Consistency with Other Continuum Theories

Abstract

The theory of pseudo-rigid bodies represents a deformable body in terms of a single point moving in three-dimensional space and a tensor measuring changes in orientation and features of deformation. This is an extremely coarse description of a real body, especially when cast against the sophistication of most modern studies of deformable media. It is simply a reflection, however, of the class of motions that we choose to consider, and it must be viewed in relation to the tractability of the theory. We choose to consider only those motions of real bodies that are characterized largely by (1) a transplacement of the mass center, (2) a change of orientation similar to that appearing in the mechanics of rigid bodies, and (3) overall measures of extension-compression and shear. This admittedly limited description of motion must be weighed against the theory itself, in which the basic equations of motion, given by (2.3.9) or (2.3.13), form a system of ordinary differential equations. By restricting the class of motions of interest, we have obtained a theory much more tractable than ones based on initial-boundary-value problems for systems of partial differential equations.