Interrelations between Various Branches of Continuum Mechanics

Abstract

The following insights are gained and/or discussed:

• 1. Mass point and continuum theories have equal rights in the classical mechanics of matter.

• 2. The main difference in the formulation of dislocation theory by Noll and that by the former workers lies in the definition of material uniformity; thus it is physically irrelevant.

• 3. Cosserat and dislocation theory show many similarities, but also fundamental differences.

• 4. The strain gradient theories reflect non-local (and dispersive) response characteristics and are successive approximations to the integral non-local theory. Physically observable effects can be predicted.

• 5. The new developments in continuum mechanics can be classified in a three-dimensional scheme according to the geometry of deformation (Fig. 3).

Acknowledgment. The present exposition has profited from numerous discussions with my coworkers, Drs. B. K. Datta and E. Grafarend, whose work was made possible by generous support of the Deutsche Forschungsgemeinschaft.