The elastoplasticity of crystalline solids was considered. It was emphasized that elastoplastic deformation proceeded by way of defects in the ordered crystalline structure. The most important defects in this regard were dislocations that produced plasticity by motion at all temperatures, and point defects that became active at higher temperatures. It was shown that the elastoplasticity of crystalline solids did not fit well into the scheme of continuum mechanics. One reason for this was that the conventional tensor of dislocation density counted only excess dislocations of one sign, whereas hardening and softening was generally due to dislocations of 2 signs. Also, the motion of typical defects in a crystalline structure destroyed the particles which constituted the body. The particles therefore did not persist during elastoplastic motion. For this reason, an elastoplastic crystalline solid was not a differentiable material manifold. During elastoplastic deformation, an irregular and often densifying dislocation network developed which could be seen via electron microscopy and was therefore characteristic of the internal mechanical state. The network could be described by the infinite set of n-point correlation functions of dislocations. It was proposed that solutions should be classified as being of first-, second-, third-order, etc., according to the highest order of correlation function which was included. The first-order theory was then the so-called mean field theory of statistical physics. The 2-point autocorrelation function gave the often-used total length of dislocations in a unit volume; which was also a state quantity.

Benefits and Shortcomings of the Continuous Theory of Dislocations. E.Kröner: International Journal of Solids and Structures, 2001, 38, 1115-34