In this chapter, a rigorous analysis is given as a reference in which dislocations are treated as discrete entities. Then the transition towards a crystalline continuum is made in a number of steps by subsequent averaging along and perpendicular to the slip direction. This procedure eliminates the short-range dislocation interactions. Based on the considered idealized configuration, a back-stress term is derived which allows the conventional theory to predict finite-size pile-ups and turns out to be virtually identical to the result obtained by means of statistical arguments.
|Title of host publication
|Mechanics of generalized continu a: One hundred years after the Cosserats
|Place of Publication
|Published - 2010
|Advances in mechanics and mathematics