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.
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Murdoch, A.I. On Molecular Modelling and Continuum Concepts. J Elast 100, 33–61 (2010). https://doi.org/10.1007/s10659-010-9248-7
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DOI: https://doi.org/10.1007/s10659-010-9248-7
Keywords
- Localisation procedures
- Spacetime averages
- Scale-dependent interpretation
- Weighting function
- Stress
- Interaction stress