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On the Mechanical Modeling of Matter, Molecular and Continuum

  • Paolo Podio-GuidugliEmail author
Article
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Abstract

Any mechanical modeling of matter depends primarily on the chosen spatial and temporal observation scales. Roughly speaking, there are three such scales, microscopic for quantum, mesoscopic for statistical, and macroscopic for continuum mechanics. This by itself demands for adequate scale-bridging procedures. This paper focuses on the passage from molecular to continuum formulations of the basic balance laws of linear momentum and energy, kinetic, internal, and total. The procedure used is a modification of that introduced by Irving & Kirkwood (J. Chem. Phys. 18(6):817–829, 1950), as improved by Noll (Indiana Univ. Math. J. 4:627–646, 1955); alternative procedures are mentioned. The proposed modification consists primarily in equipping provisionally the target continuum balances with internal-source terms accounting at the macroscopic scale for microscopic motion randomness, when, e.g., a loosely aggregated material system evolves at relatively high temperature. Attention is also devoted to those continuum notions that either are hardly given a universally accepted molecular counterpart or even cannot and ultimately need not be given one, such as the notion of material point.

Keywords

Molecular mechanics Continuum mechanics Scale bridging 

Mathematics Subject Classification

70A05 74A05 74A99 

Notes

Acknowledgements

Over the years, many of the matters I here dealt with have been the subject of a number of useful discussions with Antonio DiCarlo, which I gratefully acknowledge.

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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Accademia Nazionale dei LinceiRomeItaly
  2. 2.Dipartimento di MatematicaUniversità di Roma TorVergataRomeItaly

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