INCOMPATIBILITY-GOVERNED SINGULARITIES IN LINEAR ELASTICITY WITH DISLOCATIONS

Nicolas van Goethem (1)

1 ULISBOA - Universidade de Lisboa = University of Lisbon = Université de Lisbonne

The purpose of this paper is to prove the relation inc = Curl κ relating the elastic strain and the contortion tensor κ, related to the density tensor of mesoscopic dislocations. Here, the dislocations are given by a finite family of closed Lipschitz curves in Ω ⊂ R 3. Moreover the fields are singular at the dislocations, and in particular the strain is non square integrable. Moreover, the displacement field shows a constant jump around each isolated dislocation loop. This relation is called after E. Kröner who first derived the same formula for smooth fields at the macroscale.

Domaines: Analyse numérique [cs.NA]

Nicolas van Goethem. INCOMPATIBILITY-GOVERNED SINGULARITIES IN LINEAR ELASTICITY WITH DISLOCATIONS. 2015. ⟨hal-01203034v1⟩