Numerical implementation of static Field Dislocation Mechanics theory for periodic media

Renald Brenner (1) , Armand Jr. Beaudoin (2) , Pierre Suquet (3) , Amit Acharya (4)

1 DALEMBERT - Institut Jean Le Rond d'Alembert
2 MIE - Department of Mechanical and Industrial Engineering
3 M&S - Matériaux et Structures
4 Department of Civil and Environmental Engineering [Pittsburgh]

This paper investigates the implementation of Field Dislocation Mechanics theory for media with a periodic microstructure (i.e. the Nye dislocation tensor and the elastic moduli tensor are considered as spatially periodic continuous elds). In this context, the uniqueness of the stress and elastic distortion elds is established. This allows to propose an e cient numerical scheme based on Fourier transform to compute the internal stress eld, for a given spatial distribution of dislocations and applied macroscopic stress. This numerical implementation is assessed by comparison with analytical solutions for homogeneous as well as heterogeneous elastic media. A particular insight is given to the critical case of stress-free dislocation microstructures which represent equilibrium solutions of the Field Dislocation Mechanics theory.

Mots clés: Field Dislocation Mechanics; internal stresses; periodic microstructure; Fourier transform; in nite bicrystal; zero-stress dislocation distributions

Domaines: Mécanique [physics]

Renald Brenner, Armand Jr. Beaudoin, Pierre Suquet, Amit Acharya. Numerical implementation of static Field Dislocation Mechanics theory for periodic media. 2013. ⟨hal-00918607⟩