{"title":"求解颗粒物料稳态流动奇异边值问题的精确数值方法及其应用","authors":"Sergei Alexandrov, Chih-Yu Kuo, Yeau-Ren Jeng","doi":"10.1007/s00161-023-01269-x","DOIUrl":null,"url":null,"abstract":"<div><p>The rigid/plastic solutions are singular near certain surfaces. A special numerical method is required to solve such boundary value problems. The present paper develops such a method for two models of pressure-dependent plasticity. Both are based on the Mohr–Coulomb yield criterion. Stationary planar flows are considered. The numerical method is characteristics-based. Its distinguishing feature is employing the extended R–S method. The output of numerical solutions, in addition to stress and velocity fields, is the strain rate intensity factor, which controls the magnitude of the shear strain rate near the singular surface. The method applies to finding a solution for the flow of granular material through a wedge-shaped die. The accuracy of the solution is verified by comparison with an analytical solution for the flow through an infinite channel and an available numerical solution for pressure-independent material. An applied aspect of this study is that the strain rate intensity factor can be used in non-traditional constitutive equations for predicting the evolution of material properties near surfaces with high friction.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"36 1","pages":"171 - 195"},"PeriodicalIF":1.9000,"publicationDate":"2023-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An accurate numerical method of solving singular boundary value problems for the stationary flow of granular materials and its application\",\"authors\":\"Sergei Alexandrov, Chih-Yu Kuo, Yeau-Ren Jeng\",\"doi\":\"10.1007/s00161-023-01269-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The rigid/plastic solutions are singular near certain surfaces. A special numerical method is required to solve such boundary value problems. The present paper develops such a method for two models of pressure-dependent plasticity. Both are based on the Mohr–Coulomb yield criterion. Stationary planar flows are considered. The numerical method is characteristics-based. Its distinguishing feature is employing the extended R–S method. The output of numerical solutions, in addition to stress and velocity fields, is the strain rate intensity factor, which controls the magnitude of the shear strain rate near the singular surface. The method applies to finding a solution for the flow of granular material through a wedge-shaped die. The accuracy of the solution is verified by comparison with an analytical solution for the flow through an infinite channel and an available numerical solution for pressure-independent material. An applied aspect of this study is that the strain rate intensity factor can be used in non-traditional constitutive equations for predicting the evolution of material properties near surfaces with high friction.</p></div>\",\"PeriodicalId\":525,\"journal\":{\"name\":\"Continuum Mechanics and Thermodynamics\",\"volume\":\"36 1\",\"pages\":\"171 - 195\"},\"PeriodicalIF\":1.9000,\"publicationDate\":\"2023-11-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Continuum Mechanics and Thermodynamics\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00161-023-01269-x\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Continuum Mechanics and Thermodynamics","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s00161-023-01269-x","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MECHANICS","Score":null,"Total":0}
An accurate numerical method of solving singular boundary value problems for the stationary flow of granular materials and its application
The rigid/plastic solutions are singular near certain surfaces. A special numerical method is required to solve such boundary value problems. The present paper develops such a method for two models of pressure-dependent plasticity. Both are based on the Mohr–Coulomb yield criterion. Stationary planar flows are considered. The numerical method is characteristics-based. Its distinguishing feature is employing the extended R–S method. The output of numerical solutions, in addition to stress and velocity fields, is the strain rate intensity factor, which controls the magnitude of the shear strain rate near the singular surface. The method applies to finding a solution for the flow of granular material through a wedge-shaped die. The accuracy of the solution is verified by comparison with an analytical solution for the flow through an infinite channel and an available numerical solution for pressure-independent material. An applied aspect of this study is that the strain rate intensity factor can be used in non-traditional constitutive equations for predicting the evolution of material properties near surfaces with high friction.
期刊介绍：
This interdisciplinary journal provides a forum for presenting new ideas in continuum and quasi-continuum modeling of systems with a large number of degrees of freedom and sufficient complexity to require thermodynamic closure. Major emphasis is placed on papers attempting to bridge the gap between discrete and continuum approaches as well as micro- and macro-scales, by means of homogenization, statistical averaging and other mathematical tools aimed at the judicial elimination of small time and length scales. The journal is particularly interested in contributions focusing on a simultaneous description of complex systems at several disparate scales. Papers presenting and explaining new experimental findings are highly encouraged. The journal welcomes numerical studies aimed at understanding the physical nature of the phenomena.
Potential subjects range from boiling and turbulence to plasticity and earthquakes. Studies of fluids and solids with nonlinear and non-local interactions, multiple fields and multi-scale responses, nontrivial dissipative properties and complex dynamics are expected to have a strong presence in the pages of the journal. An incomplete list of featured topics includes: active solids and liquids, nano-scale effects and molecular structure of materials, singularities in fluid and solid mechanics, polymers, elastomers and liquid crystals, rheology, cavitation and fracture, hysteresis and friction, mechanics of solid and liquid phase transformations, composite, porous and granular media, scaling in statics and dynamics, large scale processes and geomechanics, stochastic aspects of mechanics. The journal would also like to attract papers addressing the very foundations of thermodynamics and kinetics of continuum processes. Of special interest are contributions to the emerging areas of biophysics and biomechanics of cells, bones and tissues leading to new continuum and thermodynamical models.
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