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A. Chakraborty¹, C. Anitescu², S. Goswami³, X. Zhuang¹ and T. Rabczuk²

¹Leibniz Unversit¨at Hannover Hannover, Germany
²Bauhaus Universitat Weimar, Weimar, Germany
³Brown University Providence, Rhode Island, United States

doi:10.4203/ccc.5.4.1

A. Chakraborty, C. Anitescu, S. Goswami, X. Zhuang, T. Rabczuk, "Domain decomposition deep energy method for phase field analysis in brittle fracture", in P. Iványi, J. Logo, B.H.V. Topping, (Editors), "Proceedings of the Sixth International Conference on Soft Computing, Machine Learning and Optimisation in Civil, Structural and Environmental Engineering", Civil-Comp Press, Edinburgh, UK, Online volume: CCC 5, Paper 4.1, 2023, doi:10.4203/ccc.5.4.1

Keywords: domain decomposition, deep energy method, phase field, brittle fracture, energy minimization, physics informed neural networks, artificial neural network, crack propagation.

Abstract

Machine learning techniques have been increasingly used for modeling of engineering problems. In particular, physics informed neural networks (PINNs) have been shown to be a promising approach for discretizing and solving partial differential equations. However, PINNs are best suited for smooth function approximations and have some difficulties dealing with discontinuities and rapidly changing gradients in the solution. Here, we propose a framework for the simulation of nucleation and propagation of cracks under brittle fracture using a subdomain-based phase-field approach. By subdividing the domain into smaller regions and considering an energy minimization formulation, the discontinuous displacements and singular stress fields can be more accurately represented compared to the residual-based formulation.

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Front Page Browse CCC CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Conferences ISSN 2753-3239 CCC: 5 PROCEEDINGS OF THE SIXTH INTERNATIONAL CONFERENCE ON SOFT COMPUTING, MACHINE LEARNING AND OPTIMISATION IN CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING Edited by: P. Iványi, J. Logo and B.H.V. Topping Paper 4.1 Domain decomposition deep energy method for phase field analysis in brittle fracture A. Chakraborty¹, C. Anitescu², S. Goswami³, X. Zhuang¹ and T. Rabczuk² ¹Leibniz Unversit¨at Hannover Hannover, Germany ²Bauhaus Universitat Weimar, Weimar, Germany ³Brown University Providence, Rhode Island, United States doi:10.4203/ccc.5.4.1 Full Bibliographic Reference for this paper A. Chakraborty, C. Anitescu, S. Goswami, X. Zhuang, T. Rabczuk, "Domain decomposition deep energy method for phase field analysis in brittle fracture", in P. Iványi, J. Logo, B.H.V. Topping, (Editors), "Proceedings of the Sixth International Conference on Soft Computing, Machine Learning and Optimisation in Civil, Structural and Environmental Engineering", Civil-Comp Press, Edinburgh, UK, Online volume: CCC 5, Paper 4.1, 2023, doi:10.4203/ccc.5.4.1 Keywords: domain decomposition, deep energy method, phase field, brittle fracture, energy minimization, physics informed neural networks, artificial neural network, crack propagation. Abstract Machine learning techniques have been increasingly used for modeling of engineering problems. In particular, physics informed neural networks (PINNs) have been shown to be a promising approach for discretizing and solving partial differential equations. However, PINNs are best suited for smooth function approximations and have some difficulties dealing with discontinuities and rapidly changing gradients in the solution. Here, we propose a framework for the simulation of nucleation and propagation of cracks under brittle fracture using a subdomain-based phase-field approach. By subdividing the domain into smaller regions and considering an energy minimization formulation, the discontinuous displacements and singular stress fields can be more accurately represented compared to the residual-based formulation. download the full-text of this paper (PDF, 10 pages, 574 Kb) go to the previous paper go to the next paper return to the table of contents return to the volume description
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