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A multiscale model of plasticity. (English) Zbl 1062.74008

Summary: We present a framework for investigating size-dependent small-scale plasticity phenomena and related material instabilities at various length scales ranging from the nano-microscale to mesoscale. The model is based on fundamental physical laws that govern dislocation motion and their interaction with various defects and interfaces. Particularly, the multi-scale framework merges two scales, the nano-microscale where plasticity is determined by explicit three-dimensional dislocation dynamics analysis providing the material length-scale, and the continuum scale where energy transport is based on basic continuum mechanics laws. The result is a hybrid elasto-viscoplastic simulation model coupling discrete dislocation dynamics with finite element analyses. With this hybrid approach, one can address complex size-dependent problems, including dislocation boundaries, dislocations in heterogeneous structures, dislocation interaction with interfaces and associated shape changes and lattice rotations, as well as deformation in nano-structured materials, localized deformation and shear bands.

MSC:

74C99 Plastic materials, materials of stress-rate and internal-variable type
74A60 Micromechanical theories
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