On molecular modelling and continuum concepts

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    Abstract

    Continuum concepts and field values are related to local (scale-dependent) spacetime atomistic averages. Spatial averaging is effected by both weighting function and cellular localisation procedures, and resulting forms of linear momentum balance are compared. The former yields a local balance directly, with several candidate interaction stress fields. The latter results in a global balance involving a traction field expressible in terms of an interaction stress tensor field. In both approaches the Cauchy stress incorporates distinct interaction and thermokinetic contributions. Inter alia are addressed physically-distinguished choices of weighting function; the scale-dependence of the boundary of a body, its motion and material points thereof; physical interpretations of various candidate interaction stress tensors; temporal averaging and material systems whose content changes with time; and the possible relevance of the latter to investigating a molecular context for configurational forces.
    Original languageEnglish
    Pages (from-to)33-61
    Number of pages29
    JournalJournal of Elasticity
    Volume100
    Issue number1-2
    DOIs
    Publication statusPublished - 17 Apr 2010

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    Keywords

    • localisation procedures
    • interaction stress
    • stress
    • weighting function
    • speacetime avergaes
    • scale-dependent interpretation

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