Homogenization in micro-plasticity

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.