Abstract
We investigate the initial stage of quasistatic development of plastic deformations in the vicinity of the tips of a rigid rectangular inclusion whose pair of faces do not contact with a medium. Deformation is caused by shear forces that act at infinity in parallel with this pair of faces of the inclusion. The cases of plastic deformations localized in bands that develop from the tips of the inclusion and distributed continually are investigated. The characteristics of plastic zones for loads much smaller than the yield strength are obtained.
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