A distributional approach to the geometry of dislocations at the mesoscale

Nicolas van Goethem (1) , F. Dupret (1)

1 MEMA - Unité de mécanique appliquée

We develop a theory to represent dislocated single crystals at the mesoscopic scale by considering concentrated effects, governed by the distribution theory combined with multiple-valued kinematic fields. Our approach gives a new understanding of the continuum theory of defects as developed by Kroener (1980) and other authors. Fundamental 2D identities relating the incompatibility tensor to the Frank and Burgers vectors are proved under global strain assumptions relying on the geometric measure theory, thereby giving rise to rigorous homogenisation from mesoscopic to macroscopic scale.

Mots clés: dislocations; disclinations; dislocation density; non-Riemannian; strain incompatibility; distribution theory

Domaines: Mécanique des matériaux [physics.class-ph]; Mécanique des matériaux [physics.class-ph]; Mécanique des solides [physics.class-ph]; Mécanique des solides [physics.class-ph]; Géométrie différentielle [math.DG]; Micro et nanotechnologies/Microélectronique; Matériaux et structures en mécanique [physics.class-ph]; Matériaux et structures en mécanique [physics.class-ph]; Science des matériaux [cond-mat.mtrl-sci]

Nicolas van Goethem, F. Dupret. A distributional approach to the geometry of dislocations at the mesoscale. 2007. ⟨hal-00137965⟩