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Homogenization method for a discrete-continuum simulation of dislocation dynamics. (English) Zbl 0998.74063

Summary: The question of the description of elastic fields of dislocations and of plastic strains generated by their motion is central to the connection between dislocation-based and continuum approaches to 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 solution of a 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.

MSC:

74Q05 Homogenization in equilibrium problems of solid mechanics
74A60 Micromechanical theories
82B21 Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics
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