On the identification of continuum concepts and fields with molecular variables

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    Abstract

    The need to explore a molecular foundation for continuum mechanics is here motivated by recognition of the scale dependence of mass density and boundaries of solid bodies. Modelling molecules as interacting point masses, continuum fields are defined via local spatial averaging using a scale-dependent weighting function. Local balances of linear and angular momentum, and of energy, are established directly, rather than as localised versions of integral relations. Attention is drawn to the non-uniqueness of stress, couple-stress, and heat flux, and to the physical interpretations thereof. A conservation relation for a local measure of inhomogeneity is derived and related to generalised (i.e. tensor valued) moment of momentum. Remarks are made on the scale dependence of the notions of ‘material point’ and ‘boundary’, choices of weighting function, and how further temporal averaging can be implemented, with particular reference to systems whose molecular content changes with time.
    Original languageEnglish
    Pages (from-to)1-26
    Number of pages27
    JournalContinuum Mechanics and Thermodynamics
    Volume23
    Issue number1
    DOIs
    Publication statusPublished - 2011

    Keywords

    • space–time averaging
    • weighting functions
    • couple-stress
    • heat

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