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.
|Titel||Mechanics of generalized continu a: One hundred years after the Cosserats|
|Plaats van productie||Berlin|
|ISBN van geprinte versie||978-1-4419-5694-1|
|Status||Gepubliceerd - 2010|
|Naam||Advances in mechanics and mathematics|
|ISSN van geprinte versie||1571-8689|