One of the oddities of contemporary physics education is the nearly complete absence of continuum mechanics in the typical undergraduate or graduate curriculum. Continuum mechanics refers to field descriptions of mechanical phenomena, which are usually modeled by partial differential equations. The Navier–Stokes equations for the velocity and pressure fields of Newtonian fluids provide an important example, but continuum modeling is of course also well developed for elastic and plastic solids, plasmas, complex fluids, and other systems.
Students’ main experience with continua, at both the undergraduate and graduate level, occurs in the standard courses in electromagnetism. Fields associated with simple charge distributions are encountered, as is the propagation of electromagnetic waves in various media. On the other hand, parallel experience does not typically occur in students’ studies of mechanics, in which continuum phenomena are arguably just as important. A clear understanding of stresses (not just forces) is essential for understanding how...
