[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-122019-en":3,"doc-seo-122019-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},122019,2336464648322,"Aria","https://ap-avatar.wpscdn.com/avatar/2200025388227c56fec?_k=1778556882303663488",8,"Research & Report","PHASE FIELD MODELING OF FRACTURE AND PHASE SEPARATION USING NUMERICAL METHODS AND MACHINE LEARNING","This dissertation presents phase-field modeling frameworks to simulate fracture and phase separation using numerical methods and machine learning. It develops a phase-field fracture approach coupled with an elasto-plastic constitutive model tailored to 3D printed thermoplastics and fiber reinforced composites, including cohesive-zone phase-field formulations and total energy functional construction. It further introduces a sequential training strategy for physics-informed neural networks targeting Allen–Cahn and Cahn–Hilliard equations, and develops gradient-flow based phase-field modeling with separable neural networks. Experimental-focused details, numerical implementations, and validation results for printed PLA and CFRP are provided.","Michigan Technological University  \nDigital Commons @ Michigan Tech  \nDissertations, Master's Theses and Master's Reports  \n2024  \nPHASE FIELD MODELING OF FRACTURE AND PHASE SEPARATION USING NUMERICAL METHODS AND MACHINE LEARNING  \nRevanth Mattey  \nMichigan Technological University, [vmattey@mtu.edu](vmattey@mtu.edu)  \nCopyright 2024 Revanth Mattey  \nRecommended Citation  \nMattey, Revanth, \"PHASE FIELD MODELING OF FRACTURE AND PHASE SEPARATION USING NUMERICAL METHODS AND MACHINE LEARNING\", Open Access Dissertation, Michigan Technological University, 2024.  \n[https://doi.org/10.37099/mtu.dc.etdr/1803](https://doi.org/10.37099/mtu.dc.etdr/1803)  \nFollow this and additional works at: [https://digitalcommons.mtu.edu/etdr](https://digitalcommons.mtu.edu/etdr)  \n Part of the Applied Mechanics Commons  \nMichigan Technological University  \nDigital Commons @ Michigan Tech  \nDissertations, Master's Theses and Master's Reports  \n2024  \nPHASE FIELD MODELING OF FRACTURE AND PHASE SEPARATION USING NUMERICAL METHODS AND MACHINE LEARNING  \nRevanth Mattey  \nCopyright 2024 Revanth Mattey  \nFollow this and additional works at: [https://digitalcommons.mtu.edu/etdr](https://digitalcommons.mtu.edu/etdr)  \n Part of the Applied Mechanics Commons  \nPHASE FIELD MODELING OF FRACTURE AND PHASE SEPARATION  \nUSING NUMERICAL METHODS AND MACHINE LEARNING  \nBy  \nRevanth Mattey  \nA DISSERTATION  \nSubmitted in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY  \nIn Mechanical Engineering-Engineering Mechanics  \nMICHIGAN TECHNOLOGICAL UNIVERSITY  \n2024  \n© 2024 Revanth Mattey  \nThis dissertation has been approved in partial fulfillment of the requirements for  \nthe Degree of DOCTOR OF PHILOSOPHY in Mechanical Engineering-Engineering Mechanics.  \nDepartment of Mechanical Engineering-Engineering Mechanics  \nDissertation Advisor: Dr. Susanta Ghosh  \nCommittee Member: Dr. Shiva Rudraraju  \nCommittee Member: Dr. Ramin Bostanabad  \nCommittee Member: Dr. Siva Nadimpalli  \nDepartment Chair: Dr. Jason Blough  \nDedication  \nTo my family, teachers and friends  \nwithout whom I, would neither be who I am nor would this work be what it is today.  \nContents  \nList of Figures ................................. xiii  \nList of Tables .................................. xxiii  \nPreface ...................................... xxvii  \nAcknowledgments ............................... xxix  \nList of Abbreviations ............................. xxxiii  \nAbstract ..................................... xxxv  \n1 Introduction ................................. 1  \n1.1 Phase-field fracture coupled elasto-plastic constitutive model for 3D printed thermoplastics and composites ................ 1  \n1.2 A novel sequential method to train physics informed neural networks for Allen Cahn and Cahn Hilliard equations ............. 2  \n1.3 Gradient Flow Based Phase-Field Modeling Using Separable Neural Networks ................................. 4  \n2 Phase-field Fracture Coupled Elasto-plastic Constitutive Model  \nfor 3D Printed Thermoplastics and Composites .......... 7  \n2.1 Details of Experiments ......................... 13  \n2.2 Constitutive framework and the phase-field fracture methodology . 17  \n2.2.1 Primary Variables ........................ 17  \n2.2.2 Phase field approximation of fracture ............. 18  \n2.2.3 Elasto-plastic constitutive model for the 3D printed thermoplastics .............................. 21  \n2.2.4 Total energy functional ..................... 24  \n2.2.5 Constitutive and phase field fracture modeling for 3D printed fiber reinforced composites ................... 28  \n2.2.5.1 Large deformation elastoplastic constitutive model 29  \n2.2.5.2 Cohesive zone based phase-field fracture model (PFCZM) ......................... 31  \n2.2.6 Numerical Implementation ................... 34  \n2.3 Results-numerical simulations and validations for the 3D printed PLA samples ................................. 35  \n2.4 Results - numerical simulations and validation f","cbCainMstX7yZn6o","https://ap.wps.com/l/cbCainMstX7yZn6o","pdf",18443630,1,238,"English","en",105,"# 1 Introduction\n## 1.1 Phase-field fracture coupled elasto-plastic constitutive model for 3D printed thermoplastics and composites\n## 1.2 A novel sequential method to train physics informed neural networks for Allen Cahn and Cahn Hilliard equations\n## 1.3 Gradient Flow Based Phase-Field Modeling Using Separable Neural Networks\n# 2 Phase-field Fracture Coupled Elasto-plastic Constitutive Model for 3D Printed Thermoplastics and Composites\n## 2.1 Details of Experiments\n## 2.2 Constitutive framework and the phase-field fracture methodology\n## 2.3 Results-numerical simulations and validations for the 3D printed PLA samples\n## 2.4 Results - numerical simulations and validation for the 3D Printed CFRP\n## 2.5 Conclusions","[{\"question\":\"What modeling approach is used to simulate fracture in 3D printed materials?\",\"answer\":\"The work uses a phase-field fracture methodology coupled with an elasto-plastic constitutive model, including phase-field fracture approximations and cohesive-zone based formulations for composites.\"},{\"question\":\"How does the dissertation train physics-informed neural networks for phase-field equations?\",\"answer\":\"It proposes a novel sequential training method for physics-informed neural networks addressing the Allen–Cahn and Cahn–Hilliard equations.\"},{\"question\":\"What materials and validations are included in the numerical results?\",\"answer\":\"Numerical simulations and validations are reported for 3D printed PLA samples and for 3D printed CFRP, using the developed constitutive and phase-field frameworks.\"}]","PHASE FIELD MODELING OF FRACTURE AND PHASE SEPARATION USING NUMERICAL METHODS AND MACHINE LEARNING | 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modeling approach is used to simulate fracture in 3D printed materials?","Question",{"text":75,"@type":76},"The work uses a phase-field fracture methodology coupled with an elasto-plastic constitutive model, including phase-field fracture approximations and cohesive-zone based formulations for composites.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the dissertation train physics-informed neural networks for phase-field equations?",{"text":80,"@type":76},"It proposes a novel sequential training method for physics-informed neural networks addressing the Allen–Cahn and Cahn–Hilliard equations.",{"name":82,"@type":73,"acceptedAnswer":83},"What materials and validations are included in the numerical results?",{"text":84,"@type":76},"Numerical simulations and validations are reported for 3D printed PLA samples and for 3D printed CFRP, using the developed constitutive and phase-field 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