On the generalized virial theorem for systems with variable mass

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• 作者：Jean-François Ganghoffer ; Rachid Rahouadj
• 关键词：Variable mass problems ; Generalized virial theorem ; Configurational mechanics ; Surface growth ; Discrete mechanics ; Mass flux ; Eshelby stress ; Planet accretion
• 刊名：Continuum Mechanics and Thermodynamics
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：28
• 期：1-2
• 页码：443-463
• 全文大小：695 KB
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• 作者单位：Jean-François Ganghoffer (1)
  Rachid Rahouadj (1)
  
  1. LEMTA – Université de Lorraine, 2, Avenue de la Forêt de Haye, TSA 60604, 54518, Vandoeuvre, France
  
• 刊物类别：Engineering
• 刊物主题：Theoretical and Applied Mechanics
  Engineering Thermodynamics and Transport Phenomena
  Mechanics, Fluids and Thermodynamics
  Structural Materials
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0959

文摘

We presently extend the virial theorem for both discrete and continuous systems of material points with variable mass, relying on developments presented in Ganghoffer (Int J Solids Struct 47:1209–1220, 2010). The developed framework is applicable to describe physical systems at very different scales, from the evolution of a population of biological cells accounting for growth to mass ejection phenomena occurring within a collection of gravitating objects at the very large astrophysical scales. As a starting basis, the field equations in continuum mechanics are written to account for a mass source and a mass flux, leading to a formulation of the virial theorem accounting for non-constant mass within the considered system. The scalar and tensorial forms of the virial theorem are then written successively in both Lagrangian and Eulerian formats, incorporating the mass flux. As an illustration, the averaged stress tensor in accreting gravitating solid bodies is evaluated based on the generalized virial theorem. Keywords Variable mass problems Generalized virial theorem Configurational mechanics Surface growth Discrete mechanics Mass flux Eshelby stress Planet accretion