On the microscopic interpretation of stress and couple stress

Murdoch, A.I. (2003) On the microscopic interpretation of stress and couple stress. Journal of Elasticity, 71. pp. 105-131. ISSN 0374-3535 (http://dx.doi.org/10.1023/B:ELAS.0000005552.04968....)

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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.