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A New Approach to the Problem of Plastic Deformation of Solids

The behavior of elastic-plastic material near a hole is investigated under conditions of plane deformation. Orthogonal forces act at infinity. A uniform load is applied on the contour of the hole. The plastic zone covers the hole completely. The problem on deformation of continuum with regard for the internal displacement of structural elements is considered in the pre-fracture area. The investigation is based on new approaches at strain of solid beyond the limit of elastics: Plastic deformation is realized due to fragmentation of the body into parts by sliding surfaces, the formation of regular parts, their mutual slip and rotation by a certain angle. The additional condition of a brittle fracture at the strain allows to keep the continuality of the original material. The sliding surfaces are formed because of tectonical and technogenical influences on the material. The numerical analysis demonstrates the presence of points where the principal directions of the deformation tensor change. The mechanical significance of this result is the opportunity for the material fibres to rotate. The value of inner stress on the contour of the hole effectively influences the position of these points. Thus, this point's location can be controlled by the stress-field or the variation of the operating stress on the whole contour (additional load). The existence of such points implies the possibility of crack formation or other material defects in the plastic domain.