A scale-dependent model of the boundary of a solid body

Abstract

The perceived boundary of a solid object depends upon the scale at which it is observed, yet is a primitive concept in Continuum Mechanics. Here continuum fields of mass density ϱ ϵ and velocity v ϵ, appropriate to any given length scale e, are established for such an object in terms of weighted spatial averages of the masses and velocities of its constituent molecules. The boundary of the object at scale ϵ is identified as the boundary of the common domain of ϱ ϵ and v ϵ. Implications for boundary conditions and the modelling of porous bodies are indicated.