Homogenization method for a discrete-continuum simulation of dislocation dynamics

• Published in: Journal of the mechanics and physics of solids 2001-09, Vol.49 (9), p.1969-1982
• Main Authors: Lemarchand, C., Devincre, B., Kubin, L.P.
• Format: Article
• Language: English
• Subjects: A. Dislocation dynamics; C. Finite elements; Condensed matter: structure, mechanical and thermal properties; Defects and impurities in crystals; microstructure; Deformation and plasticity (including yield, ductility, and superplasticity); Exact sciences and technology; Homogenization; Mechanical and acoustical properties of condensed matter; Mechanical properties of solids; Physics; Plastic strain; Size effects; Structure of solids and liquids; crystallography; Theories and models of crystal defects
• ISSN: 0022-5096
• DOI: 10.1016/S0022-5096(01)00026-6

The question of the description of the elastic fields of dislocations and of the plastic strains generated by their motion is central to the connection between dislocation-based and continuum approaches of plasticity. In the present work, the homogenization of the elementary shears produced by dislocations is discussed within the frame of a discrete-continuum numerical model. In the latter, a dislocation dynamics simulation is substituted for the constitutive form traditionally used in finite element calculations. As an illustrative example of the discrete-continuum model, the stress field of single dislocations is obtained as a solution of the boundary value problem. The hybrid code is also shown to account for size effects originating from line tension effects and from stress concentrations at the tip of dislocation pile-ups.