{"title":"一般加速边位错的动态能量-动量张量和对数奇异性","authors":"Luqun Ni, Xanthippi Markenscoff","doi":"10.1115/1.4062629","DOIUrl":null,"url":null,"abstract":"Abstract The near-field logarithmic singularities in the field quantities associated with the acceleration of an arbitrarily moving edge dislocation are calculated based on a conservation law involving the dynamic energy-momentum tensor integrated over a domain enclosed by a multi-scale contour (an annulus of inner radius ϵ02 and outer radius ϵ0). The existence of the logarithmic singularities is obtained solely from the conservation law and the leading 1/r terms in the near fields of the stress and the velocity (which are those of the steady-state motion with velocity the instantaneous velocity in the accelerating motion). From the equations of motion and the symmetry in the second partial derivatives of the displacements for y≠0 we obtain that all six logarithmic terms of the near-field expansions are independent of the angle in the polar coordinates. All logarithmic terms in the near-field expansion of the strains and velocity in an arbitrarily moving edge dislocation (subsonically) are evaluated.","PeriodicalId":54880,"journal":{"name":"Journal of Applied Mechanics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":2.6000,"publicationDate":"2023-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Dynamic Energy-Momentum Tensor and the Logarithmic Singularity of a Generally Accelerating Edge Dislocation\",\"authors\":\"Luqun Ni, Xanthippi Markenscoff\",\"doi\":\"10.1115/1.4062629\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract The near-field logarithmic singularities in the field quantities associated with the acceleration of an arbitrarily moving edge dislocation are calculated based on a conservation law involving the dynamic energy-momentum tensor integrated over a domain enclosed by a multi-scale contour (an annulus of inner radius ϵ02 and outer radius ϵ0). The existence of the logarithmic singularities is obtained solely from the conservation law and the leading 1/r terms in the near fields of the stress and the velocity (which are those of the steady-state motion with velocity the instantaneous velocity in the accelerating motion). From the equations of motion and the symmetry in the second partial derivatives of the displacements for y≠0 we obtain that all six logarithmic terms of the near-field expansions are independent of the angle in the polar coordinates. All logarithmic terms in the near-field expansion of the strains and velocity in an arbitrarily moving edge dislocation (subsonically) are evaluated.\",\"PeriodicalId\":54880,\"journal\":{\"name\":\"Journal of Applied Mechanics-Transactions of the Asme\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.6000,\"publicationDate\":\"2023-09-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Applied Mechanics-Transactions of the Asme\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1115/1.4062629\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Mechanics-Transactions of the Asme","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1115/1.4062629","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
The Dynamic Energy-Momentum Tensor and the Logarithmic Singularity of a Generally Accelerating Edge Dislocation
Abstract The near-field logarithmic singularities in the field quantities associated with the acceleration of an arbitrarily moving edge dislocation are calculated based on a conservation law involving the dynamic energy-momentum tensor integrated over a domain enclosed by a multi-scale contour (an annulus of inner radius ϵ02 and outer radius ϵ0). The existence of the logarithmic singularities is obtained solely from the conservation law and the leading 1/r terms in the near fields of the stress and the velocity (which are those of the steady-state motion with velocity the instantaneous velocity in the accelerating motion). From the equations of motion and the symmetry in the second partial derivatives of the displacements for y≠0 we obtain that all six logarithmic terms of the near-field expansions are independent of the angle in the polar coordinates. All logarithmic terms in the near-field expansion of the strains and velocity in an arbitrarily moving edge dislocation (subsonically) are evaluated.
期刊介绍:
All areas of theoretical and applied mechanics including, but not limited to: Aerodynamics; Aeroelasticity; Biomechanics; Boundary layers; Composite materials; Computational mechanics; Constitutive modeling of materials; Dynamics; Elasticity; Experimental mechanics; Flow and fracture; Heat transport in fluid flows; Hydraulics; Impact; Internal flow; Mechanical properties of materials; Mechanics of shocks; Micromechanics; Nanomechanics; Plasticity; Stress analysis; Structures; Thermodynamics of materials and in flowing fluids; Thermo-mechanics; Turbulence; Vibration; Wave propagation