{"title":"The adaptive coupling of dual-horizon peridynamic element and finite element for the progressive failure of materials","authors":"Yehui Bie, Kuanjie Ding, Zhifu Zhao, Yueguang Wei","doi":"10.1007/s10704-023-00758-z","DOIUrl":null,"url":null,"abstract":"<div><p>The peridynamic correspondence model (PDCM) provides the stress–strain relation that can introduce many classical constitutive models, however, the high computational consumption and zero-energy mode of PDCM certainly limit its further application to practical engineering crack problems. To solve these limitations and exploit the advantage of PDCM, we propose a simple and effective method that adaptively couples dual-horizon peridynamic element (DH-PDE) with finite element (FE) to simulate the quasi-static fracture problems. To this end, a stabilized dual-horizon peridynamic element for DH-PDCM is firstly developed that the peridynamic strain matrices for the bond and material point are constructed respectively. The nonlocal ordinary and correctional peridynamic element stiffness matrices are derived in detail and calculated by the proposed dual-assembly algorithm. Subsequently, a unified variational weak form of this adaptive coupling of DH-PDE and FE is proposed based on the convergence of peridynamics to the classical model in the limit of vanishing horizon. Therefore, the integrals of the peridynamic element and finite element in this coupling method are completely decoupled in the viewpoint of numerical implementation, which makes it easier to realize the proposed adaptive coupling by switching integral element. Moreover, the proposed adaptive coupling is implemented in Abaqus/UEL to optimize the calculational efficiency and real-time visualization of calculated results, which has potential for dealing with the engineering crack problems. Two-dimensional numerical examples involving mode-I and mixed-mode crack problems are used to demonstrate the effectiveness of this adaptive coupling in addressing the quasi-static fracture of cohesive materials.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"245 1-2","pages":"89 - 114"},"PeriodicalIF":2.2000,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Fracture","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s10704-023-00758-z","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATERIALS SCIENCE, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
The peridynamic correspondence model (PDCM) provides the stress–strain relation that can introduce many classical constitutive models, however, the high computational consumption and zero-energy mode of PDCM certainly limit its further application to practical engineering crack problems. To solve these limitations and exploit the advantage of PDCM, we propose a simple and effective method that adaptively couples dual-horizon peridynamic element (DH-PDE) with finite element (FE) to simulate the quasi-static fracture problems. To this end, a stabilized dual-horizon peridynamic element for DH-PDCM is firstly developed that the peridynamic strain matrices for the bond and material point are constructed respectively. The nonlocal ordinary and correctional peridynamic element stiffness matrices are derived in detail and calculated by the proposed dual-assembly algorithm. Subsequently, a unified variational weak form of this adaptive coupling of DH-PDE and FE is proposed based on the convergence of peridynamics to the classical model in the limit of vanishing horizon. Therefore, the integrals of the peridynamic element and finite element in this coupling method are completely decoupled in the viewpoint of numerical implementation, which makes it easier to realize the proposed adaptive coupling by switching integral element. Moreover, the proposed adaptive coupling is implemented in Abaqus/UEL to optimize the calculational efficiency and real-time visualization of calculated results, which has potential for dealing with the engineering crack problems. Two-dimensional numerical examples involving mode-I and mixed-mode crack problems are used to demonstrate the effectiveness of this adaptive coupling in addressing the quasi-static fracture of cohesive materials.
期刊介绍:
The International Journal of Fracture is an outlet for original analytical, numerical and experimental contributions which provide improved understanding of the mechanisms of micro and macro fracture in all materials, and their engineering implications.
The Journal is pleased to receive papers from engineers and scientists working in various aspects of fracture. Contributions emphasizing empirical correlations, unanalyzed experimental results or routine numerical computations, while representing important necessary aspects of certain fatigue, strength, and fracture analyses, will normally be discouraged; occasional review papers in these as well as other areas are welcomed. Innovative and in-depth engineering applications of fracture theory are also encouraged.
In addition, the Journal welcomes, for rapid publication, Brief Notes in Fracture and Micromechanics which serve the Journal''s Objective. Brief Notes include: Brief presentation of a new idea, concept or method; new experimental observations or methods of significance; short notes of quality that do not amount to full length papers; discussion of previously published work in the Journal, and Brief Notes Errata.