An Introduction to Continuum Physics

Abstract

Classical continuum physics deals with materials without a visible microstructure. That is, the scale of observation is large compared to the molecular scale, but small relative to other heterogeneities within the system. More modern continuum theories allow for a visible microstructure; amongst such theories are polar [65], mixture [21], nonlocal [63], and hybrid mixture [78]. In this chapter we concentrate mainly on setting out a general framework for classical continuum physics, however, toward the end of the chapter we set out the field equations for mixture and hybrid mixture theory. Fig. 1.1.1 illustrates the type of systems we concentrate on in this chapter. On the smallest scale (Figure 1.1.1a) individual molecules evince. Statistical mechanical theories and some micropolar field theories may be applicable on this scale. On a slightly larger scale the body appears locally uniform with no distinct microstructure. This is the scale-of-observation on which classical continuum theories apply. On yet a larger scale-of-observation large heterogeneities evince. Such media may require polar, mixture, hybrid mixture, or nonlocal continuum theories.