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On molecular modelling and continuum concepts

Murdoch, A. Ian (2010) On molecular modelling and continuum concepts. Journal of Elasticity, 100 (1-2). pp. 33-61. ISSN 0374-3535

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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.