[SY-C2] Symposium C-2

[SY-C2] Numerical simulation of model problems in Plasticity based on Field Dislocation Mechanics

^○Leo Morin^1,2, Renald Brenner³, Pierre Suquet² (1.PIMM, Arts et Métiers-ParisTech, CNAM, CNRS, UMR 8006, 151 bd de l’Hopital, 75013 Paris, France, 2.Laboratoire de Mécanique et d’Acoustique, Aix-Marseille Univ, CNRS UMR 7031, Centrale Marseille, 4 impasse Nikola Tesla, CS 40006, 13453 Marseille Cedex 13, France, 3.Sorbonne Université, CNRS, UMR 7190, Institut Jean Le Rond d'Alembert, 75005 Paris, France)

The aim of this work is to investigate the numerical implementation of the Field Dislocation
Mechanics (FDM) theory for the simulation of dislocation-mediated plasticity. First, a revisited
elastoplastic formulation of the FDM theory is derived which permits to express the set of
equations under the form of a static problem, corresponding to the determination of the local
stress field for a given dislocation density distribution, completed by an evolution problem,
corresponding to the transport of the dislocation density. The static problem is classically
solved using FFT-based techniques (Brenner et al., 2014), while an efficient numerical scheme
based on high resolution Godunov-type solvers is implemented to solve the evolution problem.
Model problems of dislocation-mediated plasticity are finally considered in a simplified 2D case.
First, uncoupled problems with constant velocity are considered, which permits to reproduce
annihilation of dislocations and expansion of dislocation loops. Then, coupled problems with
several constitutive laws for the dislocation velocity are considered. Various mechanical behaviors
such as perfect plasticity and linear kinematic hardening are reproduced by the theory.