The first part of this paper describes some important underlying themes in the mathematical theory of continuum mechanics that are distinct from formulating and analyzing governing equations. The main part of this paper is devoted to a survey of some concrete, conceptually simple, pretty problems that help illuminate the underlying themes. The paper concludes with a discussion of the crucial role of invariant constitutive equations in computation. © 2007 Birkhaueser.
Nonlinear solid mechanics • radial motions • existence • multiplicity • blowup • inverse problems • quasistaticity • control • invariant artificial viscosity and shock structure