Homogenization in micro-plasticity. (English) Zbl 1176.74146
Summary: Homogenized descriptions of plasticity on micro- and macro-scale are essentially different. A key distinction is that the energy of micron-size specimens, in contrast to that of macro-specimens, is not a functional of integral characteristics of the dislocation networks. Thus, energy must be considered as an independent characteristic of the body which is additional to all other characteristics. In this paper, a homogenized description of dislocation motion on the micro-scale is proposed. The theory is considered for the case of anti-plane constrained shear which admits an analytical treatment.
MSC:
| 74Q05 | Homogenization in equilibrium problems of solid mechanics |
| 74C99 | Plastic materials, materials of stress-rate and internal-variable type |
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