiao, Yin, Yarlagadda, Prasad and Gu, YuanTong. 2015. "Comprehensive Contribution of Filament Thickness and Crosslinker Failure to the Rheological Property of F-actin Cytoskeleton." Cellular and Molecular Bioengineering. 8 (2), pp. 278-284. https://doi.org/10.1007/s12195-015-0382-y
Trans-scale Granular Modelling of Cytoskeleton: a Mini-Review
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Tensile properties of Si nanowires with faulted stacking layers
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Molecular investigation of the mechanical properties of single actin filaments based on vibration analyses
Li, Tong, Gu, Y. T., Oloyede, Adekunle and Yarlagadda, Prasad K. D. V.. 2014. "Molecular investigation of the mechanical properties of single actin filaments based on vibration analyses." Computer Methods in Biomechanics and Biomedical Engineering: Imaging and Visualization. 17 (6), pp. 616-622. https://doi.org/10.1080/10255842.2012.706279
How to increase the accuracy of analysis and reduce the computational time in ANSYS in the case of deformation study of orthopedic bone plates
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Bending properties of Ag nanowires with pre-existing surface defects
Zhan, H. F., Gu, Y. T., Yan, C. and Yarlagadda, P. K. D. V.. 2014. "Bending properties of Ag nanowires with pre-existing surface defects." Computational Materials Science. 81, pp. 45-51. https://doi.org/10.1016/j.commatsci.2013.05.032
Studies on bending limitations for the optimal fit of orthopaedic bone plates
Malekani, J., Schmutz, B., Gudimetla, P., Gu, Y., Schuetz, M. and Yarlagadda, Prasad. 2013. "Studies on bending limitations for the optimal fit of orthopaedic bone plates." 2nd International Conference on Materials and Products Manufacturing Technology (ICMPMT 2012). 22 - 23 Sep 2012 Switzerland. https://doi.org/10.4028/www.scientific.net/AMR.602-604.1181
A coupled numerical approach for nonlinear dynamic fluid‐structure interaction analysis of a near‐bed submarine pipeline
Gu, Y.T. and Wang, Q.. 2008. "A coupled numerical approach for nonlinear dynamic fluid‐structure interaction analysis of a near‐bed submarine pipeline." Engineering Computations: international journal for computer-aided engineering and software. 25 (6), pp. 569-588. https://doi.org/10.1108/02644400810891553
A combined meshfree method and molecular dynamics in the multiscale length simulation
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