M 643

In this talk a model for dislocations at the mesoscale is proposed which makes use of the current formalism. Countable families of dislocation lines are modelled as integer multiplicity 1-currents and the associated deformation field as a Cartesian map away from the lines. The constraint to be satisfied between the deformation and the dislocation density fields generates a pseudo-force, understood as a line tension in the dislocations. The existence of such a constraint reaction is analysed in appropriate function spaces, where intensive use is made of Helmholtz-type decompositions for tensor fields.

Ph.D. Nicolas van Goethem

International School for Advanced Studies (SISSA), Trieste