On the microscopic interpretation of stress and couple stress

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    Abstract

    Exact continuum forms of balance (for mass, linear momentum, and tensor-valued moment of momentum) are established as relations between weighted spatial averages of corpuscular quantities computed at any supra-molecular length scale. Explicit expressions for stress and generalised couple stress in terms of particle interactions are obtained using a theorem due to Noll, and their physical interpretation is discussed for a specific choice of weighting function. Remarks are made on other choices of weighting function, the interpretation of partial stress in mixture theory, a link between couple stress and inhomogeneity, and other forms of moment of momentum balance. Comparison is made with the statistical mechanical viewpoint pioneered by Irving and Kirkwood.
    Original languageEnglish
    Pages (from-to)105-131
    Number of pages26
    JournalJournal of Elasticity
    Volume71
    DOIs
    Publication statusPublished - 2003

    Keywords

    • stress
    • couple stress
    • microscopic interpretation
    • weighting function
    • elasticity
    • weighting

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