{"title":"用于加压断裂相场建模的平滑点插值法","authors":"","doi":"10.1016/j.enganabound.2024.105869","DOIUrl":null,"url":null,"abstract":"<div><p>The problem of hydraulic fracturing is of great relevance to various areas and is characterised by the occurrence of complex crack patterns with bifurcations and branches. For this reason, an interesting approach is the modelling of hydraulic fracture using a phase-field model. In addition to the discretisation using the Finite Element Method (FEM), some works have already explored the discretisation of the phase-field model with meshfree methods, including the Smoothed Point Interpolation Methods (SPIM) family. Seeking to take advantage of the good convergence results of SPIM for phase-field modelling of brittle fractures, this paper proposes the use of SPIM for phase-field modelling of pressurised fractures. In order to limit the computational cost, a prescribed SPIM-FEM coupling is employed, with the purpose of concentrating the meshless discretisation only in the regions of expected crack propagation. The model is characterised by a constant internal pressure load along the fracture that is applied indirectly from the formulation of the phase-field model. A series of numerical simulations is presented. The aim is to evaluate the proposed model, verify the results and point out characteristics of the phase-field model with internal pressure.</p></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":null,"pages":null},"PeriodicalIF":4.2000,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Smoothed point interpolation methods for phase-field modelling of pressurised fracture\",\"authors\":\"\",\"doi\":\"10.1016/j.enganabound.2024.105869\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The problem of hydraulic fracturing is of great relevance to various areas and is characterised by the occurrence of complex crack patterns with bifurcations and branches. For this reason, an interesting approach is the modelling of hydraulic fracture using a phase-field model. In addition to the discretisation using the Finite Element Method (FEM), some works have already explored the discretisation of the phase-field model with meshfree methods, including the Smoothed Point Interpolation Methods (SPIM) family. Seeking to take advantage of the good convergence results of SPIM for phase-field modelling of brittle fractures, this paper proposes the use of SPIM for phase-field modelling of pressurised fractures. In order to limit the computational cost, a prescribed SPIM-FEM coupling is employed, with the purpose of concentrating the meshless discretisation only in the regions of expected crack propagation. The model is characterised by a constant internal pressure load along the fracture that is applied indirectly from the formulation of the phase-field model. A series of numerical simulations is presented. The aim is to evaluate the proposed model, verify the results and point out characteristics of the phase-field model with internal pressure.</p></div>\",\"PeriodicalId\":51039,\"journal\":{\"name\":\"Engineering Analysis with Boundary Elements\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.2000,\"publicationDate\":\"2024-07-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Engineering Analysis with Boundary Elements\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0955799724003448\",\"RegionNum\":2,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Engineering Analysis with Boundary Elements","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0955799724003448","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
Smoothed point interpolation methods for phase-field modelling of pressurised fracture
The problem of hydraulic fracturing is of great relevance to various areas and is characterised by the occurrence of complex crack patterns with bifurcations and branches. For this reason, an interesting approach is the modelling of hydraulic fracture using a phase-field model. In addition to the discretisation using the Finite Element Method (FEM), some works have already explored the discretisation of the phase-field model with meshfree methods, including the Smoothed Point Interpolation Methods (SPIM) family. Seeking to take advantage of the good convergence results of SPIM for phase-field modelling of brittle fractures, this paper proposes the use of SPIM for phase-field modelling of pressurised fractures. In order to limit the computational cost, a prescribed SPIM-FEM coupling is employed, with the purpose of concentrating the meshless discretisation only in the regions of expected crack propagation. The model is characterised by a constant internal pressure load along the fracture that is applied indirectly from the formulation of the phase-field model. A series of numerical simulations is presented. The aim is to evaluate the proposed model, verify the results and point out characteristics of the phase-field model with internal pressure.
期刊介绍:
This journal is specifically dedicated to the dissemination of the latest developments of new engineering analysis techniques using boundary elements and other mesh reduction methods.
Boundary element (BEM) and mesh reduction methods (MRM) are very active areas of research with the techniques being applied to solve increasingly complex problems. The journal stresses the importance of these applications as well as their computational aspects, reliability and robustness.
The main criteria for publication will be the originality of the work being reported, its potential usefulness and applications of the methods to new fields.
In addition to regular issues, the journal publishes a series of special issues dealing with specific areas of current research.
The journal has, for many years, provided a channel of communication between academics and industrial researchers working in mesh reduction methods
Fields Covered:
• Boundary Element Methods (BEM)
• Mesh Reduction Methods (MRM)
• Meshless Methods
• Integral Equations
• Applications of BEM/MRM in Engineering
• Numerical Methods related to BEM/MRM
• Computational Techniques
• Combination of Different Methods
• Advanced Formulations.