{"title":"Stationary shock in cohesive-frictional materials","authors":"Dmitry Garagash, Andrew Drescher, Emmanuel Detournay","doi":"10.1002/(SICI)1099-1484(200004)5:3<195::AID-CFM91>3.0.CO;2-O","DOIUrl":null,"url":null,"abstract":"<p>This paper is concerned with the theoretical analysis of a stationary shock in cohesive-frictional plastic materials. The shock is defined as a thin layer of localized deformation through which material particles travel during plastic flow, as opposed to a shear band where material particles neither enter nor leave the layer. Mathematically, the shock is regarded as a strong discontinuity in velocity and density. Shocks may occur in cohesive-frictional materials in the problem of indentation of soils and rocks, flow of granular materials in bins and hoppers, rock cutting, etc. In the paper we formulate equations on the stationary shock in rigid-plastic materials with or without hardening or softening. The analysis incorporates the effect of inertia of material crossing the shock. The solution and the necessary condition for the existence of a shock are studied under the assumption that the same flow rule is valid for the material within and the material outside the shock. Three regimes of solution are identified, depending on the ratio of specific kinetic energy and cohesion. Using particular forms of constitutive equations it is demonstrated that a stationary shock cannot exist without some hardening of the material. An example of application of the theoretical framework developed to the problem of wedge indentation is considered for one type of material behavior. Copyright © 2000 John Wiley & Son, Ltd.</p>","PeriodicalId":100899,"journal":{"name":"Mechanics of Cohesive-frictional Materials","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2000-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/(SICI)1099-1484(200004)5:3<195::AID-CFM91>3.0.CO;2-O","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mechanics of Cohesive-frictional Materials","FirstCategoryId":"1085","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/%28SICI%291099-1484%28200004%295%3A3%3C195%3A%3AAID-CFM91%3E3.0.CO%3B2-O","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
Abstract
This paper is concerned with the theoretical analysis of a stationary shock in cohesive-frictional plastic materials. The shock is defined as a thin layer of localized deformation through which material particles travel during plastic flow, as opposed to a shear band where material particles neither enter nor leave the layer. Mathematically, the shock is regarded as a strong discontinuity in velocity and density. Shocks may occur in cohesive-frictional materials in the problem of indentation of soils and rocks, flow of granular materials in bins and hoppers, rock cutting, etc. In the paper we formulate equations on the stationary shock in rigid-plastic materials with or without hardening or softening. The analysis incorporates the effect of inertia of material crossing the shock. The solution and the necessary condition for the existence of a shock are studied under the assumption that the same flow rule is valid for the material within and the material outside the shock. Three regimes of solution are identified, depending on the ratio of specific kinetic energy and cohesion. Using particular forms of constitutive equations it is demonstrated that a stationary shock cannot exist without some hardening of the material. An example of application of the theoretical framework developed to the problem of wedge indentation is considered for one type of material behavior. Copyright © 2000 John Wiley & Son, Ltd.
粘性摩擦材料中的静止冲击
本文研究粘性摩擦塑性材料中稳态冲击的理论分析。冲击被定义为材料颗粒在塑性流动过程中穿过的局部变形薄层,而不是材料颗粒既不进入也不离开该层的剪切带。从数学上讲,冲击被认为是速度和密度的强烈不连续性。粘性摩擦材料在土壤和岩石的压痕、料斗和料斗中颗粒材料的流动、岩石切割等问题中都可能发生冲击。本文建立了硬塑性材料在有或没有硬化或软化的情况下的稳态冲击方程。该分析结合了材料惯性穿过冲击的影响。在假设相同的流动规则对激波内和激波外的材料都有效的情况下,研究了激波存在的解和必要条件。根据比动能和内聚力的比值,确定了三种溶液状态。使用特定形式的本构方程,证明了如果材料没有一些硬化,就不可能存在稳态冲击。针对一种类型的材料行为,考虑了将理论框架应用于楔形压痕问题的一个例子。版权所有©2000 John Wiley&;有限公司之子。
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