Continuum Mechanics in Physics Education

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 materials stretch, bend, and break, and how fluids flow. It is easy to see why engineers are interested in fluid and solid mechanics, but the subject is also increasingly valuable for physicists and students. Continuum modeling is widely used in astrophysics at many scales, including both stellar interiors and larger-scale phenomena. The subject plays a significant role in the growing field of biological physics, in which structures such as membranes and the cytoskeleton are of great interest. With exposure to the continuum way of thinking about mechanical phenomena, students would have access to many physical aspects of nature: laboratory and geophysical fluid dynamics, the dynamics of deformable materials, part of the growing fields of soft condensed matter physics and complex fluids, and much more. Given these facts, how can we account for the nearly total absence of continuum mechanics in typical physics curricula at both the undergraduate and graduate levels? The omission may be in part a consequence of the historical relegation of some of these topics—for example, fluid mechanics—to engineering. However, other factors contribute as well. Our curricula at both the undergraduate and graduate levels are already crowded with other topics. We know from educational research that crowded curricula interfere with attaining deep understanding, so it is difficult to make additions without deleting other topics. The most popular textbooks intended for courses in classical mechanics do not generally treat fluid or solid mechanics. It is hard to teach courses that are not adequately supported by textbooks, especially at the undergraduate level. (Although there are a few fluid dynamics textbooks suitable for physics students, they are mainly intended for courses that are entirely devoted to that topic.) We physicists often do not feel prepared to teach relatively unfamiliar topics. (Co-teaching with an engineering colleague might be an intriguing solution.) We worry about appearing to infringe on subjects that are taught elsewhere in our universities. We are not yet collectively convinced that the need is compelling, despite the wide applicability of fluid and solid mechanics. Perhaps this column will help. The integration of continuum mechanics into the physics curriculum could yield many benefits. I do not presume that this integration would have to occur as a single separate course. Greater attention to this field could be distributed in various parts of the undergraduate and graduate curricula, including courses in classical mechanics, condensed matter physics, and so on.